That’s why they play the game

That claim of “statistical” predestination is confused.* We know the odds of a coin-toss or of the roll of a die before we ever pick them up. Those things are set, predetermined. But it was not preordained by the universe that Shaquille O’Neal would be a .527 free-throw shooter for his career. It’s weirdly mystical to speak of statistics that measure the outcome of an athlete’s performance over time as though they were that athlete’s “scientific” destiny.

And it’s ironic that such mysticism comes from those desperate to dismiss talk of being “in the zone” because they see that as uncomfortably mystical-sounding.

This is the second commentary of this sort I’ve seen over the weekend; unfortunately I can’t recall the first one or the article that precipitated it, but this one will suffice.

The sentiment is correct as far as it goes: anyone who is saying that statistics pre-ordain performance is wrong. But that’s a straw-man for the scientific discussion — it’s not the actual argument. I think that it’s obvious that there are parameters that affect one’s performance when one goes out sportsing. The analysis going into the phenomenon of “the streak” or being “in the zone” is not claiming otherwise, and there’s a fundamental misunderstanding of what the analysis is claiming that is in play here.

As an aside, I think it’s a similar misunderstanding that has developed with the so-called 10,000 hour rule: that you’ll become an expert when and only if you put 10,000 hours of work into your craft. Which is not to say that you’ll become world-class if you do so, but I’ve seen articles where it’s implied that the only thing standing between you and the pro sportsing circuit is the required investment of time. Bollocks. There’s innate talent for the craft as well, and the quality of your preparation, and perhaps more to it. A similar straw man has been constructed over this statistical analysis, via the retelling in a version of the “whisper game”. Purple monkey dishwasher.

The basic premise is that athletes get into “the zone” where the ball seems bigger and/or slower or perhaps the opposite, depending on what sport is being played, and the athlete does really well. Great. But we’re scientists, and we want a model of this, and the model here (for basketball, where the original study was done, by Gilo, Vallone and Tversky) is that when a player hits several shots in a row — they are “hot” — their odds of hitting shots is higher. That is, a player who hits e.g. eight shots in a row, does so because s/he is on a streak, and thus a higher shooting percentage is expected. In other words, the streaks should be deviations from a normal distribution.

The statistics, however, say otherwise. The streaks are completely consistent with a normal distribution — hitting those eight in a row is an expected consequence of some underlying probability of success and a large number of attempts. The model, which predicted a deviation, is wrong. There is no evidence of streaks.

The model isn’t rejected because of mysticism. It’s rejected because the prediction it makes is not observed, and if a model disagrees with the experiment, it’s wrong. Here’s where the subtlety comes in. What the results don’t say is that there is no such thing as “being hot”. It says that this model of streaks is wrong.

One also has to look at what wasn’t measured. The study was only an analysis of hitting shots based on making the previous shot (which is very much like the Gambler’s fallacy) but no analysis of a player that goes e.g. 16-for-20, or any other effects that might make the results end up being random. Far from being mysticism, these results just tell is where we might look next and where not to look next. However, we also know that any working model will have to give results that are consistent with the randomness we observe. We have a tendency to see patterns in randomness. This might have the same result as a lucky pair of socks — no real effect, but plenty of confirmation bias and apophenia.

The issue isn’t whether Shaq was somehow “predestined” by his 52.7% free-throw accuracy. But that number isn’t the real issue — the reality is that Shaq was a mediocre free-throw shooter, and the number reflects that. The question is whether Shaq performed differently from a player whose talent and preparation made him a free-throw shooter with ~50% chance of hitting each shot, and that answer (thus far) is no.