Advanced Metrics Handbook, Vol. 2: True Shooting Percentage

Part of an occasional series explaining some of the advanced statistical terms employed at Orlando Pinstriped Post. Today's topic: true shooting percentage, or TS% for short.

As I mentioned in the first installment of this series, effective field goal percentage is useful, but even then it's not the very best way to measure a given player's scoring efficiency. Nope, that'd be True Shooting Percentage, or TS%, which incorporates two-pointers, three-pointers, and free throws into its formula. And as we'll soon see, it's not really a percentage! But first, an example case.

On January 15th, 2010, the Orlando Magic dropped a 15-point decision to the Portland Trail Blazers, who were without franchise cornerstone Brandon Roy, as well as Greg Oden and Joel Przybilla, their two best defensive big men. The Blazers' skeleton crew made quick work of the Magic, leading by 14 points at halftime. Orlando's Dwight Howard scored 11 points on an economical 4-of-7 shooting in the loss.

Viewed through the traditional prism of field goal percentage, Howard's 57.1% figure was solid. If you're a bit fancier, you might say he scored 1.6 points per shot, which isn't bad at all. But neither of those metrics accounts for another key component of offense, namely the free throw. And Howard shot 3-of-10 at the line that night. TS% addresses that shortcoming and tells the most accurate, reliable picture of a player's scoring efficiency.

The formula:

Points / (2 * (FGA + 0.44 * FTA))

In plain English:

TS% considers the number of points a player scored relative to the shooting possessions he used, with that term encompassing field goal attempts as well as free-throw attempts; a coefficient of 0.44 corrects free-throw attempts to reflect the fact that they're often taken in pairs, as well as in other situations such as and-ones and technical fouls. Another way to think of TS% is points per shooting possession, halved.

What it's for:

I fear I may have given too much of this section away previously, but anyway: TS% corrects every other metric in that it incorporates free throw attempts. And it does something that no other shooting metric does, really, which is consider points produced. In this way, it weighs a player's offensive production against the shooting possessions he used to get there, regardless of which sort of possession (two-pointer, three-pointer, or free throw) the player used.

As you may figure, TS% is valuable for considering all types of players, but it's especially useful when looking at big men, who typically don't take many three-pointers (though we're seeing a paradigmatic shift of late, with guys like Dirk Nowitzki, Mehmet Okur, Andrea Bargnani, and Rashard Lewis stepping beyond the arc at power forward and center. Because they tend not to have three-pointers to pad their points total, a solid TS% from a big man reveals that he probably plays within himself and within the offense, and can draw fouls to boot.

The takeaway:

In our example, Howard shot 57.1% from the field. However, when considering his poor shooting at the foul line, he registered a below-average 48.2% True Shooting figure. Howard's inefficiency in this game was among the factors that led to defeat; he certainly wasn't a bright spot on offense, contrary to what his raw field goal percentage may seem to indicate.

Another example shows how TS% can work the other way too, though; it can make poor field goal efforts look good, which is the opposite of what the example that led off this post did. Against the Toronto Raptors on November 1st, 2009, Howard shot just 5-of-13 (38.5%) from the floor. But he scored 24 points thanks to his 14-of-16 effort from the line. Plug those numbers in and you'll see Howard finished the Sunday matinee with a 59.9% True Shooting mark, which is just a shade below his career average of 60.3%.

Taking a wider view, TS% stresses the role foul shooting plays in today's game. And, due to the use of shooting possessions in calculating it, we see how inadequate field-goal attempts are in measuring a given player's involvement in the offense. Consider the Magic's leaders in shot attempts per game last year:

Team Rank	Player	FGA/Game
1	Vince Carter	13.5
2	Rashard Lewis	11.2
3	Jameer Nelson	10.9
4	Dwight Howard	10.2
5	Mickael Pietrus	7.2

Based on that list, you might conclude the Magic are freaking insane for giving Howard, their franchise player, only 10.2 shot attempts--behind three other players!--and that he needs to be involved more. And while there's validity to the idea that Howard indeed needs more touches, the situation isn't as dire as traditional field goal attempts per game average paints it to be. Here now are the Magic's leaders in shooting possessions used per game:

Team Rank	Player	Shoot. Poss./ Game	Change
1	Vince Carter	15.3	+ 1.8
2	Dwight Howard	14.5	+ 4.3
3	Rashard Lewis	12.3	+ 1.1
4	Jameer Nelson	11.6	+ 0.7
5	Mickael Pietrus	7.8	+ 0.6

Indeed, considering shooting possessions vaults Howard over Lewis and Nelson and places him less than one such possession behind Vince Carter, the team leader. And although there are better methods to measure overall offensive involvement than shooting possessions--usage rate is one--it's certainly better than merely evaluating field goal attempts.