Cowen on Silver on Aaron

Tyler Cowen has an interesting post on baseball, which got a lot of positive reviews in his comment section.  So naturally I will disagree. He responded to a Nate Silver post that claimed Hank Aaron would have been a great baseball player even if all of his homers had been singles. Here’s Tyler:

OK, here is where Lucas comes in.  If Hank Aaron did not carry significant home run potential to the plate, he would have seen a lot more blazing fastballs, pitchers’ “best stuff,” and so on.  Why not challenge the hitter and try to blow it by him if all you are risking is a single up the middle?  As it was, pitchers often threw Aaron a variety of slower curves and off-speed junk, stuff he might grab a piece of with the bat but would have a harder time drilling straight over the fence.

And thus a homer-less version of Aaron probably would have had a harder time making contact at all.  And he certainly would have had many fewer walks.  But yet, with the amazing wrists he had…pitchers were afraid of him.

It is funny how the Lucas critique went from one of the most underrated ideas in economics (pre-Lucas), to one of the most overrated ideas (1980s-early 1990s), and now it is back as one of the most underrated ideas again.

In my view there are two ways of thinking about this thought experiment, and in either case Tyler is wrong:

Assumption 1:

Let’s assume it was the same Hank Aaron, with the same talent, who simply choose to be singles hitter rather than a slugger.  He slapped at the ball.  How would this have impacted his other stats?  Because major league baseball is so competitive, we can assume that most players come close to optimizing.  That means they behave like homo economicus.  There are costs and benefits from swinging harder at the ball. The benefit is more home runs and the cost is more strikeouts.  If there were no costs, then they would all swing harder.  Given that players are mostly optimizing, we can assume that for almost any player there is a tradeoff between more hits (more precisely more OBP) and more power.  That means if Aaron had chosen to hit singles instead of homers he would have had more hits and/or a higher OBP. And this claim fully accounts for the way pitchers would have responded to his strategy shift.

Assumption 2:

I think it’s more likely that Silver had something else in mind.  He was considering a different Hank Aaron, one not capable of hitting homers.  Suppose Aaron had hit 3771 singles instead.  That’s the assumption Silver is using.  Would Aaron still have been great? Silver says yes, and Tyler responds that he would have hit less that 3771 singles, because he would have been pitched to differently.  But that makes no sense, as Silver simply assumed the hit total was 3771.  He didn’t claim the hit total would actually have been 3771 if you change one part of the system but not other parts. That’s the counterfactual—how awesome would someone be with the same number of hits as Aaron but no homers. You can’t respond by saying he would have hit fewer than 3771, because that’s the assumption.

Think of it this way.  Suppose Tyler is right that pitchers would have thrown more fastballs at Aaron if he had been a singles hitter.  Does that mean he could not have had 3771 hits?  Of course not—what it means is that in order to have 3771 hits with the actual pitches thrown to him, he would have had to be capable of producing say 4000 or 4100 with the selection of pitches thrown at the real Hank Aaron. In other words, Silver is considering a 3771 singles equilibrium, allowing for all adjustments in all other areas that would have occurred. It’s a hypothetical, no hitter would ever actually produce 3771 hits and no homers.  Silver is asking how good such a hitter would be, if that far-fetched counterfactual occurred.

I completely agree with Tyler Cowen on the Lucas Critique going from being undervalued to overvalued to undervalued.  I believe the overvaluation resulted from the excessive prestige associated with new classical macroeconomics in the 1980s.  And the recent undervaluation is due to a lack or understanding of how important the Lucas Critique is in non-monetary areas, such as fiscal policy, health care, financial regulation, etc.  And this reflects the fact that many of the most important behavioral changes that occur with policy changes happen in the ultra-long run.  They tend not to show up in time series tests, but do show up cross-sectionally.

BTW, Barry Bonds is clearly the greatest baseball player of all time.  Just saying.

PS.  Which of the following should cause us to “think less” of a player’s career:

1.  A pitcher throws lots of spitballs, which the umps fail to notice.

2.  A lineman in football is cleverly able to disguise the fact that he holds defensive players, and doesn’t get called.

3.  A player uses a banned performance enhancing drug that some other players also use.

4.  A player is the only person in baseball to use a certain legal performance enhancing drug (because other players are unaware of it.)



99 Responses to “Cowen on Silver on Aaron”

  1. Gravatar of rwperu34 rwperu34
    12. April 2014 at 11:44

    I think he answers your counterfactual #2. The question is “How valuable was Hank Aaron if we ignore all of his HR?” The question is not “What if Hank Aaron weren’t capable of hitting any HR?”

  2. Gravatar of ssumner ssumner
    12. April 2014 at 11:55

    rwperu, I agree.

  3. Gravatar of Major_Freedom Major_Freedom
    12. April 2014 at 12:23

    “BTW, Barry Bonds is clearly the greatest baseball player of all time. Just saying.”

    If we ignore steroid usage, then yes.

    Did all of his opposing pitchers take steroids? No. If they all cheated like Bonds did, then his numbers would have been far more modest. But it’s because he cheated when others did not that enabled him to put up the numbers that he did. After all, he was playing against those other players and his stats are a reflection of how good he was against those players.

    I recall seeing a sign in the stands as McGuire was set to break Ruth’s record (which wasn’t the world record) of most homers in a year. It said “The Babe did it on hot dogs and beer.”

  4. Gravatar of bmcburney bmcburney
    12. April 2014 at 13:50

    Of the four options, we should think the worst of number 3 and, really, it isn’t even close.

    What Barry Bonds did during and with his baseball career was evil and consciously, deliberately, evil at that. He damaged the careers of the hundreds of “clean” players he played against and, by his actions and successes, encouraged others to damage their lives and health by following his example. He has never displayed the slightest remorse for his actions. People who act this way are generally recognized as psychopaths.

    More importantly, what evidence can you point to in support of the claim that Bonds was a great player? His career prior to steroids was very good but hardly great. All of his “great” numbers were accomplished with the help of chemicals. At that point, it is necessary to separate the player from the chemicals.

    If baseball had changed the rules to allow batters five strikes instead of three, offensive numbers would likely improve at least as much as Bonds improved after he began taking steroids. Would you then consider the “five strike era” Bonds to be superior to a “three strike era” Ruth or Aaron? Could you prove that the “five strike” version of Barry Bonds was the “greatest baseball player of all time” by pointing to his “five strike era” statistics?

  5. Gravatar of John S John S
    12. April 2014 at 14:18

    “Barry Bonds is clearly the greatest baseball player of all time. Just saying.”

    Hitter, maybe (both Ruth and Williams crush him in career OPS. And how great would Williams be w/o military service?)

    And if we’re talking greatest overall player, how can you ignore the Babe, who had nearly 100 wins and lead the league once in ERA and ERA+? He’s still top 100 all-time in career ERA+.

  6. Gravatar of ssumner ssumner
    12. April 2014 at 15:22

    bmcburney, You said:

    “His career prior to steroids was very good but hardly great. ”

    I assume you are not a baseball fan. Barry Bonds was already the greatest player in baseball before he started using steroids. The drugs put him even further ahead of the pack. He had three MVP awards when he was young, and should have had more. That’s more than Ruth, Williams or Mays had. He ended with 7 MVPs

    It’s not clear to me why #3 stands out from the rest.

    John, Bonds would have hit 70 homers/year against the lousy pitching Ruth faced, even w/o drugs. I’ll grant you that Ruth was better relative to the competition, but by the 1980s the competition was far better.

  7. Gravatar of Jaunty Rockefeller Jaunty Rockefeller
    12. April 2014 at 15:36

    Ultimately I’m agnostic about the wrongness of and benefits from steroid use. Bonds has a claim over Williams in the best-ever debate because of his superiority in the field and on the bases, but he falls short of Babe in my book. I think while better overall than Williams, Bonds is behind him as a hitter. His numbers were inflated, though not by PEDs, at least not directly. His ridiculous IBB levels, especially in ’04 (120!!! Which is about equal to the next 3 highest non-Bonds IVBs season combined) were caused by fear of his hitting prowess, but they were also totally uncalled for. Tom Tango, I recall, produced a decision chart for when to walk Bonds, but managers just blew right past any sensible IBB level. It was essentially mass hysteria. I just don’t know how to rationally consider his ca. 2002-2007 numbers.

  8. Gravatar of John S John S
    12. April 2014 at 17:59

    “Bonds would have hit 70 homers/year against the lousy pitching Ruth faced, even w/o drugs.”

    If the question is, “Who would you pick to play a 7-game series for your life?” then of course modern players would dominate. But that’s not typically the framework within which these type of “greatest ever” debates usually take place. Comparison vs. peers is more reasonable, with a tie-breaking edge given to the player from the later era.

    The fact remains that no player ever came close to matching Ruth’s skill in both hitting and pitching. The Babe probably would have had a borderline HOF career had he stuck to pitching (he’s still 17th all time in raw ERA in 1200 career innings pitched). To my knowledge, no everyday player has ever had much success at pitching. The stats of the best hitting pitcher ever, Wes Ferrell, are laughably weak in comparison with Ruth’s pitching stats (38 career homers, or 11 HR/162 games).

  9. Gravatar of Morgan Warstler Morgan Warstler
    12. April 2014 at 18:01

    Being the the greatest at sports / baseball has nothing to do with what accomplished the feat.

    We may be able to distinguish between human and robot, but even then the line is super blurry. Chemicals and genes definitely fall on the human side.

    I’m far less enthused about trans men cheating by competing with women. That’s definitely cheating.

  10. Gravatar of Benjamin Cole Benjamin Cole
    12. April 2014 at 18:13

    Rod Carew anyone?

    Also, remember Ted Williams sat out five seasons in his prime, WWII and Korea. Still hit more than 500 homers.

    Yes, different era, and yes ballplayers did not keep themselves in shape then they way they do today. Hard comparison.

    But prorating William’s numbers to Bonds, they get close on homers, while Williams BA is higher.

    Bonds did get a lot of walks.

  11. Gravatar of John S John S
    12. April 2014 at 18:15

    For offense, I’m still not convinced that Bonds is “clearly” the greatest ever. His pre-steroid on-base plus slugging (OPS) from 1987-98 (until age 33) is 0.984. That would be 10th all time, behind Ramirez and ahead of McGwire, but *way* behind Williams at 1.116.

    Here’s some perspective: Bonds didn’t have a single season above 1.000 OPS until age 27 (1992). Williams started his career at age 20 at 1.045 and had his first (and only) sub-1.000 OPS season in 1959–at age 40!

    Williams also crushes Bonds in career on-base % (.482 to .444), which most sabermetricians agree is significantly more important than slugging. Bonds of course had big edges in baserunning and fielding, but it’s not clear these outweigh Williams’ hitting advantage.

  12. Gravatar of TravisV TravisV
    12. April 2014 at 18:18

    Dear Commenters,

    What teams / players did you root for growing up? Do you follow any sports / teams now?

    Personally, I’m more of a golf / NFL guy. I like the Redskins, Texans and Saints.

    Tomorrow’s Masters Sunday could be awesome!!

  13. Gravatar of Benjamin Cole Benjamin Cole
    12. April 2014 at 18:20

    I forgot to add that at .482 Ted Williams’ lifetime OBP was 40 points higher than Bonds.

  14. Gravatar of Tom Brown Tom Brown
    12. April 2014 at 19:13

    TravisV, when I was a little kid I picked a football team at random to be my favorite team (I saw them make a touchdown: plus their symbol was on the metallic light fixture over our aquarium… can you guess?). They then won four super bowls almost in a row. After the fourth one I felt like I’d “won” at being a sports fan, and I’ve never watched again (I got out at the top of the market so to speak).

  15. Gravatar of bmcburney bmcburney
    12. April 2014 at 19:45


    As usual, strong opinions but weak factual support from Professor Summer.

    Yes, Bonds won MVP awards and had a good career before he started taking steroids. But there was a seven year gap between his Pittsburg MVP years and the steroid MVPs. During that time he was very good but not a great player. If he had been clean his whole career, he would not have made anybody’s top ten or even top twenty greatest of all time.

    On what basis do you contend that Ruth faced inferior pitching? In fact, Ruth faced superior pitching by every statistical measure. Look it up. You will find that during Ruth’s prime years, at best, a home run was hit about once every other game; during the steroid era, on average, MORE than one home run was hit every game.

    Ruth and other hitters of the time faced legal spitballs, shineballs and when a ball was scuffed it stayed in play until the cover actually came off. Ruth did not even wear a batting helmet to say nothing of the 20 pounds of additional plastic armor favored by Bonds. Despite this, in 1920 Ruth hit 54 home runs which was more home runs than any other TEAM in baseball except for the Philadelphia Phillies.

