The Hot Hand Fallacy

dice OneSixIn sports and in gambling there is a mistaken belief that a player who is performing better than normal will continue to play well, even if the odds suggest otherwise. This belief is especially strong in basketball. Players who have made several shots in a row are considered to have a “hot hand” and encouraged to continue to shoot – even to attempt very difficult baskets they normally cannot make.

A variety of scientific experiments have documented the fallacy of the hot hand in basketball. A player may make many shots in a row in the short term but his performance will eventually return to his long-term average. The law of statistics is not suspended.

Similarly, when gamblers are on winning streaks, they keep betting or even increase their wagers to take advantage of their good luck. Like in basketball, gamblers ignore statistics and mistakenly believe they are more likely to win a future bet because they have won previous ones.

Ignoring statistics while gambling is referred to as the Monte Carlo fallacy.  The name derives from a 1913 incident in which black came up a record 26 times in a row in roulette.

[There] was a near-panicky rush to bet on red, beginning about the time black had come up a phenomenal fifteen times. In application of the maturity [of the chances] doctrine, players doubled and tripled their stakes. This doctrine leading them to believe after black came up the twentieth time that there was not a chance in a million of another repeat. In the end, the unusual run enriched the casino by millions of francs.

The Monte Carlo gamblers invented all sorts of reasons to explain the long run of black, failing to appreciate that each appearance of black was a random occurrence.

Amusingly, the hot hand and Monte Carlo fallacies can lead to contradictory conclusions.  Imagine a gambler who bets on his lucky number and wins several times in a row. Under the hot hand fallacy, the gambler believes the number is likely to come up again and continues to bet on his lucky number. However, under the Monte Carlo fallacy the same gambler would believe the streak is likely to end and stop betting.

Obviously both predictions cannot be true at the same time but this contradiction is overlooked by most. It’s a reminder to us in our daily lives – emotions often overrule facts.

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8 Responses to The Hot Hand Fallacy

  1. Karlheinz December 16, 2012 at 11:57 pm #

    Interesting, and unexpected. I think I have read about research that supporded the “hot hand” – something about a positive feedback loop between a winning streak in sports and hormone levels that in turn make you better at continuing your winning streak…

    • Karlheinz December 17, 2012 at 12:00 am #

      That’s the research I had remembered. Now what’s the truth? :-)

      http://www.theatlantic.com/health/archive/2012/08/the-hormone-surges-that-keep-winners-winning/260914/

      “Scientists have suggested that there are several elements at play: First, testosterone levels rise when animals face off, producing anabolic effects on muscle mass and hemoglobin, quickening reactions, improving visual acuity, and increasing the animal’s persistence and fearlessness.”

      Should be relevant for Basketball, I guess.

  2. Timo Elliott December 17, 2012 at 6:36 am #

    A side note as pointed out by Nassim Taleb in his book “The Black Swan”: in real life, the odds are rarely known and pure.

    Given human nature, if you do ever find yourself in a casino where the roulette wheel has comes up black twenty-six times in a row, you are probably better off assuming it has been rigged — and should therefore bet on black (or leave)…

  3. Jamie Oswald December 19, 2012 at 7:09 am #

    If you’re really interested in the hot hand, you should check out the TrueHoop blog on ESPN (http://espn.go.com/blog/truehoop/search?query=hot+hand&x=0&y=0) . Those guys have been after it for years.

    To me it’s just one more reason for us to take a HANA box and a junket to the Sloan Sports Conference (http://www.sloansportsconference.com/) in March.

  4. albertgenau December 24, 2012 at 3:17 am #

    Reblogged this on albertgenau.

  5. liv4music December 28, 2012 at 1:02 pm #

    While arguably trivial, as far as statistics is concerned, there are additional variables in sports, which can weigh in on the data, while gambling is pure chance. And when you referred to the concept of averages over longer periods of time, I believe you were referencing The Law of Large Numbers, which basically says that even if you get 8 “heads” out of 10 coin flips, as you increase the sample size, you will get closer and closer to the real probability of 50%, according to the law. Getting back to sports, disproportionately good performance would be advantageous to exploit, because games really only exist in the short-term. Furthermore, there are days for athletes that are just better. As a runner, some days I can shave five minutes of normal running time. Yes, if I averaged my times over a year, they would be about the same, but for the athlete, who aim is steadier, and truer on a particular day, it is in the interest of the player, the coach, and the team to exploit those moments of irregularity.

  6. Michael CIeri (@mikec1121) January 9, 2014 at 10:26 am #

    Very interesting blog post. I think it is an interesting comparison. Going back to the sports theory, I agree with some of the other comments in that sports is a very in the moment occurrence. I am by no means a great golfer, but there are times where I play and I am just on. When this happens I attack pin positions that I normally wouldn’t go near and it is because I have the confidence to do so. Then I can play a week later and I play extremely safe because i am not playing well and do not have the confidence to play with risk. I think when it comes to the hot hand its all about confidence. I have seen basketball players go on insane shooting sprees because they made several baskets in a row and their confidence was at an all time high. I think if a sports player believes they are on fire and doesn’t let negative thoughts enter their mind, for that one game they can be dominant and as many of have said, it has to be used against the competition.

  7. Steve Asche January 9, 2014 at 11:40 am #

    There are many occasions of the “hot hand” in sports which are more than just statistical streaks. You hear of players being “in the zone”. This is a documented phenomena http://breakingmuscle.com/sports-psychology/being-zone-flow-state-athletic-endeavors . Quarterbacks notably experience this and describe the phenomena as the game around them seems to slow down.

    As for gambling, the 26 blacks phenomena, while improbable is still a real possibility and over the millions of spins of the roulette wheel does not affect the 47% probability that black will come up on any discrete spin of the wheel. What it does illustrate, however, is that generally the occurrence of red or black do not generally happen in evenly distributed patterns, but in streaks. Therefore the way to capitalize on the activity is in how you wager. While roulette wouldn’t be my game of choice, the technique does have merit in craps and blackjack.

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