Nylon Calculus 101: True Shooting Percentage

True-shooting percentage is a shooting efficiency statistic that acts like field-goal percentage but is adjusted for three-pointers and free throws.

Why Should We Use It Over Conventional Stats?

Games are decided by points, not field-goal percentage, and True Shooting Percentage (normally referred to as “TS%” or just “TS”) is based on points and possessions.

The classic example is Chauncey Billups. Given that his career FG% is 41.5 and he dipped under 40% a few times for an entire season, including the championship year, one could be quick to label him inefficient and identify his volume shooting as a “problem” on a good team. But that’s misguided. Billups had the rare ability to shoot a high number of three-pointers while getting to the line frequently, and since he was a great shooter (89.4% from the free-throw line for his career) he was actually an efficient scorer. This is an important distinction because we shouldn’t rate players with respect to efficiency based on field-goal percentage, which only describes a ratio of field goals made. For example, he had a 61.9 TS% in 2008, which ranked 8th that season among qualified players.

Conversely, there’s someone like DeAndre Jordan, who shot a bewildering 71% from the field but never takes three’s and is one of the worst free throw shooters ever, so his TS% is excellent but mortal. (There’s also the related term “secondary percentage” that signifies the difference between TS% and FG%.)

How’s It Done?

The formula is:

100*Points / [2 * (FGA + .44*FTA) ]

The first term, 100, is there so the figure is on the 100% scale (many sites don’t do this, however.) The 2 is there so it’s roughly on the same scale as field-goal percentage. Additionally, dividing points by the total of free throws and field goal attempts is a way to calculate a pseudo field-goal percentage with more weight given to three-pointers because they’re worth one more point while factoring in foul shooting.

What’s with the .44?

You want to convert free throws into a shot attempt equivalent. Since players usually take two free throws at a time, the coefficient should be around 0.50. But we have to account for and-1’s, technical free throws, flagrant foul free throws, and 3PT free throws (three in a row.) Thus, based on testing, the 0.44 coefficient is used for the NBA, and it’s surprisingly accurate.

For example, let’s look at a free throw drawing maestro, James Harden in 2015. Using data from NBAWOWY.com, he had 2217 points in the regular season with 1470 field goals and 824 free throws. Additionally, there were 52 and-1 attempts, 66 three-in-a-row free throw sets, and 38 technical/flagrant foul attempts. The traditional formula results in a TS% of 60.49% via the following: 100*2217/[2*(1470 + .44*824)]. This is very similar to the output received with the real proportions of free throws considered: 100*2217/[2*(1470 + .5*(824 – 52 – 66/3 – 38))] = 60.71%. Even with a free throw manipulator like Harden, the errors using the 0.44 estimate are usually pretty small.

In fact, using data provided by Seth Partnow, you can calculate a “real” TS% using the appropriate number of free throw possessions instead of using the 0.44 coefficient. This essentially tests the accuracy of that estimate. Looking at 2015 and players with at least 300 true-shot attempts, the correlation coefficient between the estimated TS% and the real TS% is 0.998[1. This is true whether or not you count technical foul shots. To some analysts, technical free throws do not count because they are essentially “free points” that usually aren’t created by the foul shooter and they can be replaced by whomever else is on the court. Either way, the differences are tiny and the correlation is strong.]. Only one player, Courtney Lee, had an error greater than 1% and only roughly a sixth of the 291 players in the data set had an error greater than 0.5%.

Why Doesn’t It Account for [    ]?

Some critics state that because free throw offensive rebounds are less frequent than offensive boards from field goals you can’t state equivalency as the formula does. While it’s true that you’re much more likely to get a rebound from a missed field goal than a free throw, this has nothing to do with TS% because TS% is about shooting efficiency, not rebounding. In fact, one could also consider how free throws penalize the other team with a foul or factor in the importance of spacing. There are many other pieces to consider, like shot creation, but TS% is specific.

The statistic should not be used for ranking players or even scorers because there are many dimensions of basketball to consider. TS%, or shooting efficiency in general, is just one part to consider. Consider it a first step in evaluating the effectiveness of a player before one moves onto team role, defensive attention, and other factors.

Which Values Are Good/Poor?

The league average in 2015 was 53.4% according to basketball-reference. That’s fairly typical for a season average, and it’s been like that since the 1980’s. Above the 60% range is considered elite, the unofficial record is 70.8% from Tyson Chandler in 2012, and under 50% is considered quite poor. The league leaders are typically three-point marksmen or athletic big men who dunk often, especially those who can hit their free throws too. The players at the bottom of the leaderboard are usually midrange-reliant shooters who don’t get to the free throw line frequently as well as the guys who are, well, generally awful players.

You can also adjust for the league average. This is useful when comparing players from different eras. Looking at the table below with TS%+ (simple formula: TS% – league avg. TS% for the season) the all-time leader is actually Wilt Chamberlain in 1973, whose 68.9 TS% was astronomically high compared to his peers. You can see how adjusting for the league average is useful for players like Kenny Sears in the 50’s or even Brent Barry, whose shooting efficiency was more impressive once you factored in the low scoring of that early 2000’s era.

Data from nyloncalculus.silk.co

*Shot volume% is the percentage of field goals a player takes compared to his team.

What About eFG%?

Effective field-goal percentage is exactly the same as true-shooting percentage but without free throws considered. Essentially all that’s done compared with field-goal percentage is that made three-pointers are valued 50% more. It’s useful in balancing the value of two-point field goals with three-pointers. Thus, it’s utilized frequently in shooting charts and leaderboards.

100*(FG + 0.5 * 3PT) / FGA

or

100*(Points – FT) / (2 * FGA)