I realize he’s a great defensive player, but he does seem to have some gaps in his defense. Giannis’s quickness was just too much for him. Lopez also looks great on defense in some games and unplayable in others.

]]>(My guess is that front offices have already made more progress in this area than independent outfits like Bball-index. The recent surprising selection of Scottie Barnes, a 6’8” defensive specialist, over Jalen Suggs, a more polished, hard-nosed 6’4” PG, in the draft could be evidence that some teams have concluded that it’s more efficient to stockpile switchable defenders than it is to try to find elite, massive paint protectors like Gobert or Lopez.)

Anyway, it will be interesting to see what lineup analysis has to say about “fit” in the next five years or so.

]]>But I think there is a path forward for analytics to partially answer broader questions of this type. A lot of the groundwork is being laid at Bball-index (dot) com. This site has classified every NBA player into 12 offensive archetypes (e.g. shot creator, slasher [driver], stationary shooter, movement shooter, roll & cut big) and 7 defensive roles (point-of-attack, wing stopper, anchor [drop] big, etc). (Ex: Tucker would broadly fit into “stationary shooter” and “wing stopper”.)

https://www.bball-index.com/offensive-archetypes/

Bball-index also has data on player lineups, and these lineups are rated on various dimensions (e.g. spacing, playmaking, finishing) relative to league averages. So the next step might be to identify various off/def **team** archetypes (as proxies for systems) such as “beautiful game” (UTA), “pnr-centric” (ATL), and “iso-heavy” (BKN) on offense and “drop” (reg. season MIL) and “switch” (GSW, LAC) on defense. Then historical trends might emerge that highlight which sorts of off/def player types and combos fit best in which schemes.

]]>To attack this problem, another bball statistician (Dan Meyers) used linear regression to create a new metric. But this time, instead of finding the partial contribution of each player to changes in margin, Meyers solved for the coefficients of various box score stats (namely those available from 1974 on) to estimate each stat’s partial contribution to changes in RAPM.

This new metric –- Box Plus-Minus –- takes a player’s box score stats and converts them into a pseudo-Plus/Minus number which estimates that player’s impact on team score per 100/poss (e.g. Lebron’s +13.2 in ’08-09).

Ok, to get back to the original point about DBPM: the final step is to perform the same regression (relating box score stats to RAPM), but this time for offensive impact only. The resulting metric, OBPM, is subtracted from BPM to yield DBPM. To quote from Bball-Ref:

“To split BPM into offensive and defensive components, the same style of regression is used. It outputs offensive BPM, and defensive BPM is simply calculated as Total BPM – Offensive BPM. The regression coefficients were developed to maximize the fit for both offense and defense concurrently.

The Offense/Defense regression uses the same variables as full BPM, just with different coefficients.”

So why are some people claiming that BPM 2.0 (which includes a new wrinkle, positional adjustments) overrates perimeter defense over interior defense? It comes down to the coefficients assigned to box score stats generated by players at different positions. As you can see on the first table of coefficients at Bball-Ref’s BPM 2.0 explainer, steals for PGs are given a coefficient of 1.369, while steals for a Center only have a coeff of 1.008 (for blocks, it’s a more extreme difference: 1.327 vs .703).

Since DBPM equals BPM – OBPM, the higher valuation given to PG def box score stats (and, to a lesser degree, other perimeter players) can lead to some weird results. Looking at the top 10 DBPM seasons of all time, Nate McMillan is at spots 1 and 10, while Michael Jordan is at no. 9. While I’m sure that McMillan and Jordan were both excellent defenders, does it really pass the smell test to say that either was more valuable on defense than Olajuwon was in any of his best seasons?

Meyers himself acknowledges this weakness of DBPM. He writes:

“Box Plus/Minus is a very good offensive metric, but it struggles some with defense. As mentioned before, when all you have is a box score, you cannot estimate defense very well. Not including minutes per game in the regression also hampers the accuracy of the defensive estimates. In other words–take DBPM with a spoonful of salt.”

Again, another great explainer: https://basketballstat.home.blog/2019/08/27/box-plus-minus-bpm/

]]>Thanks, I find his work to be fascinating overall.

anon,

“How do you get “perimeter defense” info for a player out of the data in a box score?”

[**Key point**: DBPM is simply BPM – OBPM. There is no explicit calculation for DBPM. I’ll come back to this point in a bit.]

To answer your question, we have to take a quick look at where BPM came from. The starting point was Simple Plus-Minus, i.e. the difference in the score while a player is on the floor. (Ex: Nikola Jokic starts a game, then comes out after the 1st quarter when the Nuggets are up by 6. His simple +/- is +6.)

