The Fallacy of the Hot Hand Fallacy

In sports there's this thing called the "hot hand." This is where a player gets on a roll and feels he can do no wrong. The Mets' Daniel Murphy is the latest person to be pegged as having a hot hand, hitting a bunch of home runs recently, after having a recent slump and being rather average for most of his career.

Statisticians claim there's no such thing as as a "hot hand," calling it a fallacious belief:

The "hot-hand fallacy" (also known as the "hot hand phenomenon" or "hot hand") is the fallacious belief that a person who has experienced success with a random event has a greater chance of further success in additional attempts. The concept has been applied to gambling and sports, such as basketball.

With random events, such as tossing coins and rolling dice, each toss or roll is independent of all others. If you roll two six-sided die the chance of a rolling a 7 is 16.7% every time, even if you just rolled a 7 the time before. If you roll 10 7s in row, the chance of rolling a 7 is still only 16.7% the 11th time.

In gambling statistical fallacies take two forms: first is the idea that if you're losing, you're eventually "due" a success. Second is the idea that if you're on a roll, your odds of success are increased. Both are wrong in games of chance like craps and roulette, where each event is random and independent of other events.

Some studies have indicated that success in sports like baseball and basketball has the same characteristic of randomness. This has lead statisticians to believe that one play has no bearing on the probability of success on the next play. That is, if a batter has a record of hitting home runs 16.7% of the time and hits a home run in the first inning, he still only has a 16.7% chance of hitting a home in third inning.

But plays in sports are not random and independent events. They are dependent on the individuals and conditions involved. During a single game, it's the same day, the same stadium, the same batter, the same pitcher, the same defensive lineup, the same weather conditions. Some days batters won't get a good night's sleep. Sometimes the pitcher had and argument with his wife and his mind's not really on the game. On a particular day, a player can play better than he ever has in his life, and his chances of success are better than his career average that whole day.

Thus, a batter hitting a ball is not a totally random independent event, like rolling dice. Many of the conditions are under the batter's or the pitcher's control.

For example, the pitcher can guarantee the batter won't get a home run by walking him intentionally. (This comes at a cost, of course.)

Similarly, if you take a professional baseball player and put him on the plate facing a 9-year-old little league pitcher, he would probably hit a home run every time the kid put the ball over the plate.

Thus, hitting a baseball is not totally random.

The "randomness" in sports comes from two sources: external and internal. External sources of randomness arise from things like air pressure, wind and lighting that may affect the flight of the ball or the player's perception of it. Internal sources of randomness arise from human beings' inability to repeat tasks identically: a pitcher cannot throw a ball at exactly the same speed along the same trajectory every time.

Finally, the player's mental state has a huge impact on performance. People who are wracked with doubts don't usually perform very well. Success breeds success by inspiring confidence and eliminating hesitation and second guessing oneself.

Having said all that, however, any hot hand effects are going to be fairly small, because human beings cannot repeatedly execute physical actions with extreme precision.

The epitome of randomness is flipping a coin. But this is random only because humans cannot consistently apply all the same forces to a coin each time it is flipped, or even flip it from the same height and location.

But if we built a device that flipped a coin in a vacuum, applying exactly the same forces each time with extremely high precision, we could increase the probability of getting the same result by reducing the variation in each iteration. We could potentially build a machine that could make a coin come up heads 9 out of 10 times, or 99 out of 100 times. (100% certainty is unlikely due to quantum effects.)

In gambling the hot hand fallacy still applies to games of chance like roulette and craps (but not necessarily to poker or blackjack, where skill matters).

But in sports where human is pitted against human and most of the factors are controlled by the actors, it is a fallacy to think that the outcome is completely random.