Nylon Calculus: Regression in shot-making and shot quality

If you follow basketball analytics you know that 3-point shooting is a source of variance to individual game results, and even over small game samples. Opponent 3-point shooting is even more noisy, with little correlation from year to year, outside of the Celtics, for whatever reason.

But, 3-point shooting isn’t the only stat with noise to it. Pretty much every early season statistic has some noise to it. It’s just a matter of degree. In fact, last year Bo Schwartz found that increased 3-point shooting had only a minor net increase in offensive variance.

One reasonably easy way to quantify the present state of noise for any statistic is to compare the current standard deviation for the statistic among teams with the expected full-season standard deviation. The idea is simple, for example, if I have thirty teams flip a coin five times the percent of times “heads” comes up is going to be much more varied than if they each have to flip 82 times.

On offense, we can look at the different shot locations using Basketball-Reference’s groupings. And there, yes, 3-point percentage is one of the noisiest numbers, the standard deviation through Sunday is 2.7 times larger than it was for a full season last year. Maybe more intuitively, the range from the best shooting team to the worst shooting team is over two times as large as it was for a full season. Through Sunday, the worst shooting team, the Oklahoma City Thunder, were at 29.1 percent and the best shooting team, the Golden State Warriors, were at 41 percent, a gap of 12.3 percentage points. By the end of last year the best to worst gap was only 5.7 percentage points. So, yes, those numbers are likely to converge. But, it’s not just 3-point percentages. Below is the standard deviation ratio for all of Basketball-Reference’s shot location areas, the higher the current ratio the more noise is likely in the current numbers:

All of the shot locations are showing more variable results than we would expect to see over the course of a season. Even the most stable, shot at the rim, are almost two times as variable as the full season numbers.

Shot locations patterns are already more established than shooting percentages, but even here there is noise. Interestingly, in shot locations, it is shots at the rim that has the most excess variability. At the extremes the Celtics are getting 21 percent of their shots at the rim, while the Lakers are getting 41 percent there, a range that’s twice as wide as a full year:

We should expect shots at the rim to normalize to some extent. Interestingly, the range on 3-point rate right now is less than it was for a full season last year. The NBA is probably continuing to adapt to the 3-point era, forty years on.

So that’s offensive shots. Opponents shots look similar, only more so. The jump shot locations have even further to regress, but here opponent shots are the rim are actually closer to the expected full-season variability than shots at the rim on offense. The best or most fortunate team on opponent 3s is, once again, the Celtics with 28 percent of attempts made against them. And the worst, or least fortunate team is the Dallas Mavericks.

Opponent shot locations are a little bit more noisy than the team’s own for every location. To start the season, Detroit is giving up the lowest percentage of attempts at the rim, but the highest percent made, while the Cavaliers have given up the highest percentage of shots there.

Putting all of that together I was able use Bayes Theorem to regress shot locations and shooting percentages to project both offensive and opponents expected effective field goal percentage compared to how they have fared so far. The projection is rather simple, in that it doesn’t account for injured players or anything like that. It simply how much regression can we expect in shot making and locations and netting that all out.

Looking at this lens on both sides of the ball many teams can expect some regression on both shot quality and shot making, though not always in the same direction.

This methodology expects the Pistons to suffer the biggest improvement in their opponent’s shooting efficiency, with more shots allowed at the rim, for an expected 2.3 percentage point increase in opponent shot quality, and a higher percent going in, for 4.9 percentage points higher on shot making. The Hornets are expected to see even more increase in opponent shot making, but the model sees their shot profile as sustainable. The Spurs and Pelicans, on the other hand, are expected to see the biggest declines in their opponent’s effective field goal percentage.

On offense, the underperforming Celtics and Rockets are expected to see the biggest improvement in their overall effective field goal percentage, with improvements in both shot quality and shot making expected. For the Celtics the model puts a considerable amount of weight on improving their shot profile, with 1.5 percentage point improvement expected there, about half of the Celtics expected regression-based improvement in shot making. The Kings and the Suns are on the other side of the regression ledger, in both cases with expected falls in shot making (To be fair to the Suns their expected defensive improvement in opponent shot making nearly offsets that). The whole list can be found here.

On both sides of the ball, the expected effective field goal percentage regression on shot quality is about one-third of the expected regression in shot making, 0.7 percentage points in shot quality vs 2.0 percentage points in shot making on offense, with a similar spread on defense. So, yes shot making is clearly less stable, but it’s not the only place a team can regress.