Geometry, Distance and Corner 3s

Oct 22, 2014; San Antonio, TX, USA; Atlanta Hawks shooting guard Kyle Korver (26) shoots the ball over San Antonio Spurs shooting guard Danny Green (14) during the first half at AT&T Center. Mandatory Credit: Soobum Im-USA TODAY Sports

It’s a bedrock principle of modern NBA offense that the corner 3 is one of the more desirable shots in the game. The numbers bear this out as the league as a whole shot 39% from the corner as compared to 35.3% above the break. While at first glance that might not seem like a huge gap, in terms of per possession efficiency it’s roughly equivalent to the gap between the best and worst (non-Philadelphia division) offenses in the NBA last season.

Almost invariably these shots are described as the “shorter corner 3.” And it’s true, the line is 22 feet from the basket in the  corner, while it extends to 23 feet, 9 inches around the rest of the arc. However, that extra distance is not the primary determining factor in the increased accuracy of the shot. As Ian noted over the summer, field goal accuracy doesn’t materially change at any distance between 5 and about 24 feet:

In fact across the NBA, corner 3s were made at a higher rate than long two point jumpers of the exact same distance. As mentioned above, those corner 3s were knocked down at right around 39%. Looking at some of the more granular shooting data released earlier this week, two pointers from 22 feet away or further were only converted at a 34.3% rate. While there are other explanations possible such as the the corner being an easier shooting background, a more likely explanation is that corner 3s are simply more open. This notion arose when I was examining who were the shooters deadliest from the corners when left wide open. It seemed that an unusually high proportion of players corner 3 attempts were completely uncontested. Given how important corner 3s are to the modern game, how could the shot be one of the least heavily contested in the game? But upon closer examination, it appears to be true. Here are the proportion of shots taken between 22 and 24 feet from the basket by the distance of the nearest defender:

Another point in favor of this theory is that above the break threes were scored at a rate of 37.9% across the NBA in 2013/14, certainly within spitting distance of the corner 3 conversion rate.  It appears[1. This is using some rough approximatios for corner vs. above  the break 3s, since I’m not (yet) working with exact X,Y coordinate data] the closest defender for a corner 3 is on average a foot further away than for above the break threes. Best guess is that this has as much to do with geometry of the court as anything else. For some of the same reasons I discussed here in terms of why big men and high usage players don’t shoot many corner 3s, by virtue of being in the corner, it’s probably harder to rotate to a shooter in the corner by virtue of court geometry. This has some potentially intriguing strategic ramification worthy of more in depth examination.

And since I mentioned it, here are the most deadly shooters left unguarded (defenders 4 feet or greater away. Korver’s percentage actually rises to an absurd 58.2% with just one more foot of space):