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How Long Does It Take For Three Point Shooting To Stabilize?

Jan 29, 2014; Toronto, Ontario, CAN; Orlando Magic shooting guard Arron Afflalo (4) shoots over Toronto Raptors forward John Salmons (25) at Air Canada Centre. The Raptors beat the Magic 98-83. Mandatory Credit: Tom Szczerbowski-USA TODAY Sports

Jan 29, 2014; Toronto, Ontario, CAN; Orlando Magic shooting guard Arron Afflalo (4) shoots over Toronto Raptors forward John Salmons (25) at Air Canada Centre. The Raptors beat the Magic 98-83. Mandatory Credit: Tom Szczerbowski-USA TODAY Sports

With the increase in three-point attempts in recent years it has become more important to have players who can consistently make threes. As a result it makes sense that players are probably putting more time in the gym working on their three-point shooting to add it to their skill set and make themselves more valuable. Three-point shots are high-variance shots, leading television analysts to use the phrase “live by the three, die by the three”, so when a career 32% three point shooter suddenly shoots 38% for a season, do we know that he has actually improved? How many attempts are enough to separate the signal from the noise? I decided to apply techniques used to calculate how long various baseball stats take to stabilize to see how long it takes for three-point shooting percentage to stabilize.

If we were trying to get a sense for how stable three point percentage is after 100 attempts, a simple way to do it would be to randomly split the 100 shots into two samples of 50 and compare the percentage made in both samples. If it were stable, the percentage of makes in each sample should be similar. A better method would be to split the 100 shots into every permutation of two sample pairs of 50 and calculate the average correlation between the two pairs. This is what the Kuder-Richardson Formula 21 calculates. From here on I will refer to this number as the reliability. To find the point at which three-point shooting stabilizes we need to find out when the reliability crosses a certain threshold. A reliability of 0.7 seems to be the standard threshold used. After this point, the skill aspect will outweigh the noise. To gather a big enough sample of players with a sufficient number of attempts, I used the past seven season’s worth of three-point shooting data from NBA.com and I found that after roughly 750 attempts the reliability crosses the 0.7 threshold.

This means that after 750 attempts a player’s percentage is split 50-50 between skill and noise. This is still a lot of noise. It is also a lot of attempts. The single season NBA record for most three-point attempts in a season is 678. This helps explain why the three point percentage leaders each year has mostly the same players but in a different order. Since it takes so many attempts to stabilize, it can be hard to really know if a player did actually improve their three-point shooting after they have a career year, especially when not many players are even getting halfway to 750 attempts. It should be noted that the 750 attempts is strictly about past performance and has no bearing on future performance. It doesn’t mean for example, that if a player shoots 36% on threes over 750 attempts he can be expected to shoot around 36% over his next 750. It does mean that if he shoots 43% on his next 750 attempts that he probably did improve. The 750 attempts are also assumed to be taken under roughly the same conditions, so if a player’s role changes, then the attempts under the two roles shouldn’t be included together. This means that if there is a big change in conditions that could affect a player’s three-point percentage, either positively or negatively, then we might be able to put more stock in a change to a player’s three-point percentage. If someone goes from a team where they have to run the offense and create shots for themselves and others to a team where all they need to do is stand outside the three-point line and catch and shoot open threes, we can be pretty confident their increase in three-point percentage is real, not necessarily because they are a better shooter  but because they are in a better situation to make threes.

The big takeaway from all of this is that it takes a long time for three point shooting percentage to stabilize. Players who have a good or bad three-point shooting season will probably regress to the mean and be closer to their career average the next season, assuming they are in roughly the same role. An example of this is Arron Afflalo, who entering the 2012-13 season was a career 40% three point shooter. He shot a career worst 30% in the 2012-13 season and followed that up by shooting 42.7% from three last season, a little better than his career average. He probably didn’t all of a sudden become a much worse shooter in 2012-13 and magically find his shooting touch again in 2013-14. He took 240 attempts in 2012-13, so that poor shooting season was probably just noise coupled with an increase in usage. This doesn’t mean players can’t actually get better, Kyle Lowry was a 24-26% three point shooter in his first four seasons and has shot 36-38% in each season since then. It just means that it’s not as simple as seeing a player’s three-point percentage increase one season and saying he is now a better shooter. If he keeps it up for multiple seasons then it’s probably safe to call it an improvement, but one season isn’t enough.

Darryl Blackport