Rare events are really common

In a recent Econlog post, I pointed out that the “inverted yield curve” predictor of recessions had failed this time around. (Recessions are supposed to occur within a year of the inversion.) Here I’ll discuss one reason why this sort of indicator is less useful than it might seem at first glance.

This tweet caught my eye:

That makes this seem like a very rare occurrence. And in a sense it is. But it’s also true that this sort of very rare occurrence is incredibly common. If you follow sports, you’ll see many similar tweets pointing out bizarre data points that don’t occur very often. It’s easy to do, as there are so many different ways to slice and dice the data in order to find odd patterns. Indeed, this very game featured another extremely weird fact, unrelated to the one cited above:

Luka and Kyrie 1-14 from 3. Mavs win by 38.

Someone should compute the number of times the two star players shoot so poorly from 3 and their team wins by 38!

I believe that people in fields like finance and economics are far too impressed by certain historical correlations. When you have a near infinite number of data points to consider, it’s not hard to find some truly unusual coincidences. Indeed, this fact probably underlies much of the distrust of the EMH. “Among America’s 330 million citizens, I spotted one person that made an unusually long string of successful investment decisions! A guy named Warren.”

Good for you.

PS. Many of the odd data points in basketball take the following form:

“First time in 26 years that a player had at least X points, Y rebounds and Z assists in 7 consecutive games. If that’s not enough, add steals and blocks to narrow the field even further. Or make it seven consecutive road games. Or make it “averaged” this many points, etc., over various time frames.

PPS. The simpler the statistic, the less likely it is due to data mining. Thus fans intuitively know that the best sports records involve a single data point for a single game (Wilt’s 100), or perhaps for a single career (Lebron’s scoring total.) Occam’s Razor for sports records.



20 Responses to “Rare events are really common”

  1. Gravatar of Sara Sara
    17. June 2024 at 16:43

    1. Assymetric information is all that exists. The entire free market revolves around human action: i.e, the whims, impulses, passions, and esoteric knowledge of individuals.

    2. Those impulses are not always rational. You hardly know anything about the companies you invest in. You don’t know their suppliers, where they get raw materials, how many employees they need to do a job, their costs of production, whether their public balance sheeets are accurate, or anything else for that matter. You invest predominately on faith, which is highly speculative.

    3. Buffet has access to information you don’t have. He can call the CEO’s of any company, and receive tours of that company. That doesn’t magically self correct. You will never have the information he has.

    4. Emperical data, such as Momentum effects, refutes your claim. It’s like the scientists who didn’t want to believe in the Big Bang, because a Big Bang presupposes a beginning, which opens the door to a creator. These hardcore, activist athiests, hung on desperately to their ‘steady state theory” even after the emperical data was presented for forty years: i.e, redshifting, cosmic background radiation, etc. To this day, these fools continue to make bizarre claims that redshifting isn’t real as a last gasp for their pathetic steady state theory. EMH proposals are the same thing. No matter how much data behavior economists present, you cling to it desperately and pathetically.

    5. People invest for psychological reasons; they believe in the person behind it, or the mission of the company which has no bearing on the data. And it doesn’t logically follow that people adequately understand information.

    6. Most people who push the EMH model, do so because they want to use that to justify a new planned economy by AI.

  2. Gravatar of Steve Randy Waldman Steve Randy Waldman
    17. June 2024 at 17:14

    I have a little trick I like, invented to get my kid thinking about probability.

    Before beginning an session of poker, shuffle the deck and deal out one hand. Whatever that had is, note it down, and make it the top hand, better than a royal straight flush.

    Of course, that hand is less likely than a royal straight flush. Even though you just dealt it.

    There is nothing special about a royal straight flush.
    Everything that actually happens is terribly unlikely. The state space is full of impossibly infinitessimal lotteries, yet one becomes a new winner every instance. What’s rare is not rare events, but the intersection of rare events with the infinitessimal slivers of the state-space in which we have meaningful stakes in such events. For better (we don’t usually just evaporate!) and for worse (we don’t usually win the lottery).

  3. Gravatar of ssumner ssumner
    17. June 2024 at 17:53

    Sara, “Most people who push the EMH model, do so because they want to use that to justify a new planned economy by AI.”


    Steve, That’s a good example.

  4. Gravatar of Kevin Erdmann Kevin Erdmann
    17. June 2024 at 18:35

    I still consider the inverted yield curve to be a very useful cyclical signal. There was marginal inversion before covid, but JPow! was potentially reacting aggressively enough to avoid recession. It’s a shame we didn’t get to see that monetary cycle play out.
    The yield curve since then has had unusual nonlinearities because of transitory inflation. I consider the inverted curve to be very important, but I have not ever considered the post-2020 curve to actually be inverted.

  5. Gravatar of Ricardo Ricardo
    17. June 2024 at 21:19

    I think we’re definetly in a recession.

    Half the country cannot even afford their grocery bill.

    Btw, here are Sumner’s libtards slapping a 12 year old for holding the American flag.


    Apparently, if you show pride in the American flag, these libtards get triggered.

    I’ve never owned a big flag with a pole. But now I have a good reason to buy one. I’m going place them all outside my house and car just to enrage the Sumner libtards. In fact, we should organize flotilla’s with a big stereo system that blasts patriotic songs just to keep the snobby woke libtards off our beach.

  6. Gravatar of Robert Simmons Robert Simmons
    18. June 2024 at 04:49

    Not a perfect recession indicator, but Y/Y NGDP has slowed by 5pp since the inversion started. Normally that would bring a recession in the US, but that just put us at 5%, plus at the same time pandemic-related supply issues continue to improve. Do we have good data on yield curves and growth during and after previous pandemics?

  7. Gravatar of Todd Ramsey Todd Ramsey
    18. June 2024 at 05:47

    What if a contrived statistic starts with a thesis, say for example “investors who buy stocks with low P/E ratios that have good prospects for continued success”, and there are several individuals who have success using that thesis? That’s different from starting with the statistic and working backward.

    Klarman, Schloss, Greenblatt, Burry, Munger, Graham, and some guy named Warren, to name a few.

    I understand that seven out of 330 million doesn’t provide anything close to statistical proof. But I also don’t have access to the names of any successful investors who are not famous.

    “Our results suggest that skillful individual investors exploit market inefficiencies to earn abnormal profits, above and beyond any profits available from well-known strategies based upon size, value, or momentum.” == http://www.bus.umich.edu/pdf/mitsui/nttdocs/coval-shumway2.pdf

    Even Fama and French amended their model to include “small beats big” and “value beats growth”.

    I’m truly grateful for your contributions, Scott. But I do think you have closed your mind to the possibility that the strongest form of EMH does not hold.

  8. Gravatar of ssumner ssumner
    18. June 2024 at 08:14

    Which of Ricardo’s first two sentences are more mindbogglingly stupid? Decisions, decisions . . .

    Robert, The last big pandemic was the 1918-19 Spanish flue, which occurred during the WWI inflation and was followed by a delation. I suspect the yield curve did invert at that time (say around 1920.)

    Todd, I agree that the successful investors had reasons for their investments, as did 100s of millions of less successful investors.

    You said:

    “Even Fama and French amended their model to include “small beats big” and “value beats growth”.”

    Did you follow their advice and stay away from the big tech growth companies like Google and Apple and Facebook and Microsoft and Nvidia?

  9. Gravatar of Robert Simmons Robert Simmons
    18. June 2024 at 08:30

    That’s what I’m asking. I suspect the same, but do we have the data?

  10. Gravatar of Tacticus Tacticus
    19. June 2024 at 05:50

    “I believe that people in fields like finance and economics are far too impressed by certain historical correlations.”

    Oh, absolutely. I always urge my clients to remember that ‘past performance is no guarantee of future results’ is not just boilerplate.

    Although I think that is true beyond finance and economics. It seems to be a pretty universal human trait.

  11. Gravatar of Tacticus Tacticus
    19. June 2024 at 05:56

    Todd, ‘investors who buy stocks with low P/E ratios that have good prospects for continued success’ hasn’t really played out very well the past ~20 odd years. Perhaps it was only true at a certain point in time?

  12. Gravatar of Todd Ramsey Todd Ramsey
    19. June 2024 at 06:20

    Scott, my point is that Fama and French walked back their original position on EMH. You didn’t really respond to that; what I did isn’t relevant.

    But since you asked, I did purchase 3 of those stocks when their valuations seemed reasonable. I purchased Microsoft in October 2008 because they had virtually no debt and the P/E was low. I purchased AAPL in 2013 and again around 2016 when the P/E was around 12, which is low for a growth company. I purchased Google in March 2020 when the P/E fell under 20 during Covid stock panic; 20 seemed reasonable since (pre-GPT) they appeared to have a self-reinforcing monopoly. I have never owned Nvidia or Meta.

    I sold 75% of my Apple in the 180s because I feared it was overvalued. That was a bad call since it’s now in the 210s.

