Metrics I Love: True Shooting Percentage

True Shooting Percentage (TS%) is one of my favorite metrics in terms of what it says about the performance of a given player in terms of his ability to score. The fundamental principle of True Shooting Percentage at its core is to determine how many points a player can be expected to generate per scoring attempt. It's simple yet extraordinarily effective in ranking players as efficient scorers. But in the sense that this really is a per possession type of metric, the fact that this concept is represented as a percentage has never quite made sense to me, I always felt it should be represented in terms of points per scoring attempt in order to help more easily explain the concept to coaches and the like.

A percentage is, by definition, a rate out of 100% or 1. For example, I missed four days of school out of five this past week - 4/5 = 0.8/1 = 80%. I missed 80% of the school days this past week. The numerator is the number of days of school I missed, and the denominator is the number of possible days of school I could have attended for. It is clear how the numerator and the denominator are linked and it's easy to see what happens when they scale down to a denominator of 1. When we look at the formula for TS%, it's not immediately clear how the numerator relates to the denominator

TS% = Points / (2*(FGA+0.44*FTA))



A player attempting to score will either (a) make the shot (b) miss the shot/have the shot blocked (c) get fouled and score (d) get fouled and not score. So given the probability of any of these scenarios, you can create a weighted average with how many points each scenario generates and the probability of the scenario happening in order to get a number which represents how efficient, so to speak, the player is at generating points per scoring attempt.

And this is essentially what the formula for TS% is getting at - you generate points on three-point field goals, two-point field goals, and free throws. But as a percentage this is confusing to try and extract meaning from - the metric below will rank players the same way as TS% but in a method that generates a point per scoring attempt type of value (for example, Kobe's TS% is 47.5%, meaning he generates 0.95 points per scoring attempt, on average).

Scoring Efficiency = Points / (FGA + 0.44*FTA)

It's a simple and small change - multiply TS% by 2 to get Scoring Efficiency. Because of this, TS% will rank players the exact same way that Scoring Efficiency will, but I believe that explaining the core concept the metric is trying to convey in terms of Scoring Efficiency is much easier when it comes to dealing with coaches and explaining the value of the metric.

For example, if a coach looked at TS% and saw that Brendan Wright at 74.6% was greater than Kyle Korver at 71.3% (as is the case now) he might start to question the value of this metric. Korver, just from the eye test (which is, very truly, important for coaches when it comes to evaluating a metric), is a better pure shooter than Wright - nobody is taking Wright in a game of horse over Korver. But the idea here is that while Korver might shoot better from more spots on the floor, Wright, by virtue of his shooting percentages, where he takes shots, and his ability to draw fouls and then make free throws, generates more points per scoring attempt than Korver.  This indicates that Wright (a) is selective - in that he'll only take shots from spots on the floor in which he knows he can convert with reasonable accuracy (b) shoots well within that selective nature and (c) likely, although you can't see it from this chart, draws fouls well and converts free-throws at a relatively high rate

                         B. Wright Shot Chart                                                   K. Korver Shot Chart

Wright only takes shots he knows he can convert with high accuracy. Korver shoots from more spots on the floor and
converts with relatively high accuracy from most places. When you incorporate ability to draw fouls and hit free throws, Wright (1.49) generates slightly more points per scoring opportunity than Korver (1.43). For comparison's sake, Kobe Bryant generates 0.95 points per scoring attempt

Another way of thinking about this is to look at a player who draws a lot of fouls, and then converts free throws at a high clip. This would be another example of a player who may have a high True Shooting Percentage/Scoring Efficiency, assuming he shoots reasonably well from the field, because the player generates free throws, which for this player due to high accuracy from the free-throw line makes this a likely possession in which he generates two points. If the player can do this consistently, his points generated per scoring attempt will be very high.

Now, all of this said - it's important to note that these are all averages. The Scoring Efficiency of each player is based on all of the shot he gets over the course of the game. It could very well be the case that Kobe, when running a play to get him an open look from his favorite spot on the court, could be more likely to score than Kyle Korver taking a catch and shoot three in the course of the game. But the concept is that over time, this averages out to show who the most efficient scorers are in the course of the plays of a game.