    Ruth began his career as a pitcher and was one of the best. Ruth played much of his career in the “dead ball era.” During Bonds time the ball and the batters were both “juiced.”

    Bottom line: Career Wins Above Replacement — Ruth 172; Bonds (with the benefit of steroids) 171.4.

    I believe you when you say “It’s not clear to me why #3 stands out from the rest.” You evidently think that something not being clear to you is evidence that the thing is not true. You are wrong about that as well.

  16. Gravatar of Steve Steve
    12. April 2014 at 20:06

    “Cowen on Silver on Aaron”

    LOL, I’d like to see a column “Lewis on Sumner on Cowen on Silver on Aaron.”

  17. Gravatar of rwperu34 rwperu34
    12. April 2014 at 20:29


    You are wrong about Bonds. Dead wrong.

    Through 1998, Bonds had accumulated 100 WAR. Borderline HOF is 60, lock is 75. He was already a 1st ballot HOFer. No doubt about it. For all players through age 33 (that’s the 1998 season for Bonds), Bonds ranked 7th of all time.

    Many of the guys ahead of him were in clear decline already. From 1996 to 1998, Bonds had 25 WAR which ranked him NUMBER ONE in MLB. To put it another way, he was still the very best player in the game. If he doesn’t juice, he still projects for another 50+ WAR from that point forward. Bonds was headed for a top 5 player of all time.

    Oh, and Babe Ruth never faced a 95 MPH fastball, let alone virtually every single night. Hell, fastball velocity is up some 2 MPH even in the last decade. I wouldn’t be surprised if a “flamethrower” threw 85 MPH to Ruth. And he never faced a slider. Or a splitter. A few guys were still allowed to throw a spit ball early in his career. Big whoop.

  18. Gravatar of anon/portly anon/portly
    12. April 2014 at 22:04

    Not a single commenter on MR or here has noticed the really weak part of TC’s argument:

    “OK, here is where Lucas comes in. If Hank Aaron did not carry significant home run potential to the plate, he would have seen a lot more blazing fastballs, pitchers’ “best stuff,” and so on. Why not challenge the hitter and try to blow it by him if all you are risking is a single up the middle? As it was, pitchers often threw Aaron a variety of slower curves and off-speed junk, stuff he might grab a piece of with the bat but would have a harder time drilling straight over the fence.”

    Tyler assumes this, but is it true? Do pitchers really pitch significantly differently to different types of hitters? I am skeptical – I think this is exactly the kind of bunk a la “clutch hitting” and “protection” that people used to believe before detailed studies proved otherwise.

    Pitchers certainly do pitch differently to LHB and RHB, and they do issue IBB’s to certain hitters and they do pitch around certain hitters, at least occasionally. But before anyone believes that the optimal approach to getting sluggers out is truly different from the optimal approach to getting singles hitters out (to the extent that pure singles hitters really exist, even Ichiro hit some home runs), they should check the data first.

    Some of the comments at MR are pretty amazing btw – here is commenter “rayward:”

    “Whenever we faced a lineup filled with power, we always used pitchers with less velocity and more “junk”. My nephew, a high school pitcher, never throws more than 70-75 miles per hour, yet the opponents’ best hitters can’t touch him.”

    I think it’s funny that rayward is clearly oblivious to the fact that this strategy has zero correlation to the strategies employed in professional baseball.

  19. Gravatar of Steve Sailer Steve Sailer
    12. April 2014 at 23:08

    Of course they pitched Hank Aaron differently than they pitched Matty Alou. Pitchers try to hit the corners with sluggers, which raises the likelihood of bases on balls.

    There’s an anecdote that Vin Scully tells about the Koufax-Drysdale era Dodger pitchers reviewing in in the locker room how to pitch the scary mid-60s Braves lineup that included Joe Torre, Rico Carty, Felipe Alou, Eddie Matthews and Aaron. For each Braves hitter, the veteran Dodger pitchers chimed in with his weak spot like: “Pitch him low and outside” or “Pitch him high and tight”.

    Then, they got to Aaron’s name. There was silence. Finally, Drysdale muttered, “Pitch him underground.”

  20. Gravatar of Major_Freedom Major_Freedom
    12. April 2014 at 23:18

    The best player in baseball history is Babe Ruth, hands down. It’s not even close.

  21. Gravatar of Major_Freedom Major_Freedom
    12. April 2014 at 23:47

    Ruth had a career .342 batting avg, .474 OBP. Bonds had a career .298 batting avg, and .444 OBP.

    Ruth took 8399 games to hit his home run total. Took Bonds over 9000 games to reach that same total.

    Ruth was RBI champion 6 times. Barry Bonds was RBI champion once.

    Ruth was AL home run champion 12 times (in a span of 13 years). Barry Bonds was NL home run champion twice.

    Ruth still holds hitting and pitching records:

    1.164 career OPS

    .690 career slugging %

    Single season record of 119 extra base hits, 177 runs, and 457 total bases (1921).

    Bonds’ best season for runs was 129 (1993), and his best season for total bases was 411 in a different year (2001). Don’t have data on Bond’s extra base hits for a single season, but I’m guessing Ruth beat him there too.

    And last time I checked, Bonds never pitched a single game. Ruth was an elite pitcher. He would have made it to the hall of fame on his pitching alone. He had a career ERA of 2.277, which stands as 16th of all time. And 5 of those who had better ERAs pitched before the year 1900. There is no active pitcher with a lower ERA than Ruth. Mariano Rivera, who is considered the best closer of all time, had a career 2.2717, which is just barely lower than Ruth.

    Ruth allowed only 10 HRs in 1,221 innings pitched. He pitched 9 shut outs in 1916, and that record stood for over 60 years until Ron Guidy tied it in 1978. In the World Series, Ruth pitched 29 scoreless innings, a World Series record that would stand for 42 years. His World Series record was 3-0 with a 0.87 ERA. He is 11th all time in pitching with a winning percentage of .671.

    Don’t get me wrong. Bonds was an incredibly good ball player. He dazzled the field. But those who really understand baseball, and don’t just look at the crowd pleasing stats like single season bursts of HRs, or drug fuelled career bursts of HRs, or MVP awards which are of course subjective, know Ruth is the best of all time. Amazing hitter and amazing pitcher.

  22. Gravatar of Jim Glass Jim Glass
    13. April 2014 at 00:26

    “Bonds would have hit 70 homers/year against the lousy pitching Ruth faced, even w/o drugs.”

    Illogical. If Ruth had a lifetime of 1980s/1990s/2000s training techniques and then traveled back in time 80 years as Bonds would’ve had to have done, he might have hit 120 homers/year against the 1920s pitching he faced.

    Objectively, the current players are always the best ever, period. But that doesn’t mean they are “the best ever”. (E.g., Vince Lombardi’s Packers dynasty teams that won five NFL championships would be crushed by mediocre college teams today, even by top high school teams — literally crushed, as they would be giving up 60+ pounds at each position across both lines, for starters. But who would say such mediocrities of today “are better than Lombardi’s Packers”?)

    The only way to sensibly evaluate ‘historical best’ players across eras is by their performance relative to their contemporaries. As to that…

    In 1920 all the other *entire teams* in baseball hit an average of 33 HRs while Ruth hit 54 by himself, more than 14 of the 15 teams. In 1927 the other teams were up to an average of 51, Ruth hit 60, more than any other team in the AL and than 12 of the 15 teams total. (Those were the only years I looked at.)

    As to outperforming peers and contemporaries, it’s hard to find words to describe this, there’s never been anything else like it. (To this day, after 80 years, Ruth is #1 all time in slugging percentage and OPS, #2 for on-base percentage and RBIs, #3 for HRs and walks, #4 for runs and #6 for total bases.)

    More than that, Ruth personally revolutionized batting. One can trace through the numbers the effects of his uppercut swing being copied by first his Yankees teammates, and then by the NY Giants and other AL teams that saw him most often, and then finally by the rest of the NL. How many individual players revolutionize an entire pro sport by personal example?

    And as a pitcher: In 1916 he won 23 games with a 1.75 ERA and nine shutouts, both league-leading. The nine shutouts remains the all-time record for left-handers, though Ron Guidry tied it 62 years later. In five starts against Walter Johnson he went 4-0 (two of the wins by 1-0, one in 13 innings). In 1917 he won 24 games (#2 in the AL, #3 in both leagues) with 2.01 ERA and six shutouts. In the World Series Ruth pitched 29 2/3 consecutive scoreless innings, which was the record for 43 years until Whitey Ford broke it.

    So he was an all-round player too. 🙂

    Other than that, comparisons between far-separated eras are speculative and dubious at best, as the game changes. This is true for all sports. (E.g., the dominating great centers of the NBA, such as Wilt, Bill and Kareem, simply don’t exist any more, so how does one compare the “best” of today to them?) In my personal opinion, all one can soundly do is have the fun of arguing subjectively from there.

    Still, stat-heads never rest. The Sabremetrics people have unleashed modern computing power to measure the increase in the overall quality of MLB play year-by-year as black players and Latin/foreign players entered the league, and as techniques, strategies and coaching improved, specialization increased, etc. While speculative to some extent, the results are plausible looking — e.g., the NL pulls ahead of the AL during the years in which it led in signing black players, average team strength dips in expansion years, and so on. And of course the statistical extremes of play move towards the middle as the quality of play improves and the worst players get better.

    The exercise makes it possible, in theory, to “norm” the numbers of any player of any era against those of any other era. As to Ruth in the 2000s, in this exercise he doesn’t dominate in anything like the staggering way he did in the 1920s, but he is still the clear #1. I have my reservations about the whole thing, but it is fun to read through, I’ll see if I can find a link to an online version.

    Bonds had HoF-course numbers, but not ‘Ye Gads-extraordinary HoF-course numbers!’ until the steroid business began. Then when almost everybody’s numbers start declining with age, his amazingly rocketed upward like nobody else’s ever did from anything like that level. But it is really hard to make sound conclusions about the effect of steroids on that (as opposed to on his hat size) because the data on the effects of steroids on baseball play don’t exist. Yes, Bonds’ late career was a mega-outlier, but all first-tier HoFers have outlier careers, Ruth was a mega-outlier. Mega-outliers occur without drugs. But if steroids generally increased the quality of baseball play, and they were used as widely as alleged, we’d have seen a much wider increase in the quality of baseball play than occurred. Unless … there are counter arguments, but no way to settle them.

    E.g., maybe steroid use has a much bigger impact on some players than others. If they really produced that dramatic effect on Bonds, this pretty much has to be true, because damn few other steroid users had a late-career takeoff upward like him. But we don’t know and have no way to find out (until they make steroid use legal in a controlled test in some minor league for a couple seasons).

    So, everybody, argue on about that.

  23. Gravatar of W. Peden W. Peden
    13. April 2014 at 01:14

    Off topic.

    I love these charts from Left Outside, because of how they show that a rich understanding of history is so important. This chart-

    – suggests an easy narrative: in the post-war period, Conservative and Labour governments both built a lot of houses, so there was no housing bubble, and all was well. Except, this was also a period of tremendous “slum clearance”. This was the very noble policy of moving people out of their communities into isolated and atomistic council estates- like “the projects” in the US- that often failed, regardless of the people’s wishes. It was the spirit of the age, when planners could say in all seriousness that it was ridiculous that housing policy be based on the aspirations of the average working class housewife.

    When you look at the actual change in dwelling stock-

    – there’s been very little change in the net rate of change of dwelling space. Less housing was built in the 1980s, but also a lot less was destroyed.

    There’s a parallel here with figures of the US income tax. Yes, the RATES were very high in the 1950s, but what were the revenues? Income tax figures that don’t take into account deductions and evasions/avoidance are just as misleading as housing construction figures that don’t take into account the mass demolition of housing.

  24. Gravatar of Michael Byrnes Michael Byrnes
    13. April 2014 at 03:36

    If we knew somehow that Barry Bonds was *the only one* using steroids, or even that he was one of small minority of steroid users in the game, that would be one thing. But it is far more ikely that PED usage was fairly common. If we judge Bonds relative to his peers, that would include a great many PED users. I don’t think it makes any more sense to single out Bonds for condemnation while ignoring a great mant other PED users than it does to blanketly condemn all players from the era including those who were not PED users. He, like all other starrs from the PED era, should be in the Hall. He’ll always have the questions about PED use surrounding him – that is condemnation enough. Unless we had much better information on 1) who was and was not a PED user and 2) what the benefits of PED use actually were, that is the best we can do.

    On the latter point, I do think it’s a safe assumption that many players were using a Bonds-like PED regimen. But none of those players came anywhere close to doing what Bonds did on the field.

    I think part of why people want to condemn Bonds is because, in this case, the fictional belief (among MLB players, Bonds was exceptionally evil) is more satisfying than the reality (Bonds was just one of many but not all).

    PED use is nothing new in baseball, BTW. Lots of ex-players talk about widespread amphetamine use, for example. Even worse is MLB’s current amphetamine policy – amphetamines are banned, but a player who can get a doctor to diagnose him with ADHD can get a medical exception. (Interestingly, not all ADHD drugs are amphetamines, but you don’t see many players getting a medical exception to use non-amphetamine ADHD drugs.) Under current MLB policy, a player who tests positive for amphetamines will be suspended… unless he’s gotten an ADHD diagnosis and a medical exception, in which case it is all fine and good.

    And, I hope none of you who condemn PED use are still football fans – in NFL policy, a player whose testosterone level is sixfold greater than normal will receive a 4 game suspension. I think that in the NFL a certain amount of PED use is accepted or even encouraged.

  25. Gravatar of Michael Byrnes Michael Byrnes
    13. April 2014 at 03:41

    Jim Glass wrote:

    “maybe steroid use has a much bigger impact on some players than others. If they really produced that dramatic effect on Bonds, this pretty much has to be true, because damn few other steroid users had a late-career takeoff upward like him. ”

    My favorite example of a player suspended for PED use is Manny Alexander, a forgettable utility infielder with career slugging percentages of .324 in the majors and .376 in the minors. 🙂

  26. Gravatar of Benjamin Cole Benjamin Cole
    13. April 2014 at 03:42

    Major Freedom:

    Congrats—you are one of the few observers to remember that Babe Ruth had a great pitching career before he switched to a field position. No one in baseball comes even close.

    The Dodgers had Don Drysdale who could hit a legitimate .300 and maybe Fernando Valenzuela.

    Years ago, many pitches at least learned how to bunt, or move the runner forward. Lew Burdette comes to mind, and he prided himself on fielding too.

    I never liked the designated hitter.

  27. Gravatar of John S John S
    13. April 2014 at 05:50

    Re: best ever comments–why no love for Ted Williams (save Benjamin Cole)?

    At the very least, he deserves the “Most Screwed Legacy” award. He won the Triple Crown twice in ’42 and ’47–and didn’t win the MVP either time. In ’41, the magic .406 year, he was only 5 RBI behind DiMags for the league lead and totally crushed him in OPS by 200 points (1.287 vs 1.083) only to lose because of The Streak.

    Williams either won the MVP (twice) or clearly deserved it in 6 consecutive active seasons (’41-’42, ’46-’49). Considering this, it’s highly likely he would have won an additional MVP in at least one of the 3 years he missed due to WWII.

    Bonds only got legitimately screwed out of 1 MVP (Pendleton in ’91), so let’s call it 4 MVPs for pre-roids Barry vs. 6 MVPs for Williams (and likely 7 or more if not for the war).

    Williams OPS for his entire career bests Bonds’ pre-PED years (1.116 vs .984, minus Bonds’ rookie year), and his on-base % utterly destroys him (.482 to .415).

    Let’s not shortchange Bonds–he was far and away the best player of the ’90s even without drugs. Ruth’s pitching leaves him on an otherworldly level, but what about #2? In my book, it’s either Williams or Bonds. I say Ted.

  28. Gravatar of ssumner ssumner
    13. April 2014 at 06:18

    As usual all the comment are on a footnote. I agree with rwperu34 about Bonds and the modern era, and I agree with Michael Byrnes about steroids.

  29. Gravatar of Enrique Enrique
    13. April 2014 at 06:20

    The answer is #4, right? Here’s why:

  30. Gravatar of ssumner ssumner
    13. April 2014 at 06:21

    John S, Wasn’t Bonds better than Williams at the non-hitting aspects of the game?

  31. Gravatar of ssumner ssumner
    13. April 2014 at 06:23

    John S, I should clarify that I agree Williams had better stats, but would he have hit .406 against modern pitching? I doubt it.

  32. Gravatar of John S John S
    13. April 2014 at 07:43

    “Wasn’t Bonds better than Williams at the non-hitting aspects?”

    Yes, but it’s tough to measure how much Bonds’ baserunning and defense close the gap. Bill James tried to do so with his Win Shares statistic, which purports to distill a players overall contributions in one number. His list of career WS/season has:

    1. Ruth 44.33
    2. Williams 39.43
    10. Bonds 35.47

    The book was published in 2002, so it doesn’t include most of Bonds’ monster seasons (though he probably started juicing around 98 or 99). It depends how you judge his roid years; include them, and Bonds gets the edge. Without, Williams. If you’re willing to penalize Williams for playing in an earlier era, I certainly think Bonds’ PED years shouldn’t count.

  33. Gravatar of John S John S
    13. April 2014 at 07:50

    “would he have hit .406 against modern pitching?”

    Another tough question. Nate Silver has a fascinating essay on comparing eras in the preface to Baseball Between the Numbers: “Is Barry Bonds better than Babe Ruth?”

  34. Gravatar of Morgan Warstler Morgan Warstler
    13. April 2014 at 07:56

    SNL’s all drug Olympics:

  35. Gravatar of Mark A. Sadowski Mark A. Sadowski
    13. April 2014 at 08:44

    Off Topic.

    Krugman on UK fiscal policy (yet again):

    April 11, 2014

    The Return of Expansionary Austerity
    By Paul Krugman

    “Here we go again. There’s now a full-court press of the usual suspects claiming that the recovery in the UK proves that fiscal austerity isn’t contractionary after all, that the IMF had it all wrong, and so on.

    Jonathan Portes has an extended takedown; but the simple version is that the Cameron government did a lot of fiscal contraction in 2010 and 2011, but then slowed the pace of consolidation dramatically. Unfortunately, uncertainty over how big the UK’s output gap really is makes it hard to agree on a measure of fiscal policy, but just about every measure does indeed show austerity tapering off sharply after 2011. Here, for example, is real government non-interest spending:


    So the UK government did a lot of austerity, then stopped doing more, and the economy began to grow thereafter. Does this vindicate expansionary austerity? To use an analogy I’ve used before, if I keep hitting myself in the head with a baseball bat, and then I stop, I will start to feel better; this doesn’t mean that hitting yourself in the head with a baseball bat is a good thing…”

    Krugman gets his data from AMECO. The series name is OUTGI if anyone wants to check.

    The thing that struck me right away is the both his description and the graph show that fiscal austerity took place in 2010 and 2011 which is now over three years ago. Are we to believe that the cessation of fiscal austerity in 2012 is causing economic growth in 2013 and 2014? Those seem to be some very long fiscal policy lags don’t they?

    To put this in some perspective let’s look at the figures for RGDP and NGDP growth in percent by calendar year:


    You can see that there has indeed been a big increase in the rate of RGDP growth in 2013 but that’s not because aggregate demand growth was so spectacular. NGDP growth was actually less in 2013 than it was in 2010, which happened to be one of the two years of fiscal austerity that Krugman refers to. Thus a large part of the increase in RGDP growth in 2013 must be due to better aggregate supply performance compared to the previous three years. That’s not something which can be accredited to policies meant to impact aggregate demand.

    So since the largest increase in aggregate demand occurred during a fiscal austerity year, and the smallest increase in aggregate demand occurred the year it ended, the timing seems to be all off if one were to accredit this to fiscal policy.


  36. Gravatar of Mark A. Sadowski Mark A. Sadowski
    13. April 2014 at 08:48


    Maybe this is attributable to fiscal policy lags, or to the revenue side of fiscal policy? For that we need to turn to the less simple version as presented by Jonathan Portes.

    “…a) What does the recovery tell us about fiscal multipliers?

    Here the answer is actually rather clear, and is shown in this chart from the Office of Budget Responsibility.


    This shows the OBR’s estimate of the impacts of fiscal consolidation on the level of GDP. The OBR thinks consolidation reduced GDP by about 1.5%, with almost all that impact feeding through by 2012. Now, of course, Krugman and others argued all along that the multipliers were in fact larger, and hence the impact more negative. Well, suppose we were right, and – for the sake of argument – the multipliers were in fact twice as big. In that case, the negative impact on GDP would have been about 3%. But again, almost all that impact would have been seen by 2012 – all you would do to the OBR’s chart is double the size of the bars. What would bigger multipliers imply for growth now? Well, in fact, the chart suggests that the OBR thinks fiscal consolidation is now having a (very small) positive impact on growth. So if the multipliers are in fact bigger than the OBR thinks, that small positive impact would be larger. As Simon Wren-Lewis put it

    “In the textbook case austerity implies a deeper recession but then a subsequent recovery that is stronger as a result. So in that case rapid growth provides evidence in favour of the ‘fiscalist’ case, not against it.”

    So the Chancellor is flat wrong, at least if you think the OBR is reasonably close to being correct about the timing of the impacts of consolidation. That doesn’t mean, in this particular case, that larger fiscal multipliers can explain the current recovery – it just means that those who argue that the recovery supports the view that multipliers are small simply don’t understand the basic economic concepts here. [I explain this in a bit more detail here]…”

    The OBR’s chart can be found on page 54 of the following report:

    If you read the surrounding text you’ll note the graph depicts the varying effects of each type of fiscal policy change, including both spending and revenue, on level real GDP by fiscal year. (Fiscal years in the UK run from April 1, through March 31.) *The estimates in this chart are comprehensive and fully account for the lagged effects*.

    The chart shows that fiscal policy is estimated to have the following effects on level RGDP in percent by fiscal year:


    Since these are *level* effects we need to convert them to *changes*:


    Now let’s turn to the actual NGDP and RGDP growth in percent by fiscal year:


    The interesting thing about this is that both NGDP and RGDP performance are perfectly inversely correlated to the degree of fiscal austerity.

    This is hardly verification that fiscal multipliers are large. Rather it strongly suggests that the fiscal multiplier is in fact *zero*.

  37. Gravatar of W. Peden W. Peden
    13. April 2014 at 09:21

    Mark A. Sadowski,

    Fascinating. So, when the alleged “u-turn” on austerity took place, UK growth actually slowed down?

    Tough times for the Keynesians…

  38. Gravatar of Mark A. Sadowski Mark A. Sadowski
    13. April 2014 at 11:27

    Off Topic.

    Binyamin Applebaum notes that Jason Furman claims that the Great Moderation is back.

    April 11, 2014

    The Great Moderation Is Back
    By Binyamin Applebaum

    “Perhaps you remember the Great Moderation, the comforting term economists pinned on the period of relatively steady growth that began in the early 1980s.

    Perhaps you’ve even looked back and laughed at the very idea.

    Jason Furman has a more complicated view. The head of the president’s Council of Economic Advisers argued in an interesting speech on Thursday that the Great Moderation is still in progress.

    The growth of jobs and economic activity over the last five years has snapped back into the same kind of steady pattern that prevailed before the recession, a pattern documented in the chart below.

    Including the Great Recession does not change the basic pattern. Economic volatility, on average, is still lower now than in earlier decades.


    This is a hollow victory for those who championed the idea of a Great Moderation. They saw the trend as evidence that the economy was less likely to experience a dramatic downturn. Mr. Furman is essentially arguing that those economists were right in describing the phenomenon, but not its implications…”

    Jason Furman ignores the most obvious reason why the volatility of RGDP and employment growth decreased dramatically in the mid-1980s, namely that that’s about the same time that the Federal Reserve started systematically targeting the inflation rate. Thus I thought it might be helpful if Furman’s exercise with RGDP and employment volatility be repeated using NGDP and core PCEPI.

    Here’s the standard deviation of quarterly NGDP growth at an annual rate during expansion periods.


    And here’s the standard deviation of monthly core PCEPI inflation (which only starts in 1959) at an annual rate during expansion periods.


    Note that NGDP growth volatility is only just a hair above its previous record low, and that core PCEPI inflation volatility is at a record low. And note further that this has occurred despite the supposed fact the economy has been in a “liquidity trap” all of this time and has been buffeted by a series of fiscal cliffs.

    So if the Fed has been doing a better job of keeping NGDP and core PCEPI going in a straight line since the Great Recession, maybe all it really needs to do is to aim a little higher.

    P.S. Marcus Nunes has done not one, but two posts on this same topic.

  39. Gravatar of rwperu34 rwperu34
    13. April 2014 at 11:58

    The problem with Williams is he screwed himself for being such a damn fine fighter pilot. His hitting stats were better than Bonds, but Bonds had 3000 more PA. So to give Williams an offensive edge (not even accounting for basestealing and baserunning), you have to give him full credit for all the seasons he missed due to wars. That still doesn’t account for defense! I think you can stretch it that far, but even then, it’s a tossup at best. In that case, you have to give it to the guy who actually realized the production…ie Bonds.