There are two main problems: 1) If your teammates are great (2017 GSW), the fifth guy could be a scrub and still look great; and 2) It doesn’t take into account the quality of the opposing players (e.g. bench guys vs. starters, weak/strong teams).

So to correct for this and other factors (garbage time, etc), a guy named Dan Rosenbaum came up with the idea of “stints” — a period of play in which there are no substitutions for either team — and used linear regression to figure out how much each player contributed to the change in score (i.e. “margin”) during each stint (the initial work looked at 60,000 stints over two years).

In the following equation, home players (P1-P5) are assigned a value of pos. 1, and away players (P6-P10) are assigned -1. b0 is the y-int (home court advantage, roughly 3.5 pts/100 poss). Rosenbaum used linear regression to calculate the value of the coefficients (b1-b10) to estimate the partial contribution of each player to the changes in margin (per 100 poss).

Margin = b₀ + b₁P₁ + b₂P₂ + b₃P₃ + b₄P₄ + b₅P₅ + b₆P₆ + b₇P₇ + b₈P₈ + b₉P₉ + b₁₀P₁₀

This and other adjustments corrected some of the flaws of simple +/-, giving birth to Adj +/- (APM). However, there were still problems due to outsized coefficients for some players with limited playing time. A new metric, Regularized Adj P-M (RAPM), was devised which uses ridge regression to correct for these outliers and improve APM’s predictive power.

Notice that box stats haven’t entered the picture at all. A key benefit of RAPM is that we can finally start to get a hint of how players can influence changes in team scores in ways that are **not** reflected in box stats (e.g. screen setting or Draymond-style def quarterbacking).

More here (a great explainer): https://basketballstat.home.blog/2019/08/14/regularized-adjusted-plus-minus-rapm/

]]>Now I’m very confused. How do you get “perimeter defense” info for a player out of the data in a box score? Here’s what it says in the “about BPM” thing:

“It is based only on the information in the traditional basketball box score … BPM uses a player’s box score information, position, and the team’s overall performance to estimate the player’s contribution in points above league average per 100 possessions played.”

]]>“There is indirect evidence for a player when his **teammates** leave the lineup. Let’s say we wanted to know how much Scottie Pippen contributed to the Bulls +9 point-differential in the early ’90’s. In 1994, when Michael Jordan left the Bulls, we could infer something about **Pippen** based on the change caused by Jordan’s absence. How?

If Jordan left and the team remained a +9 team, then it would be fairly safe to infer that Jordan was not the reason the Bulls were +9…which tells us that key remaining players on the team, like Pippen and Horace Grant, were the ones responsible for the large point differential.

Conversely, if Jordan left the Bulls and they unraveled into a -5 team, not only does that say amazing things about MJ but it would mean that the players left behind, like Pippen and Grant, weren’t integral to that +9 differential…. So while Bill Russell didn’t miss as much time as Jerry West, there’s a bevy of evidence about Russell left by his teammates and all of the time that they miss over the years.”

https://backpicks.com/2016/09/06/ii-historical-impact-introducing-wowyr/

Anyway, I think the most important thing about these kinds of lists isn’t the exact ranking — I mean all of these guys are definitely all-time greats. It’s just interesting as a fan to learn the specifics of **why** these guys were so good in their own particular way (e.g. I was blown away by Walton hitting cutters and KG’s help defense) and even what their weaknesses were.

]]>1. Relative to one’s era

2. Picking a team to play for your life in a best-of-7 (under modern rules — that’s usually what most ppl mean)

3. What if? i.e. “How would the greats from the past do today?” (with modern nutrition, training, and skill development)

The first, a purely relative ranking, is the most important b/c (1) it ensures that the great players of the past get their due and (2) it is by far the most tractable problem since it avoids the difficulties of inter-era comparisons.

Lists #2 and #3 seem similar, but they’re really quite different. For List #2, you’d be crazy to pick anyone who retired before 1980, and your list would be heavily weighted towards more recent players since they are “proven commodities” who have risen to the top of the deepest talent pools.

List #3 seems to be the most popular in actual barroom discussions, but it really is little more than wild speculation. How could we possibly project how players from other eras would do in today’s NBA if they were born in 1995? I mean, teams still make first round draft mistakes all the time in spite of access to more scouting data and tools than ever.

So Ben’s approach sensibly focuses on the first, trying to estimate how much each player would impact a random team’s chances of winning a championship **in his own era**. (E.g. Jordan, might have about a 40% chance of winning a title if placed on an avg team during his career.) The only inter-era comparison is determining which players had the greatest “Championship Odds over Replacement Player” effect.

https://fansided.com/2017/10/19/nylon-calculus-championship-odds-short-lived-megastars-corp/

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