The law of small numbers is well neigh inescapable, in any small sample expect regression to the long term mean. In basketball social media circles this gets referenced as 'small sample size theater,' as a winking acknowledgement of the overwhelming urge to make too large conclusions from a couple of games even while doing exactly that.

It's most obvious in basketball in three point shooting, that most variable offensive statistic.

For draft purposes that means that anytime we reference a shooter's three point percentage we have to keep in mind their number of attempts as well. Simply, the more attempts they take the more sure we can be of their true talent shooting the three.

In addition, looking at the NBA I have that consistently more attempts at the three is a sign, in and of itself, that the player can make threes. I also, by the way, found the same thing for mid-range shots.

With that in mind I looked at the attempts and efficiency of draft prospects, and plotted a trend line that gives a very rough idea of the regression to expect. The more attempts a player has the closer their long term mean is to their current percentage and the higher the expected mean they're regressing towards. (1)

The visualization below is the number of three point attempts (approximately, actually, as it's using pace adjusted numbers) and the accuracy of prospects in this year's draft for any player with at least 10 attempts.

- Expect regression from Noah Vonleh and Kyle Anderson.
- Doug McDermott, Nik Stauskas and Shabazz Napier can shoot. The issues with their games is in other areas though.
- Don't pay any attention to Bogdan Bogdanovich's field goal percentage, or anyone else's, he took alot of threes. Many of them as pull ups due to his ball handling duties with Partizan.
- I included age as a color coding because in addition to regressing, young players develop and the jump shot is one of the more developable skills through gym work and reps. (Though not easily and not always).

1. Regression towards the mean does not imply regression to the population mean. Based on the variance of three point shooting in the NBA I estimated that a decent formula for estimating a player's 'true' three point shooting prowess is their current average times actual attempts plus their expected mean times 150 attempts, then divided by actual attempts plus 150. So a player shooting 40% on 150 attempts with an expected regression to 34% would, have an expected long term mean of 37%.

## Comments

You can follow this conversation by subscribing to the comment feed for this post.