# Explaining True Shooting Percentage (TS%)

There’s a lot of misunderstanding over the true shooting percentage metric and I wanted to write a short article clearing up some common misconceptions.

The source of most of the confusion seems to be one of the more unique players in basketball, James Harden. Harden has a field goal percentage (FG%) of 43.6% this season, which is below the league-average of 45.8%. However, Harden also boasts a 61.8% TS%, which is considerably higher than the league-average TS% of 56.2%. How does this make sense? There must be something wrong with TS%, right? Harden is known for drawing a lot of shooting fouls, so a lot of fans claim that the formula for TS% must be “skewed towards free throws” or “weighs free throws too heavily.” This is certainly not the case.

First of all, here’s the formula for field goal percentage:

Pretty simple. The number of made field goals over the number of attempted field goals. The problem is that it is essentially useless. FG% entirely ignores the very important fact that all field goal attempts are not equally valuable.

Here’s an example to illustrate the problem with FG%:

Player A and Player B both attempted ten shots. Player A hit six of their ten shots, while Player B connected on just five shots. Player A had a higher FG% — surely they must have been a superior scoring option? No, they were not. Despite shooting a lower FG%, Player B scored three more points than Player A because they hit more three-pointers.

In summary, the problem with FG% is that it doesn’t take into account the fact that three-pointers are worth three points, while two-pointers are worth just two points. Simple. That’s an easy fix, though. Instead of simply calculating FGM divided by FGA for FG%, why not add a bit of extra juice for 3PM? That’s the basis behind effective field goal percentage (eFG%):

In this formula, a 3PM is weighed 1.5x more than a 2PM. That makes sense, because 2 * 1.5 = 3, right? It’s a good stat. Player A had an eFG% of 60%, while Player B’s eFG% was 75%. That appears to match up with the fact that Player B shot at a more efficient rate once accounting for the value in their shot selection.

There’s one problem, though. eFG% is not an all-around metric of scoring efficiency — it measures shooting efficiency. There are three ways to score points in the NBA: two-pointers, three-pointers, and free throws. eFG% only tackles the first two options. The free throw is the most valuable shot in basketball1 and drawing fouls to get to the line is an extremely important skill. Therefore, a measurement of scoring efficiency must incorporate free throws.

Here’s another way to look at eFG%: (PTS – FTM) / FGA. It’s the number of points obtained from FGM divided by the number of attempts. The resulting value is not on the same scale as eFG%, but the relationship is perfectly linear — they represent the same thing.

That formula could be thought of as ‘points per shot.’ We essentially want a scoring metric that represents ‘points per shooting possession,’ including possessions in which a player attempts a shot that isn’t counted as a FGA because they were fouled. It would intuitively make sense to just multiply FTA by a coefficient of 0.50 to get the number of trips to the line because free throws are shot in pairs. However, we have to account for technical free throws, free throws after a missed three-pointer, and “and-one” plays. If you searched for the best approximate coefficient, you’d find that 0.44 is the sweet spot. It’s an approximation, but it’s a pretty good one.

Here’s what we got:

And that’s basically what TS% is. A measure of scoring efficiency based on the number of points scored over the number of possessions in which they attempted to score.

The actual TS% formula multiplies the denominator by 2 to put the number into a percentage scale, but it’s the same result on a different scale.

Free throws are not weighed too heavily. They’re weighed exactly as they should be.

1. Based on league averages this season, a two-pointer is worth 1.04 points per shot and a three-pointer is worth 1.07 points per shot. Meanwhile, players hit 77.1% of their free throws on average. Therefore, a shooting foul yielding two free throw attempts is worth 1.54 points per shot.
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