    As for Ruth, nobody forgets he pitched. It was in fact mentioned several times before it was mentioned that nobody remembered. As a position player, Ruth and Bonds are close and you can give the nod to either. Once you factor in the pitching, Ruth was clearly the best player relative to his peers of all time. I don’t think anybody would even argue that…unless they forgot about the pitching:)

  40. Gravatar of Philo Philo
    13. April 2014 at 12:07

    A counterfactual statement such as: “Hank Aaron would have been a great baseball player even if all of his homers had been singles,” seems clear and definite, but is actually quite obscure, because it seems to contain an implicit *ceteris paribus* clause. While we are imagining all Aaron’s homers to have been singles, what exactly are we also imagining to be kept as it actually was? Aaron’s powerful physique? Then how could he have hit no home runs? The pitchers’ fear of Aaron? But why should they be equally fearful if he never hit a home run? Newspaper reports of Aaron’s performance? But these include reports of his *hitting home runs*. (But if the newspaper reports are kept the same, something else has changed: the newspapers’ *accuracy*.)

    The situation that the counterfactual calls upon us to imagine has really been quite indefinitely specified: there are many different scenarios in which all of Aaron’s home runs have been converted into singles, and in *none* of them is *everything* else really being kept as it was in reality. Perhaps, instead of *ceteris paribus*, what is really being implicitly invoked is some notion of *minimal departure from reality*: the question is, what would be true if all Aaron’s homers had been singles and *everything else were as nearly as possible the same as in reality*? But this notion of *as nearly as possible the same* is surely very vague in the minds of most people, and has eluded the efforts of philosophers (such as David Lewis) to analyze it.

    Of course, the vagueness and ambiguity of language does not prevent it from serving many practical purposes. One must hope that is the case also for many of the counterfactual statements in which we are interested–that the special conceptual obscurity of such statements does not make them completely useless.

  41. Gravatar of bmcburney bmcburney
    13. April 2014 at 13:56


    The issue here is not whether Bonds makes it into the Hall of Fame without steroids, I have heard people I respect make that case and agree it is plausible. In my opinion, the best hope for a non-juiced Bonds career is about the level of Mike Schmidt. Terrific player, easily a Hall of Famer, but not in anybody’s top ten of all time. The argument here is about whether Bonds should be considered the greatest of all time. On that issue it is simply a fact that Bonds, juiced to the eyeballs for the last TEN YEARS of his career, still comes up short of Ruth’s total WAR. Ruth never even had a cortisone shot.

    And, in fact, Chief Bender is generally credited with inventing the slider and he last pitched professionally in 1919. The splitter, then called the forkball, was invented in the 1920s during the early part of Ruth’s career. Presumably, Ruth faced both pitches many, many times. “Oh, and Babe Ruth never faced a 95 MPH fastball.” Prove it.

  42. Gravatar of Britmouse Britmouse
    13. April 2014 at 14:15

    Mark Sadowski, why aren’t you blogging yet?

    That question out of the way: great comment. If you add in 2009 it looks even worse, since we had a fiscal stimulus and falling RGDP and NGDP.

    The VAT rise in 2010 partially accounts for the relative weakness of RGDP growth in 2010 versus 2013; ironically, the “fiscalist” narrative works best for the supply-side not the demand-side. Nominal GVA (at basic prices) growth was +3.6% over year to 2010 Q4, and +3.9% over year to 2013 Q4.

  43. Gravatar of ssumner ssumner
    13. April 2014 at 14:37

    I think there’s a lot of silly hypocrisy on the drug issue. At least a decade before the Lance Armstrong scandal broke it was widely known that almost all the top bicyclists used banned substances. No one cared. Then there is football. Then there’s the differential treatment of baseball players with bad personalities who use drugs vs. baseball players with good personalities that use drugs. I don’t take any of it seriously. Just a bunch or moral posturing.

    Regarding the good old days, yes Ruth was the best relative to the (weak) competition of the 1920s. Imagine removing all the black and hispanic players from MLB, and also half the whites. That’s baseball in the 1920s, at best. And the money was also less so there was probably less obsession with training, diet, etc. Ruth looked fat. I imagine many of the people who would have done well in baseball, based on genetics, were farmers, etc. In 1968 Yaz won the batting title hitting 301. In 1930 the league average was 303. So the best AL hitter in 1968 was worse than an average player around 1930? I don’t think so. Pitching sucked in the 1920s.

    John S, Yes, Ruth’s “numbers” are better than anyone.

    Mark, I recall pointing out that fiscal policy wasn’t that austere back in 2012, and being hammered by Keynesians who insisted it was very austere. Now they are arguing the opposite. It seems like they start from the RGDP data, and then work backward to assume whatever fiscal policy stance is required to make the Keynesian model work.

    Mark, No question that the business cycle since 1983 has been radically different from the sort of high frequency cycle that we saw in the 1950s. The question is why.

    Philo, It’s very simple. He was simply trying to show how great Aaron was by pointing out that even a player with 3771 singles would have been considered great. That’s all. There was no claim that hitting 3771 singles was plausible, by Aaron or anyone else.

  44. Gravatar of Jaunty Rockefeller Jaunty Rockefeller
    13. April 2014 at 17:25

    @bmcburney: Bill James ranked Schmidt as the 21st best player of all time–and that includes a few pitchers and Negro Leaguers listed ahead of him. James is sometimes idiosyncratic, true, but saying Schmidt is “not in anybody’s top ten of all time” is wrong, if you mean top ten of Major League batters, which seems to be what we’re discussing here. And Schmidt accumulated 106 WAR in 18 seasons; by 1998, when it’s said Bonds began juicing, he already 100 WAR in 12 seasons. So not only is it a bit uncharitable to Schmidt to say he’s nobody’s idea of a top-ten player, it’s also obtuse to say Bonds was “only” as good as Schmidt. As James describes Bonds, he was Willie Mays, who then turned into Babe Ruth.

  45. Gravatar of Nick Nick
    13. April 2014 at 18:01

    I’m not sure the question in your PS is phrased correctly. It’s not which of these *should* cause us to think less of a player, it’s which of these *does* cause us to think less of a player. It’s like the difference between “Do you like having a designated hitter?” versus the question “Should you like having a designated hitter?”, “Should we prefer baseball with 5 or 6 bases?” versus “Would you prefer baseball with 5 or 6 bases?” The rules, both written and unwritten, of (successful) sports are determined by what the participants (players, fans, businesses, etc) want them to be.

    We like what we like in sports and it’s not a normative question of what we should like (playing a little devil’s advocate here, some people against PED might argue that it is harmful and therefore it is a question of morality but I’m assuming that is not a position that Prof Sumner holds). If people say they don’t like Barry Bonds because of PED, then I don’t think they need to support it. If that’s not “the game” they like, then that’s ok. Maybe “the game” has moved on, and they will gain 2 fans for every one that they lose, but since it’s all a context-bound system anyways then that’s the choice that the participants of the game can make.

  46. Gravatar of Jim Glass Jim Glass
    13. April 2014 at 18:14

    As usual all the comment are on a footnote.

    Aw, c’mon. When a footnote makes a flat decoration that X is the best baseball player ever, period, then goes on to be provocative about illegal drugs, that’s begging for it. Don’t be coy. 🙂

    But OK, back to the original point. I agree with you, Nate was was just illustrating how valuable Aaron’s performance was apart from his home runs. “Assume all his HRs were degraded to mere all singles” is perfectly reasonable for that purpose. Tyler’s response was unconstructive. This was not general equilibrium analysis.

    BTW, note how in Nate’s data Ruth produced *less* of his total value from his HRs than did any other player with 500+.

    For an empirical look at steroids in baseball, here’s an economics paper that estimates the impact of steroids on player performance, player salaries, team revenue (findings: significant on all counts) plus the effects of various drug enforcement schemes, etc.

    I think there’s a lot of silly hypocrisy on the drug issue.

    Of course, as there is everywhere.

    I don’t take any of it seriously. Just a bunch or moral posturing.

    A mistake. You shouldn’t be so flippant about it. There’s a lot of silly hypocrisy about many serious issues – *especially* about serious issues, as that’s where people reap the most social returns from easy posturing – but that doesn’t make them any less serious.

    There are women’s track records from the 1980s that will never ever be broken because the Eastern Europeans so loaded their women up on steroids, testosterone and all the rest. Those results were horrible across-the-board, to the health of the women (many gruesome results) the integrity of the sport, the effects on the young and so on.

    Nobody can want that in baseball. Just opening the doors to “try out any chemicals you want, possible reward millions and millions of dollars, risks all yours” will get the same thing — a competitive flood into it, health disasters for the losers, vast inequalities from disparate results among the rest of the player-users, the immense “trade value” of baseball’s recordbook being destroyed, fans going “wtf?” as the game develops the integrity of 1950s pro wrestling, and the effects ‘on the children’ — in this case it really matters, kids idolize and imitate star athletes — horrible.

    I’m very much a free-market, libertarian-sympathetic guy — but free markets require laws and rules accepted by consensus to operate.

    The laws and rules about steroids in baseball have been a travesty, but the main problem there has been lack of information. Nobody knows the effects of steroids on baseball players and the game, so opinions are madly all over the place, with no way to resolve them, and that’s no way to come up with a sensible, optimum set of laws and rules that people can accept voluntarily by consensus. I’d like to see steroids legalized in a minor league or two for a couple years — all users doing so openly in public, under medical supervision, full data collected — to get such information. Until something like that happens, this situation is just going to continue as it is forever, IMHO.

  47. Gravatar of ssumner ssumner
    13. April 2014 at 18:32

    Jim, I think you misinterpreted me. I have no problem with baseball banning steroids, I think it’s clearly in the players’ interest for them to do so. (It’s not in baseball’s interest, it’s in the players interest, as their health is at stake and its a zero sum game for players as a whole.) But it’s an externality problem. My complaint is that sports like baseball (and even more so bicycling, football, and track in the old days) were not enforcing the rules, knowing that under those circumstances players would have a strong incentive to cheat. How much “holding” would occur in football if the penalty was never called–if it was on an honor system.

    And then everyone is shocked, shocked, by what’s been happening . . .

    I would object to the government banning steroids in the major leagues, as there is no market failure involved.

  48. Gravatar of John S John S
    13. April 2014 at 19:00

    Re: Ruth–yes, I agree that timeline adjustments would considerably weaken his case as the best ever if we look solely at offensive numbers. But he was also a top echelon pitcher, which can’t be waved away by saying “well, everyone sucked.” How Ruth’s pitching affects his all-time ranking is a tough question, a point that any reasonable barroom conversation should acknowledge.

    (Fwiw, James’ Win Shares stat does include a slight downward linear adjustment to penalize players from earlier, and presumably weaker, eras. And fat ballplayers can be very good hitters; see Kruk, Puckett, and Cecil & Prince Fielder).

    In 1930 the league average was 303. So the best AL hitter in 1968 was worse than an average player around 1930? I don’t think so. Pitching sucked in the 1920s.

    No offense, but you’ve cherry-picked two years to reach a dubious conclusion. As I’m sure you know, 1968 was the “Year of the Pitcher”; the combination of the expanded strike zone and higher pitching mounds depressed offensive numbers throughout the 60s. Offensive numbers rebounded quite quickly after these changes were reversed.

    1929 and 1930 were anomalous upward blips in league OPS (.770 and .790), which quickly fell to a historically normal .731 in ’31. It won’t do to simply look at the 1930 league batting average and conclude that “pitching sucked in the 20s.” Using such an approach, one could easily look at the historically low ERAs from 1900 to 1920 and falsely claim that pitching was superior in this era. That the 20’s and early 30’s were a somewhat hitter friendly era doesn’t imply that the pitchers “sucked” any more than the 1960s suggests that the pitchers suddenly became “awesome.” [It is of course likely that pitcher quality was lower overall due to a smaller talent pool, but this is a completely different argument.]

  49. Gravatar of John S John S
    13. April 2014 at 19:54

    Your only knock on Williams seems to be that he wouldn’t do as well as Bonds against modern pitchers. Again, I think it’s reasonable to penalize Williams somewhat; the question is, “How much?”

    Keep in mind that Williams had stupendously good seasons in ’57, ’58, and ’60 (league leader in OPS in 2 yrs, over 1.000 OPS in all 3) from ages 38-41. 1960 was the last year before modern expansion started in 1961, and the league was already 9% black and 9% Latino.

