The Wall Street Journal is helping Leonard Mlodinow tout his book The Drunkardâ€™s Walk: How Randomness Rules Our Lives. Among other things, Mlodinow, like academics Tversky, Kahneman, and Gilovich before him, wants to show that streaks in games like basketball don’t exist. Or, rather, they do exist, but they can be “explained by randomness.”
Listen: randomness can’t explain anything.
Statisticians imagine—I choose this word carefully—a basketball player has an ineffable probability of making a free throw, and they try to guess the probability’s value through modeling. Suppose a guess is 80% for a particular player and then suppose our player has just made his last 10 shots. A fan might say our man has a hot hand. Mlodinow:
If a person tossing a coin weighted to land on heads 80% of the time produces a streak of 10 heads in a row, few people would see that as a sign of increased skill. Yet when an 80% free throw shooter in the NBA has that level of success people have a hard time accepting that it isn’t. [Tversky and others] showed that despite appearances, the “hot hand” is a mirage. Such hot and cold streaks are identical to those you would obtain from a properly weighted coin.
This statement is confused. Each time a “properly weighted coin” is tossed something makes it fall heads or tails, some physical cause. “Randomness” does not make the coin choose a side. Spin and momentum cause it to land on one side or the other. There is nothing “random” in a coin toss: there is only physics. If you knew the amount of force propelling the coin upwards, and the amount of spin imparted, you can predict with certainty the outcome of the flip. (Persi Diaconis and Ed Jaynes—both non-traditional statisticians—have written multiple papers on this subject.)
“Randomness” is not a physical property; it does not exist inside the coin. Mlodinow acknowledges this in the words “weighted coin” used to describe his thought experiment. He is aware implicitly that modifying a physical property of a coin like the weight changes whether it shows head or tail. But he fails to realize that there is no difference in philosophy between changing the weight or modifying the spin or the momentum. Like Nelson reading the signal flags, he has turned a blind eye to the physics and has taken refuge in “randomness” to explain how the coin behaves.
Similarly, something, some physical—and biological and mental—process is causing the basketball player to make his shot. Again, the spin, the momentum, the aim, and the mental pathways that give rise to those properties are what determines whether the shot falls through the hoop or misses.
Our man has made his last 10 and is setting up for the 11th. Now the fans behind the basket distract him, or maybe he starts thinking too much about the shot, or there is excess sweat on his finger, or whatever, but he misses his shot and his streak ends. Randomness does not explain why the streak ends: physics and biology do.
Random means unknown and nothing more. Before the player takes the shot, or Mlodinow flips his weighted coin, we do not know what the outcome will be because we do not know what the values of the physical properties that determine the outcome are: it is these properties that change from shot to shot and from flip to flip that cause the different endings. If we did know the physics—like we can if we practice with coins—we can predict the outcome. That is, the outcome becomes certain, or known, and is therefore not random.
Our knowledge any outcome depends on what information we condition on. What might be random to you might not be random to me if I have different information than you. For example, right now my cell phone is either in my left- or right-hand pocket. To you, the outcome (finding out which pocket), is random because your conditional information consists solely of the knowledge that it might be in one or other pocket. The information I condition on allows me to know with certainty the outcome.
Same thing in basketball: if we knew what amount of force a player uses etc. we can predict whether his shot will go in. But that sort of information is hard to measure, so we look for proxies, like statistical models of the player’s past performance. Conditional only on those models, we can say “There is an 80% chance the next shot will go in.”
If the 11th shot is sunk, our man’s streak continues. The mental state of the player certainly played a part in that shot and so did his “hot hands.” Because we cannot predict who will have a hot hand or when, does not mean that hot-hand streaks do not exist. We should not mistake our models for reality.