Defensive Statistics Year-to-Year Stability
Mandatory Credit: Steve Mitchell-USA TODAY Sports
Earlier, I compared the defensive side of my beta plus-minus metric to a few of the more established metrics. One of the things that came out of that exercise for me was the need to look a little closer at the noise level in some of the components of the PT-PM as well as the overall measure.
To do that I lined up the component measures from this year[1. Through March 19th] with the same components measures last year, as well as the overall metric using my most up to date defensive version, discussed briefly here. The primary change in this version is to regress the player’s opponent percentage at the rim against the frequency that they defend shots at the rim. That is used as the regressor rather total field goal attempts defended at the rim, as the data indicates the role of defending the rim is a better indicator of prowess[2. The shot percentage of back up center with 8 opponent shots at the rim defended per forty minutes with a lower total defended shots at the rim is a better indicator of skill than the percentage of starting guard with 2 opponent defended per 40 even if the total number of shots defended by the guard is more].
Bring the Noise!
Below are the R^2 of most of the important inputs for defensive PT-PM and the overall metric using a weighted least squares regression for all players with at least 400 minutes played in both 2014 and 2015.
The overall R^2 is just 33% year to year, in addition, looking at the components we can see which ones are less or more stable year to year. Offensive fouls drawn per 40 minutes, steals per 40 minutes, contested rebounds per 40 minutes, and uncontested rebounds per 40 minutes[3. As well as shooting fouls committed, omitted from the graphic] are all more stable year-to-year than the overall metric. The regressed version of opponent rim percentage is slightly less stable, but appears to bring some orthogonal information, which is fancy stats talk for information I can’t get from other data. The least stable measures are the plus-minus on closest defended two-point shots via SportVU and defensive rating (DRTG), simply defensive performance when the player is on the court not the Basketball Reference version.
Both measures indicate a need to minimize their effect on defensive PT-PM as a predictive measure or a measure of defensive skill. For the two-pointer plus-minus there is a similar systematic relationship to where shots are defended and a player’s shot defense, that can be used to regress the number to a more stable indicator. In addition, the shot logs from SportVU[4. via Darryl Blackport] have interesting data on how close the ‘closest’ defender actually is at the time of the shot, and it can vary widely. That opens the possibility of exploring how close a defender is compared to the ‘expected’ distance based on shot location[5. There is a curve linear relationship between defender distance and distance of shot from the rim. Close shots have, on average, closer defenders. Tony Allen, Kawhi Leonard, and Draymond Green were all closer defenders than expected by the distance, so that’s at least intriguing.], and alternatively also weeding out the non-close closest defender shots.
In addition to the overall numbers, I was able to look at the year to year relationship for players that were on the same team both this year and last and those that weren’t[6. Only players on the same team for the entirety of the last two years, anyone traded mid-year was in the changed team group.]. Players changing teams had fewer average minutes and the statistics tend to stabilize more with more minutes played, so a part of the difference between the same-team group and changed-team group is due the playing time difference. But, the trend is pretty clear.
Below are the R^2 split by same and changed team players.
The noisier measures are much more noisy when changing teams, while the rebounding, steals, and offensive fouls drawn are fairly stable. The regressed rim protection figure is again in the middle to a degree. On the other hand, both the two-point shot plus-minus and defensive rating provide little information for a player changing teams.
When I ran a few regressions for Defensive PT-PM from last season to the current season for players on the same team two-point shot defense and DRTG were significantly discounted. For players that changed teams, those variables were completely negated.
It is maybe a little disappointing that the new SportVU measures aren’t more reliable, though if there is some consistency and the measure is giving independent information they are still worth exploring. We also have to explore how best use and measure the information they’re giving us.