    So Williams dominated a pre-expansion, 18% non-white league at the tail end of his career. Imagine that instead of Yaz, a 20 year old Williams clone entered the league in 1961. Yaz maintained a high level of play well into his late 30s, posting an OPS of .812 in 1980 at the age of 40. Is it crazy to imagine that Ted Williams II would be a much better and consistent version of Yaz (or a sharper-eyed, power-hitting version of Boggs had he started in the 80s)? The recently published “Sabermetrics Revolution” showed that strikeout rate, walk rate, and isolated power (SLG – BA) are the stats with the highest level of autocorrelation year to year; Williams excelled on all of these measures, so it’s certainly plausible these attributes would translate well to the modern game.

    There’s also ample anecdotal evidence. Williams had famously good eyesight (I’m sure you’ve heard the stories); he had the reflexes to be an excellent fighter pilot; and he had arguably the sharpest hitting mind of all-time. Tony Gwynn met Williams in 1992. After a series of conversations with Williams, Gwynn altered his batting mechanics and approach and arguably had his best 5-year stretch from ’94-’99 (ages 34-39), with permanently elevated HR totals (possibly due to juiced ball effects, see below). The fact that Williams could impart useful advice to Tony Gwynn of all people in the late 90’s, decades after retiring, is at least strongly indicative that Williams’ knowledge of hitting was in a class by itself.

  50. Gravatar of rwperu34 rwperu34
    13. April 2014 at 19:54


    Again, you are wrong. Bonds already had an equal career to Schmidt BEFORE he started juicing. He was also still the very best player in the game. So he had another 50 or so WAR coming…without steroids. Jaunty Rockefeller said it very well. Bonds was going to arguably be a top five player, and steroids turned him into arguably the best position player ever.

  51. Gravatar of John S John S
    13. April 2014 at 20:16

    As shown above, Williams’ stats aren’t just a bit better than pre-PED Barry–they absolutely destroy them. There’s a 130 point gap in career OPS. Would you immediately say a .870 OPS player is anywhere near the caliber of a 1.000 OPS player, even accounting for timeline effects, baserunning, and fielding? (At any rate, James’ Win Shares analysis, with a mild timeline adjustment, still says Williams’ per season overall contributions handily outweigh those of Bonds).

    Another wrinkle: there was a permanent home run surge from 1993, likely due to a livelier ball. To quote a summary of sabermetrician Tom Tango’s research:

    “There was a large increase in major-league baseball hitting in 1993 and 1994, one that continues today. In 1992, there were 0.721 home runs per game. In 1994, there were 1.033 home runs per game. It wasn’t a one-time increase: the 1994 rate has pretty much stayed with us to the present day.”

    Park and expansion effects can’t account for the league-wide change, and I don’t see how everyone could start using steroids simultaneously in the off-season.

    “According to Dr. James Sherwood, MLB’s ball tester, minor-league balls travel 391.8 feet under the same conditions that major-league balls travel 400.5 feet, for a difference of 8.7 feet. And, according to Greg Rybarcyzk of HitTracker Online, if you eliminated all home runs in 2006 that cleared the wall by less than 8.7 feet … you’d have roughly the same home run rate as before the jump.”

    Bonds obviously would have peaked around ’93 anyway, at age 28, but how many of his subsequent pre-PED peaks benefited from ball effects? Hard to know precisely, but it certainly creates a further statistical gap between him and the Splinter.

    It’s still not a slam dunk for Williams, but it’s very, very close.

  52. Gravatar of Jim Glass Jim Glass
    13. April 2014 at 21:08

    I mentioned above that we are near totally ignorant about how steroids affect baseball players and thus the game — and that if they do so, they do so with massive inequality among players for reasons … we don’t know. But look at the data…

    What’s really unique about Bonds is that he had an entirely routine career arc (HoF quality) that peaked at age 28 and gradually but steadily slipped after that, the normal pattern for athletes.

    Then, *after* age 35, with his peak year apparently a good seven years behind him(!), his performance suddenly rocketed upward far above that career peak, as has happened to nobody else in the history of the game, and I mean *nobody*. He suddenly exploded above himself.

    His post-age 35 stats compared to his own former 15-year career — a pretty substantial sample for a base line — are not even close to being precedented or matched by anyone else in baseball history, nobody else, ever, is even in the same proverbial ballpark.

    “Wow. Bonds absolutely towers over everyone else in his ability to … tower over himself. Was the young Bonds really such an underacheiver that he was leaving historic levels of talent untapped when he batted .336/.677/.458 for what looked like his career best season at age 28?”

    OK, so what’s the explanation for this ‘miracle’? This was just when Bonds started with the steroids, so the mind naturally jumps to “steroids!”

    This might be supported by a study by Bill James (no longer online) in which he used 10 measures of “unusual” career performance to compile a list of players with the “the most unusual careers”…

    Rank/ Player/ points measure
    1 Barry Bonds, 1974
    2 Mark McGwire, 803
    3 Sammy Sosa, 521
    4 Babe Ruth, 511
    5 Roy Thomas, 393
    6 Yank Robinson, 323
    … [regular players from all eras]

    Again, nobody else is even in sight of Bonds, although the next two names are noted for steroids too.

    But if steroids per se are the explanation for Bonds (or James’ top three) then the question is … where’s everybody else?

    If steroids had any kind of general effects likes these, then in the steroid era we should suddenly have seen *a lot* of late-career rocketing upward and of “unusual” career patterns, as never seen before. Yet after Bonds (and the much milder cases of McGwire and Sosa, maybe Clemens among pitchers) steroids-era players are remarkably absent from these lists. And after the top handful of players the outliers are gone, steroids or no. All *the rest* of the entire generation of steroids players just isn’t there.

    So … why? Did Bonds’ body have some sort of unique chemical reaction to steroids? Did he somehow know much more about steroids than anyone else? Did his mega-outlier late-career performance in fact have nothing to do with steroids? (With the same true to a milder extent with McGwire and Sosa?) We just don’t know.

    But I find it hard to believe that players would want to play this lottery, where some other *few* players who have a unique chemical reaction or know the secret formula or whatnot can blow up due to no particular baseball merit to take your job away and take your money. While you are either risking your career and health to stay even by drugging too, probably as a lottery loser even if you do drug up, or risking your career by not drugging. Maybe that’s why there was a political swing in the union driving it to agree to new drug enforcement terms.

    I’m not a drug prohibitionist, or any kind of prohibitionist, but the wildly unequal effects of steroids in baseball and our total ignorance about them can’t be good either for the players or “the game” — if there is one place where the customers want an even playing field it is sports. So again I say: experimentally legalize and study and learn, then go from there.

    Until that happens I’m agnostic about the whole issue. Won’t happen though.

  53. Gravatar of rwperu34 rwperu34
    13. April 2014 at 21:27

    John S,

    For pre PED Bonds to have had a career OPS of anywhere near .870, you would have to suspect him as starting in 1992. Nobody suspects that. Through 1998, his career OPS was .966. Not sure where you’re coming from with .870, but it doesn’t really matter. Bonds had 100 career WAR through 1998, 20 shy of Williams. Bonds was still the best player in the game, having not falling below 8 WAR the previous three seasons. There is no way he doesn’t project for at least 20 WAR sans PED. For you to make the argument that Williams was had a better career, you need expunge all of Bonds PED accomplishments giving him zero credit for those years. That’s just not realistic. Using a future projection from 1999 forward, Bonds was expected to get another 50 WAR. Lucky for me, I don’t even bother discounting at all, so I’m just going to claim the full 170. Giving Williams full WAR credit for his war years nets him another 45 or so, still short of Barry.

    As for ball/league/park effects, just use OPS+. Or even better, batting runs. Williams career OPS+ was 190, Bonds 182 (in 3000 more PA), pre 1999 Bonds was 164 in 1600 less PA.

  54. Gravatar of Doug M Doug M
    13. April 2014 at 22:48

    If something is against the rules but the rules are not enforced, is it really illegal?

    Steroids were not banned until the 1990s. So, Jose Canseco’s steroid abuse happened before steroids were banned.

    I am a huge Barry Bonds fan, but Babe Ruth was the best player in baseball history. He changed the way the game is played.

  55. Gravatar of W. Peden W. Peden
    13. April 2014 at 23:11

    Mark A. Sadowski and Britmouse,

    I recall seeing similar stats from Tim Congdon, who compared budget balances and growth in at least two places (a recent one for the US, I think, and an older one for the UK).

    For the UK, he found that changes in domestic demand and fiscal stance were correlated prior to about 1973, but inversely correlated afterwards. Presumably, that’s because monetary policy and fiscal policy tended to move the same way through the post-war period, whereas e.g. the Lawson boom was a boom that coincided with very good public accounts figures.

  56. Gravatar of W. Peden W. Peden
    13. April 2014 at 23:14

    On baseball: like most Brits, I know next to nothing about baseball, but I think most of the stats people are quoting are very misleading. I looked up a site called and it pointed out that, due to changes in the sport, Barry Bonds had 100,000 home runs in modern terms.

  57. Gravatar of W. Peden W. Peden
    13. April 2014 at 23:15

    Or Babe Ruth, rather. See: I literally know more about roadworks in Massachusetts than baseball.

  58. Gravatar of Gordon Gordon
    14. April 2014 at 00:55

    “And then everyone is shocked, shocked, by what’s been happening . . .”

    I didn’t read all of the comments so I don’t know if this was brought up already. According to the accounts of ex-players, amphetamine use was prevalent in baseball for decades starting in the 40’s and steroids dates back to the 70’s. And one former teammate of Aaron’s believes that the PED use was worse in the 70’s. I’ve felt that sports reporters jumped on the phrase “steroids era” to draw attention away from the fact that they were looking the other ways for many years.

    As for Bonds’ change in numbers, it’s hard to evaluate how much of that was due to PED’s. There was the move to AT&T Park, a major change in his swing, and he had Kent hitting behind him. With the change in his swing, his bat speed improved. This allowed him more time to evaluate the pitch. Prior to that he had problems with both fastballs and sliders on the inside part of the plate. Also before the change in his mechanics, he was very prone to chasing pitches out of the strike zone in critical at-bats. Bonds improved his plate discipline around the same time he changed his swing. After these changes, the Dodgers eventually figured out to mostly throw off speed pitches on the outside corner of the plate. At worst, Bonds might get a single. I never noticed any other team clue into this as the approach to take.

    So, like many other players, Bonds sought to help his game through PED’s. But he also made improvements to his mechanics and his plate discipline late in his career even though he was already a successful hitter.

  59. Gravatar of John S John S
    14. April 2014 at 02:55


    I’m not saying Bonds’ pre-PED OPS was .870.

    Ignoring his rookie season, his OPS from 87-98 (when he likely started using) is .981. Williams’ career OPS is 1.116.

    1.116 – .981 = .135, which I eyeballed to be around 130 points.

    I used the example of a gap between an .870 OPS player and a 1.000 OPS player (130 points) to dramatize just how big a difference that is. People might just look at .981 vs. 1.116 and say, “Oh, they were both great, it’s too close to call.” But no one would ever do that when comparing .870 to 1.000 (call it OPS illusion).

    As you said, including his rookie campaign drops pre-roids Barry to .966, widening the gap with Williams to 150 points. Put differently: even across eras, it’s far from certain (though certainly possible) that a 150 OPS difference can be explained by league difficulty alone.

    Please don’t misunderstand, Bonds is clearly in the mix for top 3 (ahead of Mays and Mantle). I just think Williams vs. Bonds is too close to call w/o really digging into the numbers.

  60. Gravatar of John S John S
    14. April 2014 at 03:14

    For you to make the argument that Williams was had a better career, you need expunge all of Bonds PED accomplishments giving him zero credit for those years.

    No, you don’t. It depends where you stand on the “rate stats vs. cumulative totals” and “peak vs. longevity” debates when arguing over “greatest ever” lists. I lean towards rate stats and peak. How many seasons should define “peak” is arguable. I think something around 15-18 full seasons is plenty for baseball players, with longevity achievements acting as tiebreakers (or pushing the lower peak player over the top, if longevity is exceptional).

    To use a non-baseball example: Kobe, if he’s healthy, will soon pass Jordan in total points (a counting stat). But does that mean he’s better than Jordan, who has a much higher PPG and adj. FG% (rate stats)? Of course not. At the same time, I don’t think it’s fair to penalize Kobe’s rate stats by including his first few years in the league, when he was still learning (or Jordan for the Wizards seasons). Compare peak vs. peak (perhaps 10-12 years for the NBA) and look at per game rates or advanced metrics.

    Here’s a nice post on peak vs. longevity on the excellent “Brodeur is a Fraud” hockey blog:

  61. Gravatar of John S John S
    14. April 2014 at 04:52

    Williams had 9788 total plate appearances, good for 93rd all-time (more than Foxx, Gehrig, or Hornsby). So that’s plenty large enough of a sample size to make meaningful comparisons versus other players’ peaks.

