True Shooting Percentage
I was listening to yet another excellent Bill Simmons podcast and when he talked about Stephen Curry having a 70% True Shooting Percentage he mentioned that he doesn't really understand what True Shooting Percentage is, which somewhat surprised me because he's a fairly smart guy. True Shooting Percentage is listed on espn.com under Hollinger Statistics, and unlike other stats such as value added or player efficiency rating which are somewhat mysterious statistics

^{1}, true shooting percentage is a very intuitive stat that has or at least should have a very satisfying mathematical foundation. Bill Simmons probably won't read this, but I thought I'd give my interpretation of what True Shooting Percentage is, or at least should be. ESPN defines True Shooting Percentage as "what a player's shooting percentage would be if we accounted for free throws and 3-pointers", which is exactly what the name implies. Basically, if someone shoots 3/5 on 2-pointers they will score 6 points. If another player shoots 2/5 on 3-pointers they will also score 6 points. And if yet another player shoots 6/10 on free throws they will also score 6 points. The first person had a 60% field goal percentage, the second person a 40% field goal percentage, and the third person a 0% field goal percentage since they only took free throws, but a 60% free throw percentage. Ideally True Shooting Percentage would make these three players equivalent and the formula would be (2-pointers made + 1.5*3-pointers made + free throws made)/(2-point attempts + 3-point attempts + free throw attempts). The formula listed on espn.com for True Shooting Percentage is wrong, which may be the source of Bill Simmons' confusion. It lists True Shooting Percentage as total points/(FGA+(.44*FTA)). It is very easy to see this is wrong because if someone scores 10 points on 5 attempts they would have a 200% True Shooting Percentage, which is double what is should be. Plugging in Stephen Curry's numbers into this formula gives a number double what ESPN lists it as, so clearly ESPN isn't using this formula. Wikipedia lists True Shooting Percentage as total points/2*(FGA+(.44*FTA)), so ESPN just forgot to list the 2. That typo however does not explain the WTF .44 in the formula, which is not a typo. Where does that .44 come from? The answer is likely from someone's ass, but as we will see there is an argument to be made to do something special to free throws. First of all, the ESPN formula and my formula are not that different. After taking into account the typo and doing some simple math, the ESPN formula can be written as (2-pointers made + 1.5*3-pointers made + .5*free throws made)/(2-point attempts + 3-point attempts + .44*free throw attempts), which gives a little more weight to free throws than my formula. So why would someone want to adjust free throws in this formula? Well imagine there is a technical foul and someone is chosen to shoot it. That free throw is a gravy free throw. The player did not use up a possession to get that free throw, so if they miss it should it really affect their True Shooting Percentage? Similarly, if someone gets an and 1 attempt, should that miss be penalized? Ideally a new stat would be created called gravy free throws and then these would be used to perfectly calculate True Shooting Percentage. Is this what ESPN is trying to do with the .44? Maybe, or maybe they just wanted to make a simple calculation seem more complicated than it actually is. Basketball-reference.com only lists effective field goal percentage, which ignores free throws entirely.^{1. But will get you hired in the Grizzlies' front office.↩}