Defending the Three-Pointer Means Avoiding the Three-Pointer

Feb 7, 2015; Philadelphia, PA, USA; Philadelphia 76ers forward Robert Covington (33) shoots a three pointer as Charlotte Hornets forward Gerald Henderson (9) defends during the third quarter of the game at the Wells Fargo Center. The Sixers beat the Hornets 89-81. Mandatory Credit: John Geliebter-USA TODAY Sports

A quick follow-up from my post last week on the variability of team’s defending the three pointer as well as the further observation that individual three point defense is so noisy as to appear meaningless:[1. At least at the level of sensitivity available in public data. Chart represents top and bottom 20 players in 3% “allowed” as closest defender, min 50 attempts through Feb 5, 2015 along with each players’ average distance to shooter.]

First, it occurs to me this is another demonstration of the wisdom of this xkcd comic. As one analytics professional within the league observed: “pretty crazy how much narrative is driven by that very chart.” (referring to this graphic showing just how volatile opponent’s three point shooting can be over short samples:

Second, and more importantly, friend of NC and sometime guest poster Johannes Becker (@SportsTribution) followed up with this email, reproduced with permission and slight edits:

"Early in the season, there were a number of articles citing “shooting percentage against James Harden” statistics as part of the case for Harden’s improvement on defense this year. While Seth already pointed out that it seems like defending a 3 pointer is mostly luck, I want to drive the point home: it seems the best way that to defend a three point attempt, is to  make it disappear. Which of course is much more complicated to measure.Walking through the argument step-by-step.If we use the binomial distribution as our underlying model, we expect 5% of players to be outside of our 95% confidence interval. Using a minimum threshold of 50 attempts (against our defender), we find that 4.4% of players are outside of this interval – so that’s a first indicator that the distribution is close to the binomial ‘coin flip’ distribution. There is a tiny negative correlation (-0.136) between attempts against and 3FG%. (More on this later.)Furthermore, if we take the simulated distribution that we would get from a ‘coin flip experiment’ with our real distribution of players, we find practically identical distributionsThus, arguing ‘Player A is a good defender, because of the 3pt% against him stat’ is most likely a citation to statistical noise than a measure of real ability. This issue is one that we (as a data community) have to be careful of! Especially, since this “coinflip effect” can be reflected in a number of other defensive metrics such as various defensive plus/minus stats and so on.Some additional observations:1. Looking at the biggest average distance and smallest average distance from attempts (min 50 shots), we find the following:Largest distance: Tyson Chandler, Nikola Vucevic, Ed DavisSmallest distance: Shelvin Mack, Tony Parker, Ty LawsonMy guess is that if you would plot player size against average distance, you would see a big correlation (with Kobe as an outlier. Check out his numbers!). My primary theory: players mainly shoot three pointers when they feel relatively confident, so the taller the defender, the more space they need. This also helps explain the completely random distribution for observed percentages allowed. Ideally, we would measure  ‘3 point avoidance’ instead. This would be a much more convoluted stat of course.2. The small negative correlation between shots attempt against and 3ptFG% might reflect  players who defend many three pointers pointers are more often in situations where the opponent is FORCED to take the shot such as near the end of shot clock or trailing late in games, thus allowing for a heartier contest."

Great food for thought. Not to put words in Johannes’ mouth, but I think he’d agree that the defense can still affect the shot by being closer to the shooter, but beyond that whether the shot is made or not is largely out of the defender’s control. As a final note, Krishna likely will have more in depth on this topic later in the week.