    From 1986 to 2000 (age 35), Bonds played 2143 games with 9141 plate appearances (this likely includes one or two PED seasons, just for good measure). Total WAR: 111.1

    Excluding only his final (and very good) final season, Williams played 2179 games with 9398 PA. Total WAR: 120.1

    This includes 598 games played after age 35 for Williams!

    Also, Bonds didn’t have a single double digit WAR season during this span (9.9 once), despite playing longer seasons. From ’41, Williams’ WAR season totals were:

    1941: 10.6
    1942: 10.6
    1946: 10.9
    1947: 9.9

    Given his incredible consistency, it’s highly likely Williams would have had one, two, or even three more double digit WAR seasons.

  62. Gravatar of Niko Niko
    14. April 2014 at 09:03

    If Bonds was “evil” than so was Ruth for promoting playing against only whites and willfully ruining the lives and careers of hundreds of black athletes during his generation and for years afterwards. Ditto all the guys who did greenies which were expressly illegal at the time and certainly helped over a 162-game season (especially if the guy only ate hot dogs and beer). Singling out one generation or worse, one guy in a generation who was “evil” or cheated more than others is silly. Bonds was the best of his generation, and is at least close to Williams and Ruth for all-time greatest.

  63. Gravatar of Mike Sax Mike Sax
    14. April 2014 at 16:01

    Figured I’d comment here first-as just looking at the title of your latest post I got a feeling I’m probably going to disagree-though I will try to go in with an open mind-as I always do believe it or not.

    However, I liked this post-as I’m also a baseball fan. This is what I hope economics can provide which is why I’m always trying to learn more about it-even if you’re right that I’m ignorant I have the desire to get it-the ability to think about counterfactuals.

    On baseball I’m particularly happy to say that Barry Bonds is the greatest ever. I got really tired of the endless piling on he’s taken. As you rightly point out other players could also use steorids if they chose-there is a risk with it so you might say that players who use steroids don’t have an unfair risk over those who don’t as they paid for it with the greater risk to health.

    My sense is a lot of the umbrage thrown his way is more moralistic than rational-well really all of it is. People just doni’t want to admit that there’s nothing ‘natural’ about what athletes can do. I mean the crazy weight lifthing regimen and diet isn’t ‘natural either.’ Yet people think it’s not fair to use anything more than what ‘God gave you’ so to speak.

    In any case not all ‘steroids’ are the same thing and some of them may not even have that high a risk level-the same is true more broadly of ‘drugs’-which only means the illegal substances not what’s in your medicine cabinet.

    Meanwhile, you have all these people saying that there should be an asterik next to everything Bonds-and others like Sammy Sosa and Mark McGuire achieved. I couldn’t disagree more and I’m happy to see you feel the same way-as it shows that my instinct here is backed up by some decent econ logic.

  64. Gravatar of Mike Sax Mike Sax
    14. April 2014 at 16:02

    “On baseball I’m particularly happy to say that Barry Bonds is the greatest ever.”

    I meant I’m happy to hear you say that he’s the best ever.

  65. Gravatar of Mike Sax Mike Sax
    14. April 2014 at 16:04

    This piece at CNBC made me think of you-and Stephen Williamson.

    The sharp stock market decline last week””fueled by the bloodbath in momentum names””doesn’t look like it will continue this week, Jonathan Golub, chief U.S. market strategist at RBC Capital, told CNBC. And better-than-expected earnings and revenues from Citigroup are giving stocks a boost Monday.

    “When interest rates go up it’s good for banks,” Golub said on “Squawk Box” Monday. Let Federal Reserve Chair Janet Yellen raise rates, and let the banks get healthy. “It’ll be good for the economy,” he added.

  66. Gravatar of rwperu34 rwperu34
    14. April 2014 at 17:36

    John S,

    Gotcha. I don’t know why I didn’t pick up that you were referring to the difference.

    As for park and league, in 1990 Bonds had a .970 OPS for an OPS+ of 170. The closest Williams came to a 170 OPS+ was 168 in 1950, where his raw OPS was 1.099. This illustrates the difference between Boston and Pittsburgh which was immense. Bonds had two other 170 OPS+ seasons in San Fran (1.009, 1.031), and Williams had a 172 OPS+ (1.084). Which just goes to show that you have to use some kind of adjustment for park and league.

    Baseball reference has a fun little tool that lets you put players in different contexts. If I take Barry Bonds and put him in 1948 Boston (roughly equivalent to the context Williams played his entire career), Bonds hits .318/.465/.645 for an OPS of 1.110 (compared to Williams 1.116) with over 800 HR! Unfortunately I can’t do only pre 1999 on that tool.

    For me I like to argue Bonds and Ruth as #1 position player and Williams and Mays as #3/4.

  67. Gravatar of ssumner ssumner
    14. April 2014 at 18:59

    I’ll let John and rwperu fight it out, as both know much more about baseball than I do. Just to clarify my original claim:

    1. I did not claim pre-steroids Bonds was the greatest ever, I said he was the greatest of his era.

    2. I believe post-steroids Bonds was much better than pre-steroids Bonds. So he went from being best of his era to being far ahead of the field.

    3. When I said Bonds was the greatest player ever, I was making two assumptions. First, the game has gotten more competitive, and is played at a higher level than in the 1920s. Second, I gave him full credit for his steroids production. It may be tainted, but all those games count. Unlike the NCAA dealing with cheaters, the games haven’t been removed from the records.

    I also want to identify myself with several commenters who pointed out that there is lots of hypocrisy. People like Ruth broke other rules. People get selective about which rules matter. Dems reelect Congressmen that drive drunk, and get upset over a Congressman that tweets pictures. The GOP is outraged by illegal immigration, but brushes off other offenses that they care less about. Yes, rules should be obeyed, but there are a lot of double standards here. I recall one pitcher treated as a lovable rascal for getting away with spitballs (I forget his name.) That’s cheating too.

    Bonds had a difficult personality–I suspect that cost him support.

  68. Gravatar of Jim Glass Jim Glass
    14. April 2014 at 21:21

    When I said Bonds was the greatest player ever, I was making two assumptions. First, the game has gotten more competitive, and is played at a higher level than in the 1920s.

    But that’s not right. This and all the comments along the lines of “Ruth faced lousy pitchers, didn’t face blacks and Latinos and Asians, didn’t face specialist relievers, was fat…” are all banally true and thoroughly uninteresting. They make the basic mistake of confusing “best” with “greatest”.

    Objectively, current mediocrities are always better than the champions of years ago. All today’s baseball players are the best ever — and today’s Division II college football teams would flatten Lombardi’s Packers, having a 60-pound edge at every line position for starters. But when talking about the *greatest* football teams, nobody says “Lombardi’s Packers weren’t even as good as a Division II team”.

    Ted Williams’ .406 in 1941 was about .270 against today’s pitching, the sabermetrics people will tell you. Does anybody say the .280 hitters of today are “greater than Ted Williams”?

    There is extraordinary bias in saying “today’s players are ‘greater’ because the game is played now at a much higher level” — it credits the current players with the benefit of decades worth of development of training and technique, while penalizing the players of 80 years ago for living before it occurred. That’s just not fair.

    Isaac Newton said “If I’ve seen further it’s because I’ve stood on the shoulders of giants.” Today every university physics prof knows more about physics than Newton did and has better techniques too, largely from standing on his shoulders. Are they all ‘better’ than Newton? Yes, they are! Are they all ‘greater’ than Newton? No.

    ‘Greatness’ is how one performs relative to one’s contemporaries and peers under like conditions using like resources. Newton v his contemporaries, Lombardi’s Packers and Ted and Babe and Barry v theirs.

    Babe hit more HRs than 14 of the 15 other *teams* in 1921 (54 v the team average of 33) more than 12 of 15 teams in 1927, etc. And he could have been a HoF pitcher too: 29 2/3 consecutive scoreless innings in the World Series (the record for 43 years), he still has the record for most shutouts in a season (tied by Guidry in 1978), etc. Nobody ever dominated contemporaries like Ruth did.

    OK, the competitive field is much tougher today. The weakest players are much stronger, there is far more specialization due to greater skills on average, all of which means the best are much less ahead of the pack statistically and the worst are closer too it. The .400 and .150 hitters of yore are long gone.

    This can be compensated for across eras, in principle at least, starting by measuring performance by standard deviations apart from the norm, and the like. Doing this (and far more sophisticated adjustments) to treat Babe as if he played on the 2000s (standing on his own shoulders) the sabermetricians get numbers for him that of course don’t dominate near as much as his did in the 1920s but which are still best for the decade, entirely Bonds-like … with one exception.

    That is, Babe’s HRs-to-plate appearances ratio was more than 8 standard deviations above the major league average in the early 1920s. Well, *nobody* is 8+ standard deviations better than all the other best professionals at anything due to skill alone — what happened is that Babe invented the HR as we know it, he invented the uppercut long-ball swing. You can trace its spread via player and team statistics, as he was imitated by first his own teammates (“Murderers Row”) then by the NY Giants and AL teams who saw him and the Yankess most often, then finally through the rest of the NL.

    Babe invented a new way to bat and by personal example over much resistance (see what Ty Cobb said about it) changed the way the game is played to this day. Talk about dominating contemporaries, in the ‘greatness’ tally he deserves about 100 extra points for that, all his stats aside. Barry Bonds took all his at bats standing on Babe’s shoulders.

    It’s easy to statistically convert the stats of one era to the equivalent numbers for another — but it is uninteresting, you’ll always find the more recent players are “best” empirically. OTOH, “greatness” is a relative concept, subjective, and converting the stats only gives suggestions, which makes the arguing endless — and a lot more fun. 🙂

    But Ruth was pretty damn great.

  69. Gravatar of John S John S
    15. April 2014 at 04:14

    Excellent comments by Jim Glass, and I love your distinction between “best” and “greatest” (Ruth’s 4-0 record vs. Johnson is also a wonderful bit of trivia).

    You’ve convinced me that Ruth’s role as an innovator justifies his rank as the greatest of all-time solely based on his hitting. Adding his pitching ability on top of this gives his career a wondrous, mystical quality. How poetic that the inventor of the modern homerun swing was not only its greatest practitioner but also one of the best ever at preventing homeruns! (13th all time in HR/9 innings, albeit in the deadball era)

  70. Gravatar of John S John S
    15. April 2014 at 05:16

    rwperu, let me add a few fun hypothetical scenarios (by the way, I’m enjoying this discussion; looks like there are fewer sabermetrics nerds on this blog than I would have guessed):

    1. Bonds’ career WAR total is 162.4. If you credit Williams with 45 WAR for his military years, that would put him at 168.1–ahead of Bonds even including the PED years.

    2. As you said, pre-PED Bonds was headed for around 150 WAR. Even assuming fairly mediocre seasons (by Williams’ standards) in his missing seasons (say 8 WAR/season for ’43-’45 and 9 total WAR for 1.5 Korean War seasons) would give him 156.1 WAR, or about dead even with Mays for best position player ever. Just one breakout season within that frame puts him over Mays.

    So based on any reasonable WAR projections, Williams clearly rates above pre-PED Bonds.

    3. Here’s a fun one. Williams played 2292 games (with 123.1 WAR). Let’s look at Bonds’ peak production only (ages 26-42, 2269 games). Total WAR: 129.3. Say Williams had only one extra Splinter-esque season (e.g. give him back a year from the Korean War at 7 WAR). Subbing out Williams’ age 40 -.2 WAR and replacing those games with a pro-rated equivalent would give Williams an extra 5 WAR, or 128.1.

    So Bonds’ peak, steroids and all, is about even Williams’ WAR production for an equivalent number of games stretched out over Williams’ entire career (sans 1 bad year, plus one reasonable estimate). Give him back a WWII year instead and Williams comes out comfortably ahead.

    Projecting 4.5+ seasons is tricky work, I’ll agree. But one season? C’mon, 7 WAR seasons were just another year at the office for Ted.

  71. Gravatar of John S John S
    15. April 2014 at 05:35

    A few more points:

    1. You and Scott both mentioned Bonds’ baserunning and defense. But WAR accounts for both of these dimensions. It also corrects for park and league effects, nullifying the effects of Fenway and Bonds’ home stadiums (Williams of course played half his games on the road).

    2. WAR isn’t perfect. Defensive stats in particular are currently a murky area for sabermetrics. But baseball reference rates Bonds as great fielder in his early years, average for most years, and poor toward the end while mildly penalizing Williams’ glove for his entire career. Reasonable, imo (most of Bonds’ GG’s were based on reputation).