    Again, I have utmost respect for you and believe your Macro work will change the world. I am tremendously grateful for all you do. I’m just offering some evidence that perhaps EMH strong form doesn’t consistently hold.

    “in any sort of a contest – financial, mental, or physical – it’s an enormous advantage to have opponents who have been taught that it’s useless to even try.” – Warren Buffett

  13. Gravatar of ssumner ssumner
    19. June 2024 at 09:49

    Robert, I’m too lazy to search the history books, but I seem to recall short rates peaking at about 7% in 1920, which was probably above longer yields.

    Todd, My joke was the point Tacticus made, that F-F “refutation”: has not held up in recent decades.

    I don’t find concepts like “strong form” to be very useful. All economic theories are false, in the sense of not being completely true. They are all approximations of reality. Even supply and demand, which requires perfect competition.

  14. Gravatar of Student Student
    20. June 2024 at 06:27

    I don’t have access to the necessary data to compute this empirically, but on game 4… Making some rough approximations (a std dev of 0.1 around ones career 3 point shooting percentage in any given game and that these follow a normal distribution are the important prior assumption) and only looking at the joint prob for the actual 3 point shooting percentages that occurred in game 4.

    # Career 3-point shooting percentages
    luka_3p_percentage = 0.391 # Luka Doncic’s career 3-point percentage
    kyrie_3p_percentage = 0.393 # Kyrie Irving’s career 3-point percentage
    team_avg_3p_percentage = 0.275 # Calculated career 3-point shooting average for the rest of the team (played more 10 min game 4)
    team_actual_3p_percentage = 0.6087 # Actual shooting percentage in the game (15/37 minus irving/luka 1/14).

    # Prior Assumptions – Standard deviation (this a tough assumption, but i dont think that unreasonable.)
    # Based off: Julius Randall career 10 per moving average: https://www.thestrick.land/strick/a-study-on-3-point-shooting-should-we-change-how-we-contextualize-3-point-defense-in-nba-advanced-stats-analytics
    std_dev = 0.1
    team_std_dev = 0.1

    # Calculate the probability of Luka and Kyrie shooting less than 10% in a game
    luka_prob = stats.norm(luka_3p_percentage, std_dev).cdf(0.1)
    kyrie_prob = stats.norm(kyrie_3p_percentage, std_dev).cdf(0.1)

    # Calculate the probability of the rest of the team shooting better than their average and achieving 60.87%
    team_prob = 1 – stats.norm(team_avg_3p_percentage, team_std_dev).cdf(team_actual_3p_percentage)

    # Calculate the joint probability
    joint_prob = luka_prob * kyrie_prob * team_prob

    – prob of luka shooting less than 10% from 3 = 0.18%
    – prob of irving shooting less than 10% from 3 = 0.17%
    – prob of rest team shooting an avg of 60.87% = 0.042%

    Joint probability = 1.3 in a billion.

    If we assume an stddev of 0.15 on shooting percentages (one stddev is .25 to .55 around an bag of 0.4), the probs are still small.

    – prob of luka shooting less than 10% from 3 = 2.6%
    – prob of irving shooting less than 10% from 3 = 2.5%
    – prob of rest team shooting an avg of 60.87% = 1.3%

    Joint probability = 8.7 in a million.

    This was indeed a rare event.

  15. Gravatar of Todd Ramsey Todd Ramsey
    20. June 2024 at 07:06

    Scott and Tacticus, I think it’s more likely than not you’re right about EMH.

    I think I keep poking at this because I want smart people to challenge my beliefs. Thanks for your help.

  16. Gravatar of ssumner ssumner
    20. June 2024 at 08:47

    Thanks student.

  17. Gravatar of Student Student
    20. June 2024 at 09:13

    Oops, I got Lukas career 3 avg wrong. It’s .347 not .391. Which about doubles the probabilities in both sets. But still, very unlikely.

  18. Gravatar of Tacticus Tacticus
    20. June 2024 at 09:58

    Todd Ramsey, it’s unlikely that both Scott and I are right about EMH, as we completely disagree about it!

    As I’ve said elsewhere recently, I think it is at best useless and at worst nonsense.

  19. Gravatar of Todd Ramsey Todd Ramsey
    21. June 2024 at 12:50

    Tacticus, I guess I misinterpreted your comment. Sorry about that.

  20. Gravatar of Tacticus Tacticus
    21. June 2024 at 19:21

    No harm done! I was more amused than anything, as it’s one of the (few?) things Scott and I very much disagree about.

    Like I said, I think the EMH is either useless or incorrect. I was just pointing out that a lot of ‘factors’ do not seem to be universally true. The market is a constantly changing beast!

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