Errors in True Shooting%

As discussed before, True Shooting percentage is an estimate of points per shot. But it’s not exact, counting a free throw attempt as 0.44 shots. Why isn’t a free throw 1/2 a shot, you ask? Because of “And One” opportunities, when someone scores and is fouled for one extra bonus free throw. In Marv Albert’s language, it’s known as “Yes, and it counts.”

These are bonus chances after a successful conversion, so to count these free throws as half an attempt would actually be penalizing players for drawing an And One and missing compared to players who never drew the foul at all. To obtain a precise measurement of points per shot (PPS), we’d have to differentiate between And One free throw attempts and the conventional trips to the line. Without doing that, the 0.44 coefficient minimizes error across the league between points per shot and True Shooting percentage.

So how much can TS% be off by measuring PPS? Mathematically speaking, we can observe the following:

• Free Throw percentage essentially does not affect TS% accuracy.
• The ratio of And One FTA to total FTA affects TS% accuracy. 12% is perfect accuracy. The smaller the ratio, the more TS% will overestimate PPS. The larger the ratio, the more TS% will underestimate PPS.
• The ratio of FGA/FTA slightly compounds TS% accuracy. The more free throws taken relative to field goals, the more TS% errors are magnified (both overestimating or underestimating PPS).

The 0.44 coefficient used for FTs in the TS formula is designed to minimize these errors as much as possible. It does that well across the league, But obviously, not all players have the same frequency of 3-point play opportunities.

The way to generate a truly accurate percentage would be to comb through play-by-play data and separate And Ones from other free throw attempts. In 2005 and 2006, 82games provided some And One data we can look at for an idea of how accurate TS% is among high-volume players. PPS/2 is points per shot divided by two, which is what TS% is trying to measure:

% of And1s is the percentage of total FTA that are And1 FTA. PPS/2 is points per shot divided by 2, which is the what TS% is trying to approximate. Error is the difference between the actual player efficiency and his listed TS% using 0.44 for free throw attempts.

As we can see, TS errors are generally small. In the games I’ve tracked this year, Wade and Bryant have And One ratios of around 12% (0.1% error for both) and James is just over 8% (for an overestimation of 0.3%). It would be nice to add And Ones to box scores, or completely track them in play-by-play, but in the meantime, TS% does a great job approximating points per shot.