APBRmetrics

[Dan Rosenbaum]

(This was inspired by the thread started by Nikos, but once this post got really long, I figured it probably made sense to start a new thread.)

Below I have included regression results relating my adjusted offensive and defensive plus/minus rating to various box score statistics. These are not quite the series of regressions I used to produce my statistical plus/minus ratings, but I think these should be useful in talking about how box score statistics related these offensive and defensive adjusted plus/minus ratings.

Here are some important points. The way you should read the coefficients is the following. In the offenive regression, the offensive adjusted plus/minus rating increases by 0.70 points per 40 minutes with every one point increase in points per 40 minutes, holding all of the other variables (including true shot attempts) constant.

1. The offensive regression has a much higher R-squared than the defensive regression, which confirms the expectation that our box score statistics do a better job explaining offensive effectiveness.

2. There is slightly more variation in offensive ratings than defensive ratings.

3. The results suggest that holding the other variables constant, a player with better than a 37% true shooting percentage tends to increase offensive efficiency. My interpretation is that the reason this is not higher is that players who can create shots are valuable, i.e. that most players will see their true shooting percentage fall as their true shot attempts increase.

4. Interestingly, even after accounting for points scored, players with more three point attempts tend to have higher offensive adjusted plus/minus ratings. This suggests that in addition to the points they score, the ability of three point shooters to spread the floor is very important for offenses. Also, note that more three point attempts is not associated with worse defense. It does not appear that the long rebounds from missed three pointers is typically leading to easy transition points.

5. Players who go to the line more, holding the other variables constant, tend to be more effective on offense and defense. In fact, the effect is larger on defense.

6. As expected, offensive rebounds predict offensive effectiveness and defensive rebounds predict defensive effectiveness. Note, however, that the offensive rebounds appear to be more important.

7. Holding the other variables constant, players who turn the ball over tend to be not only less effective offensive players, but also less effective defenders.

8. Holding the other variables constant, steals are almost as important a predictor of offensive effectiveness as they are of defensive effectiveness. Part of this may be that steals often generate high percentage scoring opportunities for teammates, but I wonder if part of this isn't that players who get steals tend to do a better job of spacing and collecting loose balls on the offensive end. This may help explain why steals may not be a good predictor of team success, but are important at the individual level. Players who steal the ball a lot may do a better job helping their teammates avoid turnovers and bad shots.

9. For the whole sample there is not a strong relationship between assists and defensive effectiveness. But when I limit the sample to big men, I find that better assisters tend to better defensive players, holding the other variables constant.

10. Holding the other variables constant, blocks predict defensive effectivenss, but not offensive effectiveness.

11. Holding the other variables constant, players with more personal fouls tend to be more effective defenders, with little effect on offensive effectiveness.

12. Holding the other variables constant, players who play more minutes per game tend to be more effective on offense and defense. This is pretty strong evidence that coaches do observe contributions that players make that are not picked up in box score statistics.

[kjb]

I think this is GREAT stuff. I'll let others comment on the math, but I love stuff like:

[Eli W]

Sorry if this is obvious, but what's the formula for true shooting attempts? I haven't seen that terminology.

[Dan Rosenbaum]

[olcoach43]

Dan I assume that these ratings are a function of what happens to the team when a given player is on floor? (If not can you clarify?)
If so, the defensive performance is most likely negative when a poor ballhandler (turnovers) is on the floor, because of two perfectly logical factors:
1. There may well be a points off of turnovers factor, depending upon where and what type of turnover occurs. Eg, a quick basket
2. Even if the turnovers do not lead directly to quick baskets, points per possession will suffer while turnovers are occuring, and chemistry and defensive effort will break down within the team concept.

On the bench we would be focused upon breaking a negative momentum and assistants would be hollering for me to get his a** out of there!

[Eli W]

Dan, this stuff is great. I've already plugged in the coefficients to an Excel formula and gone to work. One initial thing I noticed was how poorly Ben Gordon came out defensively. I didn't use any pace adjustments, but I have him ranking third worst in the league for 04-05 (behind Troy Hudson and DeShawn Stevenson). You have Hudson and Stevenson both ranked in the 0 percentile in defensive statistical plus/minus in your 82games article, but Gordon is listed as in the 52nd percentile. Is this big difference for Gordon due to the fact that you used slightly different regressions (or due to pace adjustments)? Or did I err in my calculations?

[olcoach43]

John,
I am not capable of doing the statistical work you just described. However, I am heartened by your findings. My work shows Gordon to be one of the worst "off the ball" players in the NBA, ranked 5th from the bottom of all 500+ players.
His A/TO ratio is .88 and he contributes virtually nothing in any other categories. He is a known poor defender, so I have been
wondering about this issue as well.

[jkubatko]

Dan, did you look into the problem of multicollinearity at all? If you are just interested in obtaining predictions, then multicollinearity is not a big deal. But if your goal is to understand how each predictor influences the response, then multicollinearity is a *big* problem. Based on your initial post it seems like you are interested in the latter.
_________________
Regards,
Justin Kubatko
Basketball-Reference.com

[Dan Rosenbaum]

[Dan Rosenbaum]

[jkubatko]

[Dan Rosenbaum]

[jkubatko]

[jkubatko]

Dan, have you thought about using FTA/FGA instead of FTA? I'm just curious how that would influence the results.
_________________
Regards,
Justin Kubatko
Basketball-Reference.com

[Eli W]

What are the coefficients for estimating overall adjusted plus/minus? Are they just the sums of the offensive and defensive coefficients?