NBA players are creatures of habit

Hello everybody,

this is a follow-up to my last post on 'distancology' – the science of turning all shot charts into one colorful picture. You can find a half-way clean code in my github account. If you run MakeHeatMap.R, you should actually be able to reproduce the result.

One question that one naturally can ask, when comparing the shot distribution of players, is how consistent or reliable those shot distributions are. For example, in my last article I sorted around 200 players into 10 distinguishable groups, using a (vague) cutoff. But I could as well have used 5 or 20 groups. Now, the question regarding reliability is: If you compare year to year, how many players would remain inside the same shot cluster?

Because, if I would label somebody as a 'corner three guy' due to his shot distance distribution in one year, but the next year there is a 50% chance that he's actually a 'typical wing player' guy – that would be pretty useless.¹

Long story short, what I did is to combine the distance distributions for two years – and the result is pretty mindblowing². The following plot works very similar to the one that I used in my previous article. I just changed the column on the left, so that it indicates the effective field goal percentage instead of the shot attempts. This way it is easier for people to be in awe about Stephen Curry. It shows both seasons for every player that had at least 600 attempts (data is from the 3rd of March) during this and the last season – and here it is³:

Before this probable nonsense about 'fouling while leading' gets spread

Hi everyone,

I thought about letting it slip, but then I read this quite from an SI.com article:

"28. The most staggering NBA stat from Sloan? Fouling when winning can increase your chances by 11 percent, according to a paper written by Franklin Kenter of Rice University. The paper shows that fouling near the end of games pretty much makes sense in every situation, whether you’re trailing or leading. When behind, it advises fouling one minute out for every six points you are behind. When leading, it suggests fouling one minute out for every three points you lead."

Side note here: 'The paper shows that fouling...' is a typical case of 'reporter overstates what scientist says'. I guess 'The paper says that their model indicates...' would be more realistic.

But more or less, that's what the paper said. Their reasoning was the following:

"The concept of fouling when ahead may be counterintuitive. However, toward the end of the game, the main goal of the trailing team is to increase the total variance in order to widen the window of possibilities that win the game. One main component in this wider variance is the riskier 3-point shot. The trailing team can limit this variance by fouling. the leading team may give up points, on average, but limit the trailing team to 2 points per possession. This decreases the total variance and, with a sufficient lead, increases the leading team’s chances of winning."

Now, I could go on a very lengthy statistical rant about this. I tried to figure out where they made the mistake in their model, but the paper was too vague in terms of their methods.
The point is this: