Although I wasn’t able to attend it, Yonatan Loewenstein apparently gave a talk at a Cosyne workshop about decision-making and related it to NBA players. I was curious to find the paper and while ultimately I could not, I did find that he had a different one that was interesting. One of the most commonly used methods in neuroscience to model learning is reinforcement learning. In reinforcement learning, you learn from the consequences of your actions; intuitively, a reward will act to reinforce a behavior. Although inspired by psychological theories of learning, it has gained support in neuroscience from the patterns of activity of dopamine cells which provide exactly the learning error signal you’d expect.
Basketball is a dynamic game where players are constantly evaluating their chance of a shot, and whether they should pass it and make a 2 or 3 point field goal attempt (FGA). One of the most contentious issues in basketball (statistics) is the ‘hot hand effect’: if you’ve successfully made a 3 point shot, are you more likely to make the next one? Maybe it’s just one of those nights where you are on, your form is perfect and every shot will sink. Problem is, statistically speaking there is no evidence for it.
But the players sure think that it exists! Now look at the figure to the right. Here, the blue line represents how likely a player is to shoot a 3 point field goal if their last (0, 1, 2, 3) shots were made 3 point field goals. In general, they shoot 3 pointers about ~40% of the time. If they made their last 3 pointer, they now have a ~50% of shooting a 3 pointer on their next attempt. And if they make that one? They have a 55% chance of shooting a 3 pointer. Similarly, the red line follows the probability of shooting a 3 pointer if you last few shots were missed 3 pointers.
Okay, so basketball players believe in the hot hand, and act like it. Why do they act like it? If we take our model of the learning process, Reinforcement Learning, and apply it to the data, we actually get a great prediction of how likely a player is to shoot a 3 pointer! Our internal machinery that we use for learning the value of an action is also a good model for learning the value of taking a 3 pointer – and shooting a 3 pointer will only reinforce the idea that the next shot for a 3 pointer (get it?)!
Alas, this type of behavior does not help anything; a player who makes a 3 pointer is 6% less likely to make his next his 3 than if he had missed his last 3 pointer. In fact, if you take our Reinforcement Learning model and see how each player behaves, we can estimate how susceptible that player is to learning. Some players won’t change how they shoot (unsusceptible) and some players will learn a lot from each shot, with the history of made and missed shots having huge effects on how likely they are to shoot another 3. And believe it or not, the players that are least susceptible to learning are the ones who get the most points out of each 3 point shot. Unless you are Antoine Walker, then you will just shoot a lot of bad 3 pointers for the hell of it.
Finding non-existent ‘hidden patterns’ in noise is a natural human phenomenon and is a natural outgrowth of learning from past experiences. So tell your parents! Learning: not always good for you.
Neiman, T., & Loewenstein, Y. (2011). Reinforcement learning in professional basketball players Nature Communications, 2 DOI: 10.1038/ncomms1580