Calculating NBA shooting consistency What would be the proper way to evaluate/determine an NBA player's 3-point shooting consistency? For instance, I have a player that shoots 37% from 3-point range and takes 200 attempts all year.
I was considering taking the rolling average 3-point% of an arbitrary number of shots (say 20). Then using those averages to determine the standard deviation from the 37% mean. Using a rolling sample size of 20 shots only allows for a precision of 5% in shooting percentage, but I'm concerned that using too many shots won't reveal the inconsistencies in performance.
Is there a better approach to determine consistency?
 A: As another user stated in the comments above, a runs test is the way to analyze your shooting data.  It tests the hypothesis that the elements of the sequence are mutually independent.  If the hypothesis is rejected, then you could say that the player's 3-point shooting is inconsistent.
I would like to also point you towards this article since it's directly related to your analysis.
A: I think a runs test is a good idea. To me, by analysing the data in "chunks," your intention is to create a proxy for or control for "hot hands" in player consistency. There's a huge literature on this phenomenon out there. One of the best papers was discussed by Gelman on his blog back in July 2015. The title of his post was, "Hey-guess what? There really is a hot hand!" (http://andrewgelman.com/2015/07/09/hey-guess-what-there-really-is-a-hot-hand/).  The paper Gelman reports on is a rebuttal to much of the previous literature insofar as it details the errors made by previous analyses of the hot hands phenomenon. The earlier work focused on overall as opposed to conditional probabilities. This paper posits a new sequential probability model (see the link for a reference to the paper). 
One good metric of consistency which should control for differences in, e.g., number of shots taken, is the coefficient of variation. The CV is a dimensionless, scale invariant measure of variability and is calculated by dividing the std deviation by the mean. The problem it attempts to solve is that std deviations are expressed in the scale of the unit under measure, i.e., it is not scale invariant. This means that metrics with high average values will also tend to have higher std deviations than metrics with low average values. So, for instance, due to differences in their average values, measures of the variability in diastolic and systolic blood pressure are not directly comparable. By taking the CV, their variability becomes comparable. The same thing holds for many other metrics such as stock prices, online metrics such as the number of impressions or hits to a web page, and so on.
Thus, the CV can be calculated for many metrics and scale types, excluding categorical information and measures with negative values.