    3. The only argument left seems to be timeline adjustments, i.e. the greater difficulty of the modern game. That’s a reasonable argument. But on stats alone, I’m still going with Williams.

  72. Gravatar of John S John S
    15. April 2014 at 05:42

    Scott, Nate Silver has an interesting reply on Aaron. Cliffs: singles Aaron would be something like Rod Carew. Worth a read.

  73. Gravatar of Jim Glass Jim Glass
    15. April 2014 at 11:31

    John S, thanks for the kind words.

    Though I must fess to I think being too hard on Ted with that “.270 against today’s pitching.” That was late-night memory of a study in a book in storage. In the light of day, coffeed-up, it seems more like if the Ted of 1941 faced today’s pitchers that .406 would be closer to .350.

    The first study ever done along this lines is online and normed historical batting averages to 1979. E.g. it put Honus Wagner’s .354 in 1908 at .292 against 1979-quality pitching. That’s 60 points down in 70 years, probably around the same for Ted. That’s with his 1930s training arriving via time machine to meet 2013 pitching.

    OTOH, by standard deviations above the mean, Ted’s .406 in 1941 translates to .395 in 2013, nearly the same and #1 by a lot. That’s what he’d a done if he’d arrived today by being reincarnated as a baby in the late 1980s, to meet 2013 pitching with 21st century training. Probably. Maybe. If he didn’t choose a career producing new videos for Netflix instead. Thusly the arguments about “who was the greatest ever” go.

  74. Gravatar of ssumner ssumner
    15. April 2014 at 16:43

    Jim, I find it interesting, even if you don’t.

    John, That’s an interesting piece by Silver. I should say that while I read Bill James in the early 1980s, I haven’t followed baseball at all in the past 20 years. All I know is that offense is roughly OBP plus slugging percentage, with a slightly higher weight on OBP. Is that still right?

  75. Gravatar of rwperu34 rwperu34
    15. April 2014 at 17:40

    Scott, yes, that is just about it. If you go to fangraphs, they have an all encompassing stat called wOBA. If you want to adjust for park/league effects, then you can go wRC+ (fangraphs) or OPS+ (baseball reference). If you want to do it yourself, 1.8*OBP+SLG is fine. OBP+SLG gets you 95% of the way there and is also acceptable. Whatever you do, just don’t mention batting average or RBI.

    Jim Glass, There are two questions. Any time you use the players contemporaries and talk standard deviations above the mean, you are answering who was the best relative to their peers. The other question is, who was the best player (ie biggest, strongest, fastest, most skill…etc). It’s like Citzen Kane, supposedly the best movie of all time (relative to its peers). Yet when I watched it was a complete snoozer. Everything Orson invented in that movie has been in every movie I’ve seen since I was a kid. Since the greatness of the movie relies on the new inventions, it meant nothing to me (although I am very appreciative for Mr. Wells inventing all that stuff). The question I ask is, if I could pay to watch any player from any time in history, and that would be the only player I’d get to watch, who would it be? If you want to go back to watch an overweight, out of shape, fat, greezy, bloated, 12-sandwich eating Babe Ruth beat up on the league because he’s the only one that had the sense to take half the swing that everybody takes nowadays, that’s your prerogative. But me? I want to watch Barry Bonds.

    John S, Like I said, to get Williams there, you have to give him full credit for killing Nazis and Commies. Otherwise Bonds is up by 40 WAR. I just can’t give him that full credit for production he didn’t produce. Likewise, I can not penalize Bonds (or anyone else from that era) for the production they did produce.

  76. Gravatar of John S John S
    15. April 2014 at 19:07

    Jim Glass, very interesting study. Do you know of any similar modern studies focusing on advanced metrics (wRC+, OPS+, etc)?

  77. Gravatar of John S John S
    15. April 2014 at 19:35

    I’ve learned a lot through this discussion!

    As rwperu mentioned, wOBA (weighted on-base average) weights batting outcomes more accurately than OPS. For example, a point of on-base percentage is about 1.8 times as important as a point of slugging. A double isn’t worth twice as much as a single (two singles save two outs, which is better than a double and an out).

    Weighted Runs Created Plus (wRC+) is probably the best single metric of offensive value. From Fangraphs:

    “Weighted Runs Created Plus (wRC+) measures how a player’s wRC compares with league average. League average is 100, and every point above 100 is a percentage point above league average. For example, a 125 wRC+ means a player created 25% more runs than league average. Similarly, every point below 100 is a percentage point below league average, so a 80 wRC+ means a player created 20% fewer runs than league average.”

    Using wRC+ is another point in favor of Williams since he has the highest on-base % of all-time. Here is the top 10:

    1. Ruth 197
    2. Williams 188
    3. Gehrig 173
    4. Hornsby 173
    5. Bonds 173
    6. Mantle 170
    7. Cobbs 165
    8. Jackson 165
    9. Pujols 164
    10. Musial 158

    So for his career, including PED years, Bonds created 73% more runs than the league avg; Williams, 88%.

  78. Gravatar of John S John S
    15. April 2014 at 20:08


    Career WAR is essentially a counting stat. A basketball example clarifies this. Karl Malone has 234 Win Shares, Jordan 214. Does Malone’s longevity mean that he is better than Jordan? No, who would claim that?

    Rate stats are better than counting stats. By wRC+, Williams beats Bonds handily on offense, even w/o addressing the steroids question.

    The question I ask is, if I could pay to watch any player from any time in history, and that would be the only player I’d get to watch, who would it be?

    I feel this is a totally subjective criterion that differs for every fan and has very little to do with trying to create an “objective” list of greatest players ever (e.g. picking a roster to play for your life in a 7-game series, etc). If you’re going to introduce aesthetic aspects into the discussion, then I think Williams’ career is far more interesting than that of Bonds.

    – .406 vs. The Streak in ’41
    – Three massive MVP screw-jobs
    – The war years (a “Sandy Koufax” what if effect)
    – His proficiency as a fighter pilot
    – The “Williams shift” and Ted’s obstinacy in pull-hitting directly into it for his entire career
    – The Eephus pitch home-run in the ’46 all-star game
    – Going out in a double blaze of glory: great final season at 41 (after a terrible age 40 year) and a homerun in his final at-bat

    Even aspects of Ted’s “abrasive” personality (by 1950s standards) come off as charming today, for example his steadfast refusal to tip his cap after homeruns, including his final one.

    What are Bonds’ “magical” moments or seasons? I can’t think of even one off-hand. His main legacy is that he decided to use steroids because he was jealous of the adulation given to Mark McGwire.

  79. Gravatar of rwperu34 rwperu34
    15. April 2014 at 23:59

    Uh, Bonds has the single season and career HR record. That’s something to me (I remember driving around listening to games on the radio and racing into malls and sports bars when his at bat came up. I have never done anything like that for anything in any sport). He’s the only player with 500 HR and 500 SB in his career (or 400/400 for that matter). Five time 30/30 guy, one time 40/40 guy. He got screwed out of an MVP or two himself…yet still won 7!!! The absolute fear he instilled in pitchers, culminating in the all time record for walks and IBB. All time single season OBP, SLG, and OPS record. Did I mention he was the most feared hitter in the history of the game!? There’s plenty to see. But that’s really not what I’m talking about. I want to see the biggest, strongest, fastest, most skilled hitters face the biggest, strongest, fastest, most skilled pitchers. That’s what I pay for.

    As for rate stats, Williams averaged 8.6 WAR/650 for his career in 9788 PA. If I take Bonds’s best 9875 PA (1989-2004), he averages 9.7 WAR/650**. He also beats Williams in OPS+ (194-190) over those PA. I’m not willing to punish the guy because he had another 2800 PA that were merely all star caliber. The basketball analogy doesn’t apply. Malone did not have the peak of Jordan. He relies totally on longevity. That’s more like Hank Aaron vs Ted Williams. In Bonds case, his peak was actually better than Williams AND he had the longevity. Bonds had 8 seasons of 9+, Williams had 6. Bonds had 6 more seasons of 7-9, Williams 3 (plus a couple just shy). I understand Williams gets hurt by Hitler, but again, Bonds actually realized that production. For Williams we have to speculate.

    **Bonds averaged 8.9 WAR/650 for his career, so I didn’t even need to cherry pick years.

    One interesting note, both had their worst season by WAR at age 40.

  80. Gravatar of Michael Byrnes Michael Byrnes
    16. April 2014 at 02:50


    Cut 4.5 seasons out of the prime of Bonds’ career (the amount of time Williams lost to service in WWII and Korea) and the comparison would look different.

  81. Gravatar of John S John S
    16. April 2014 at 09:06

    As I wrote in a previous comment, my opinion is:

    It depends how you judge his roid years; include them, and Bonds gets the edge. Without, Williams.

    You want to take those years at face value; I don’t (we’ll likely never agree, which makes these arguments fun).

    Do you believe Williams shouldn’t get any credit for his missed seasons? That seems rather extreme, considering he had no choice. Also, shouldn’t Bonds’ PED years warrant some kind of discount? I don’t think any reasonable person believes that steroids played no part in his late career surge.

    Re: numbers–take out Williams’ age 40-41 years and he’s at 9.2 WAR/650 PA (9067 PA). Credit him just one WWII year at 650 PA, 9.2 WAR and he’s at 9717 PA, 9.2 WAR/650 PA.

    For Bonds, knock off his bad rookie year and include his two BEST, PED enhanced seasons (up to age 37). 9933 PA, 9.0 WAR/650 PA.

    For Bonds’ PED-free career (excluding rookie year, 1987-99): 8050 PA, 8.6 WAR/650 PA. I don’t think PED-free Bonds projects to better than this rate from ages 35-39.

    Obviously, WAR isn’t perfect (fwiw, Fangraphs WAR shows a smaller gap btw Bonds and Williams’ career WAR totals, 164 vs 130.3; any idea which is better?) But I still think Williams vs. Bonds is close (and Mays might even be better than both, although his Fangraph WAR is lower).

  82. Gravatar of rwperu34 rwperu34
    16. April 2014 at 13:44

    I use BR solely for the ease of navigating the site. The adding seasons feature is huge. I actually like wOBA and wRC+ the best as rate stats, but OPS+ is close enough that the ease of navigation makes it about 97% BR and 3% fangraphs. With WAR, now that they’ve calibrated replacement level, probably the best is just a straight average (although I never do that).

    I don’t discount Bonds stats at all. He was on the field and that’s what he did. I saw some of it with my own two eyes. I do give Williams some credit for the time he missed, but I can’t give him full credit, because it’s speculation. It’s kind of like DiMaggio and Yankee stadium. If I really had to rank them I’d go Ruth, Bonds, then have a good debate about Williams and Mays with probably Williams coming in #3 (or Mays).

    Michael Byrnes,

    I don’t discount anything any “PED” player did. Not McGwire, not Sosa, not Clemens, not Manny Alexander, not Bonds. Not even A-Roid (he’s paying the dues that his peers feel fit). If you weren’t using PED when there were no rules against them, there was no backlash for using, and everybody else was using, then IMO, you weren’t trying. This has always been a player vs player issue, and for the longest time, the players didn’t care. The simple truth is, the owners and fans benefit from players sacrificing their bodies.

    We have already celebrated many PED users and given them full credit for their career, inducted them into the HOF…etc. We just aren’t sure who. Although I’d say this. Anybody who played from about 1996-2003 was probably 95% likely to have used at some point. And that doesn’t even count for amphetamines (“greenies”). What we really need is for someone who isn’t a usual suspect to come out and admit it. How sweet would it be if Maddux came out right in his HOF speech? Or what about the revered and loved Nolan Ryan, who almost certainly used PED at the end of his career? I’d love to have one of those two (or any other non suspect) just come out so we can put this whole thing to bed. Because in 50 years nobody is going to care who took what. They are going to look at the stats and say “Wow! I really wish I was alive to see Barry Bonds play!”

  83. Gravatar of John S John S
    16. April 2014 at 15:08

    This has been an interesting discussion. I’ve learned a lot, and the history of drug use in baseball is quite fascinating.

    What we really need is for someone who isn’t a usual suspect to come out and admit it.

    Schmidt’s comments seem to come fairly close. Kudos to him.

    rwperu, one last question: I’m curious about the overlap of certain areas of blogosphere nerdiness. You obviously like monetary econ and sabermetrics. Did you ever get into in the poker boom? (I did). Nate Silver and John Aziz played a lot of poker, too. You?

  84. Gravatar of John S John S
    16. April 2014 at 15:17

    They are going to look at the stats and say “Wow! I really wish I was alive to see Barry Bonds play!”

    Or Trout or Harper. A stronger testing policy might significantly improve the public’s perception of this generation.

