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The Truth About True Shooting Percentage

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“Yeah but what’s his TS%?”

The acceptance and widespread usage of true shooting percentage (TS%) among basketball fans and analysts has been at the forefront of a mini revolution in the way we view scoring numbers and the players who produce them. We’ve long known that scoring efficiency was important and that field goal percentage only told part of the story. But for much of the game’s history, there was no reliable statistic available to reconcile all the components of scoring. Cue TS% and, today, it’s rare to find a discussion about basketball stats that doesn’t feature someone like me bringing up the gold standard of scoring efficiency metrics. It has become a trump card of sorts that any stat guy worth his salt stands ready to play at any given opportunity (oh he did not just call Cousins a more efficient scorer than Love). But while its acceptance has helped shape the way we discuss basketball, there’s not too much discussion on the merits of the stat itself.

How good is it really?

TS% = PTS*100/(2*(FGA + .44*FTA))

If you’re one of those “good ol’ days” guys, who laments the pushing of all these fancy advanced stats, this formula alone is probably enough to get you to stop reading. But it’s actually pretty simple; a far-cry from convoluted meta-stats like PER, whose bloated algorithm would be better suited for churning out NBA 2k player rating than producing substantive estimations of player abilities. That’s not to say Hollinger’s metric is useless – while his amalgam of stats is messy and extremely difficult to parse, there’s something to be said for a quick estimation of which players are putting up the biggest numbers – but where PER is complex and overextended, TS% is singularly focused.

Let me break it down (warning: things are about to get technical)

The first thing to note is that TS% is an “artificial” shooting percentage. It measures the amount of points scored per field goal attempt (FGA) or trip to the line. The points are multiplied by 100 and FGA are multiplied by two to match the conventions of FG% (FG% = FG*100/FGA). Threes are inherently accounted for by the fact that they net an additional point while still adding a single attempt to the denominator. Free throw attempts (FTA) are roughly halved because the standard two-shot trip to the line is treated as the equivalent of an attempted field goal (more on this soon). TS% is essentially effective field goal percentage (eFG%), which adjusts FG% to account for threes being worth three points, but now free throws, the black sheep of the scoring family, are invited to the party. It all seems to make a lot of sense.

As you might expect, it’s those pesky free throw pariahs that complicate things. Their inclusion is the formula’s greatest strength; it’s what shows us that Dwight Howard (eFG: 59%, TS: 60%) is not a more efficient scorer than Kevin Durant (eFG: 56%, TS: 64%). But it’s the formula’s lone oddity – that .44 multiplier – which proves to be its biggest flaw. It would be nice and clean if FTA could simply be halved and added to shot attempts, but thanks to and-ones, shooting fouls on missed three-pointers, and technical and flagrant fouls, not every pair of free throws on a player’s stat line represents a single possession being put on the line. The creators of TS% thus used league-wide averages to estimate that 12% of all FTA should not count towards players free throw total.

This is where it gets messy. The 12% estimation is applied to every player in NBA history despite the vast differences in play-style and the significant changes in the NBA’s rule book. Three-pointers weren’t adopted by the NBA until 1979 and were a very small part of the game for many years after. The rules regarding flagrants and techs have also changed numerous times. In a given year, the scoring habits of different players vary greatly. Last year, LeBron James was approximately twenty times more likely to go to the line for an and-one on a given field goal than Steve Novak, who was fouled more often on three point attempts than Dwight Howard (shocking, I know). Yet the number always stays constant. That breeds inaccuracy.

Then there’s the admittedly small issue of the formula’s treatment of techs. These trips to the line are removed from the equation’s denominator because a team does not lose possession after a technical free throw is taken. As a result, they are treated as free points. This is bullshit. They should either be removed from both the numerator and denominator – as no possession is at stake – or treated as the wager they are. When a player steps up to take one of these shots, he does so knowing that another player could just as easily take them and make them at a very good rate. This of course assumes the team is not devoid of reliable free throw shooters (I’m looking at you, Detroit). If a player makes all his techs, he helps his team. If he shoots 60%, he almost invariably hurts his team. If anything, these misses should be treated more severely than the average miss in a two-shot scenario. Regardless, by handling techs this way, TS% overvalues free throws, especially for the majority of players who never shoot them and have FTA removed from their denominator for absolutely no reason.

So far, all these potential inaccuracies haven’t amounted to all that much. We’re looking at differences of maybe one or two percentage points. The real problem with the treatment of free throws in TS% stems from the assumption that missing two free throws on a standard trip to the line is equivalent to a missed shot. This is fundamentally flawed logic because of the simple fact that an offense is much more likely to retain possession after a missed field goal than after a missed free throw. Exact numbers are hard to come by, but this article from 2004 shows that offenses rebounded just 13.9% of missed free throws, compared to 29% of missed field goals. This suggests that missed field goals are more than twice as likely to stay with the offense. That’s what people in the stats biz call “a big fuckin’ deal”. Once again, free throws are being overvalued, but in this case quite drastically.

Of course, there are a couple potential caveats here. It’s possible that missed field goals not rebounded by the offense typically result in more favorable positioning for the opposing team. It also seems likely that an offensive rebound after a free throw might be more likely to result in points for the offense than your average rebound after a missed shot. These factors may mitigate the discrepancy in offensive rebounds and are worth considering, but years of watching the NBA tell me that they aren’t nearly enough to erase it. But hey, you can be your own judge.

So what’s the solution here? We fans lack the resources to seamlessly integrate and-ones, three-shot fouls and flagrants into the equation. I also don’t expect anyone to start adjusting that .44 to account for the fact that free throws are harder for the offense to rebound (but damn it, you should try). The point here is awareness. Awareness that TS% is an imperfect estimation that always assumes the average when it comes to free throws. Any time you’re dealing with an exceptional player – especially one who shoots an inordinate amount of and-ones – there is likely going to be a discrepancy. And most importantly, be aware that TS% fundamentally understates the negative effect of missed free throws and overstates that of missed field goals; most glaringly, those close to the basket, which have the highest chance of being rebounded by the offense and producing more points.

Until we have a more accurate and logical measure of scoring efficiency, true shooting percentage will continue to occupy an important place in the wild world of basketball statistics. But just remember that “true” can be a relative term.

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1 Comment on The Truth About True Shooting Percentage

  1. Aaron Winslow // March 6, 2014 at 4:24 PM // Reply

    Great read. Well done.

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