  85. Gravatar of ssumner ssumner
    16. April 2014 at 17:06

    Interesting comments. One quick point about Malone and Jordan. I don’t follow this issue closely, but years back when I saw numerical ratings of NBA players they seemed flawed. Lots of centers and power forwards were rated too high relative to wing players. I don’t know why, but I suspect it has to do with the way offenses are run. The guard feeds the ball to the post, and the post player tries to score. Or the guard tries to score directly. But when the guard feeds to the post player a certain amount of passes will be stolen, and hence post players must shoot a higher percentage to equal the effectiveness of guards. Does anyone know if that problem has been fixed?

  86. Gravatar of rwperu34 rwperu34
    16. April 2014 at 17:32

    I was definitely part of the poker boom. It’s how I made nearly 100% of my income for 10 years. I was really crushed by Black Friday and still haven’t recovered. I spent last summer in Mexico. This summer I’m off to Canada.

    This is the only monetary blog I read regularly. I was directed here from Cullen Roche’s site (in 2010?), which I just recently stopped reading. I read two baseball blogs (Tom Tango’s site, and John Sickles) regularly and a blog that predicts whether TV shows get renewed or cancelled (despite only watching one current show that is about to get ousted, leaving me zero hours in prime time next year). Plus what comes to me on Facebook (which is quite a bit). If I have any extra time, I just scroll through my Twitter feed. I could probably know everything about everything if I used Twitter more and had about 50 free hours every day.

    Two other things I check daily are the prices of unleaded gas, oil, and gold (all on one page). Then I take that information and try and predict which way the stock market went that day (I’d say I get it right 40% of the time so far). I also check TIPS spreads.

  87. Gravatar of John S John S
    16. April 2014 at 18:03

    I was definitely part of the poker boom.

    KNEW IT (lol) 🙂

    Though it does make me wonder why you initially focused on cumulative totals over rate. Perhaps you view cumulatives at $$$, which is ultimately more important to a grinder than win rate.

    Basically, my contentions are: Williams BB/100 is at least as good as Bonds’; 9000 PA is a pretty big sample size for ballplayers; and projecting 3 wartime peak years isn’t different in principle (although certainly in degree) from extrapolating from one’s hourly earn.

    You probably see PEDs as equivalent to HUDs (no explicit ban, those non-users are just fish). I view PEDs as kind of a super -bot (with potential health risks). Certainly there’s no consensus on bots on twoplustwo, so from that angle I hope you can see how my point is somewhat valid. Suppose it were proven conclusively that some but not all top HU players used super-bots and that Jungleman was among the super-bot users; surely that would cast doubt on his ranking among all time HU players, no?

    Anyway, for monetary fun, you should definitely check out JP Koning’s blog Moneyness (

    Too bad about BF, good luck in Canada. Are the games much tougher post-BF compared to pre?

  88. Gravatar of John S John S
    16. April 2014 at 18:08

    Scott, sorry no idea about basketball metrics on post vs. wing players. If you’re interested in top notch bball analysis, I recommend this youtube channel:

  89. Gravatar of rwperu34 rwperu34
    16. April 2014 at 19:32

    In poker, playing time makes a big difference in winrate though. If you just cherry pick peak times and weak games, you’ll have a higher rate than the grinder that sits there for several hours at a time. Then you end up with less money (despite the higher rate) despite putting in the same number of hours. I’ve always focused on $/hr for everything I’ve ever done, and in fact usually use an increase in hourly to work less hours (rather than buy more stuff). So I see where you’re coming from. Then again, there is some point where I would take a lower hourly for more hours, so long as it was above my minimum threshold.

    Agree the PED and HUD issue is very similar. It’s not that the guys have HUDs that makes them better players. It’s that they know what to do with the extra information. The biggest thing the HUD does is let me play more hands than I normally would. Likewise, PED did not make Barry Bonds square the bat on the ball. It just made him a little bigger and a little stronger. He was the best at leveraging that extra size and strength. And the most important thing PED does, especially for older players, it keeps them on the field (ie lets them play more than they normally would)!

    In poker, HUDs don’t make decisions, but bots do. So yes, if a poker superstar turned out to be using a bot, then I’d think less of him. Also, if Barry Bonds had some kind of futuristic google eyeball that let him see in 100 frames per second, then this is a completely different discussion.

    I can’t really tell if the games are tougher or not. I lost a ton of skill in my two year layoff, so I’m just trying to get a feel for it. I suspect they are, based on all the extra software that’s available (that I didn’t have last summer but will this summer) and the shrinking market (down 13% yoy after a ~5% drop last year). Twoplustwo seems to think so, but they thought so a lot when I thought everything was the same.

  90. Gravatar of John S John S
    16. April 2014 at 22:28

    Scott, the best rate stat for basketball seems to be Win Shares/48 minutes. Jordan leads for career WS/48, and the top 10 seems reasonably balanced between front and backcourt players (surprisingly, Chris Paul is #4).

    Basketball’s a much tougher game to measure, though (e.g. teammate interactions, how to account for different offensive systems). I can’t possibly agree with David Robinson at #2. So it looks like there’s a lot more advanced metric work to be done there.

  91. Gravatar of John S John S
    17. April 2014 at 00:17

    One point in favor of Bonds is that if many players were using in the early to mid-90s–a likely supposition–his pre-PED WAR and other measures of relative dominance should be adjusted slightly upwards. Exactly when and how many of his peers started using, and the boosts they got from PEDs, is something we’ll never know.

    However… I still don’t think we, as the fans, should feel universally compelled to fully accept his PED-aided accomplishments. Bonds was well aware of the high probability that his PED usage would be exposed and that it would kill his HoF chances and reputation. He took that risk, and it paid off: $15 million for his last year, some portion of his $90 mil contract in 2002, and the personal satisfaction of re-writing the record books.

    Bonds didn’t care if he lost respect in the eyes of some fans and admission to the Hall. Fair enough. But as a fan I’m also free to exact my miniscule measure of retribution by placing an asterisk next to his late career numbers.

  92. Gravatar of John S John S
    17. April 2014 at 01:02

    In poker, HUDs don’t make decisions, but bots do. So yes, if a poker superstar turned out to be using a bot, then I’d think less of him.

    I’m not so concerned with the mechanism (automated decision making vs. data collection) as with the issue of securing advantages that, in principle at least, go against the norms of acceptable behavior. Did steroids in the 90s and early 2000s cross that line? I don’t know, it’s a tough question. But it’s definitely a gray area, not a black and white one as you and Scott seem to believe.

    [I appreciate that the players were in a prisoner’s dilemma and that the fault lies with MLB for it’s toothless drug enforcement policy. But I still can’t respect the “defectors” for profiting at the expense of the “cooperators” and then continuing to lie about PEDs when confronted.]

    In the poker community, there are gray areas, too. Just when does a HUD cross the line to becoming a bot? Is giving advice during sweat sessions legit? Multi-accounting? Stinger/sbrugby sharing HHs vs. Isildur? SNG/cash collusion? There are plenty of “unenforceable rules” here, too, but on the whole the poker community still considers certain behaviors to be acceptable and other not, and there is a vigorous debate on each of these issues.

    Honesty, last time I checked, still seems to be prized in poker. Witness the whole Girah/Dogishead scandal. There is no explicit “rule” against creating a sham prodigy to try and bilk unsuspecting dupes with coaching fees. But no one on twoplustwo (as far as I know) was saying, “Well, it’s not against the rules, so it’s ok. Caveat emptor.” The online poker world (what’s left of it) still relies heavily on informal trust and honor to function, and cheaters who threaten to disturb that order are justifiably reviled.

    Rationally or irrationally, in poker the accepted norm among players and “fish” is human decision making, one person to a hand. In baseball, steroids fall outside of the accepted norms among most of the fans, writers, and the players who chose not to use (and there certainly were some, perhaps the majority).

    I certainly don’t want to get involved in a long debate on poker ethics, but I just want to stress that, in my view, simply sweeping the steroids issue under the rug and embracing Bonds is the wrong solution. This isn’t moral posturing, it’s recognizing the role of informal constraints in preserving order. Public censure isn’t much, but it’s better than nothing.

  93. Gravatar of rwperu34 rwperu34
    17. April 2014 at 06:17

    PED was never the owners responsibility. Never. It always has been and always will be a player vs player issue.

  94. Gravatar of ssumner ssumner
    17. April 2014 at 16:48

    John, Thanks for that list. Anything that has Jordan number one can’t be all bad. Here are a few that stand out:

    Manu at 13, Oscar Robinson at 17, Yao at 21, Dantley at 28, Kobe at 34, Olajuwan at 43, Amare Stoudemire at 53?

    I like Manu a lot–but better than Oscar Robinson? Kobe is overrated, but below Dantley? Olajuwan closer to Stoudemire than Yao Ming? Isn’t he actually better than Yao? And is Stoudemire any good, or did he benefit from Nash?

    I also wonder how much Jabbar was hurt by his longevity. He was better than Robinson, until he got old.

    There are good things on that list too. Moncrief is often overlooked, and scores high, for instance.

  95. Gravatar of John S John S
    17. April 2014 at 21:31

    I agree there are a lot of issues (e.g. Manu has played a lot of his minutes as a 6th man). Also, the NBA didn’t record a lot of key stats during Robertson’s era (turnovers, steals, blocks). And then of course there’s defense, which can’t really be measured only with steals and blocks (e.g. players should be penalized for gambling and getting out of position too often).

    Robertson, and esp. Kareem, are good examples of why I think it’s so important to focus on peak stretches rather than career totals. Looking at Big O’s first 12 years only would put him at .217 (#9 ahead of Barkley now, although a similar readjustment puts Chuck at .226). Kareem goes from .228 to .262, actually ahead of Jordan’s career number (Jordan’s top 12 yr stretch would go to .281, regaining #1).

    I think 12 seasons is pretty reasonable for comparing NBA players (Magic’s pre-HIV career was 12 yrs, Isiah Thomas only played 13 yrs total). [Btw, I never realized how effective Magic was in his comeback–17.6 pts, 8.3 ast, 6.9 reb per 36 min. Impressive after a 5 year layoff].

    Basketball metrics aren’t perfect, but they’ve changed my opinions on a lot of players. For a long time, I had a hard time believing Duncan could rank so much higher than Olajuwon. But I’m convinced now Duncan is one of the best ever (I’d pick him as PF on my all-time dream team, ahead of Barkley or Malone–not what I’d have said before looking at advanced metrics).

  96. Gravatar of John S John S
    17. April 2014 at 21:47

    Yao benefits from a very short career (less than 8 full seasons, pretty much all peak) and low per game minute totals. He was better than most would assume, though I agree Olajuwon was far superior during his championship years.

    Stoudemire’s one of those guys who plays crap defense that’s hard to capture in numbers. Nash likely helped his offense a lot.

    To me, the biggest weakness in these metrics seems to be inability to account for offensive systems. Popovich gets great production out of players that other coaches couldn’t. Every team in the NBA now uses systems to a much greater degree than previous generations, which I think makes inter-era comparisons a lot harder than baseball (which is essentially the same at its core: throw the ball and try to hit it).

  97. Gravatar of ssumner ssumner
    18. April 2014 at 05:48

    Yikes, Did I really write Oscar Robinson?–I am getting senile.

    All very good points. The other day I heard some TV people discussing a half dozen options as the greatest scorer of all time, and Kareem wasn’t even mentioned. Funny how he is often overlooked on “best” discussions. Younger people probably recall his declining years with the Lakers, but he came into the league as a great player from the very first year.

    Question: Did Kareem score more points from the skyhook than all other NBA players in history combined?

    I never saw Wilt in his prime, so that probably affects my view of him. I’ve always wondered how he would have done against modern defenses.

  98. Gravatar of John S John S
    18. April 2014 at 15:14

    Here’s an interesting economics question re: the skyhook–it was obviously effective, so why hasn’t any other big man since Kareem adopted it? (The only player who made a real attempt to incorporate it was Magic, who famously used it in the ’87 finals).

    Every few years an article will come out lamenting the lack of great big men in the NBA, and there will often be a sidebar about how everyone has eschewed the traditional sweeping hook shot for the supposedly quicker (but much more awkward looking) jump hook. When asked why, the players’ general response is that the old-time hook shot looks dorky.

    But is the risk of looking “dorky” (IMO the skyhook is more elegant) worth leaving millions of dollars on the table? It seems hard to square this with athletes as homo economicus optimizers.

  99. Gravatar of ssumner ssumner
    19. April 2014 at 09:35

    Speaking of dorky, did Rick Barry make more underhand free throws than everyone else in modern NBA/ABA history?

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