APBRmetrics

How is Dirk in the top 5 despite having a negative raw plus/minus?

1.) Raw plus minus is barely related to regression-based plus-minus.

2.) He's barely played this year, especially before the ASB, so his rating is dominated by his prior.

It has taken longer than expected for all sorts of reasons, but I should be posting an up-to-date, improved version of these later today once I have pulled the data down.

A big problem in robustly fitting RAPM is properly configuring the (co)variance matrix for the priors. For single-year RAPM it is no issue, but when using past ratings as a prior there is an important consideration as to what confidence you have in that prior, as that has a large effect on your results. As far as I know JE never tackled this in the Bayesian formalism, deciding upon a fine but more arbitrary method I believe. Anyway, the big deal here is that the strength of priors for rookies is very important. The best example I can give for this is the Durant-Westbrook relationship. The two were virtually never on court apart in Westbrook's rookie season, and as such since Durant was bad the year before, Durant's progress in Westbrook's rookie year gets assigned to Westbrook rather than Durant if the rookie priors (and indeed non-rookie priors) aren't properly calibrated relative to each other. This anti-Durant problem could also be further compounded by the further introduction of rookie Harden later too.

Long story short: RAPM will always have problems with player combinations that almost always play together, but minimising those problems is very important, and can't be done at all using single-season numbers.

So I'm doing 1-yr RAPM with no prior and finding something very, very strange (or maybe not considering the post above):

https://docs.google.com/spreadsheet/pub ... utput=html

No, not that Amir Johnson is near the top. Or Chris Paul or Tim Duncan or Kevin Durant.

What is strange is that LeBron is at #363 with a rating of -1.70.

I'm calculating RAPM exactly the way I've done it in the past (using cv.glmnet to find lambda that gives minimum cv-error). The lambda I'm getting is ~100. This is puzzling, to say the least.

v-zero, have you found something similar when you do 1-yr non-prior-informed ridge regression?

To clarify, you're calculating single year RAPM for 2013 with a prior vector of all zeros and precision values all equal to lambda?

I haven't calculated it so I can't say I have seen the same result, but the lambda looks right assuming your weights vector is right. I'll calculate it later and let you know.

As for the strangeness... I wouldn't be surprised. Single year NPI RAPM is right next to APM in the chocolate teapot stakes, it's seriously useless. Beyond the standard collinearity issue there is also the major issue of DoF for a single-year study.

v-zero wrote:It has taken longer than expected for all sorts of reasons, but I should be posting an up-to-date, improved version of these later today once I have pulled the data down.

A big problem in robustly fitting RAPM is properly configuring the (co)variance matrix for the priors. For single-year RAPM it is no issue, but when using past ratings as a prior there is an important consideration as to what confidence you have in that prior, as that has a large effect on your results. As far as I know JE never tackled this in the Bayesian formalism, deciding upon a fine but more arbitrary method I believe. Anyway, the big deal here is that the strength of priors for rookies is very important. The best example I can give for this is the Durant-Westbrook relationship. The two were virtually never on court apart in Westbrook's rookie season, and as such since Durant was bad the year before, Durant's progress in Westbrook's rookie year gets assigned to Westbrook rather than Durant if the rookie priors (and indeed non-rookie priors) aren't properly calibrated relative to each other. This anti-Durant problem could also be further compounded by the further introduction of rookie Harden later too.

Long story short: RAPM will always have problems with player combinations that almost always play together, but minimising those problems is very important, and can't be done at all using single-season numbers.

How is this going? Will you have time to post some new results this week?

Updated ratings will actually, genuinely be going up tomorrow. I have been incredibly busy of late unfortunately.

On the single-year RAPM note, I managed to find time to run it, and found that LeBron had one of the best ratings in the league, with only Amir Johnson (guy is obviously doing something very right) beating him out in substantial minutes.

The link in the OP will now take you to the most up to date version of RAPM for 2013 - significant improvements have been made in the implementation of the priors, data is up to date as of today on BBREF.

Thanks v-zero. The results look to mostly conform with my subjective feel for these players, with some surprises to keep things interesting. Its great to finally have some RAPM-based defensive ratings.

What are the standard errors like on these ratings? Would they be proportional to Possession count? Also, any plans to publish or share your method for improving the priors?

Standard errors don't really make sense as it's a ridge estimate, but you can basically assume that the variance in the estimate is inversely proportional to the number of possessions. No plans for revealing specifics just now, in part because it's still a work in progress.

v-zero wrote:The link in the OP will now take you to the most up to date version of RAPM for 2013 - significant improvements have been made in the implementation of the priors, data is up to date as of today on BBREF.

Looks really good. Prior is based on previous season's data? I'm asking because Granger can't be far from his prior with so few possessions played.

DIIIIIIRK

Granger is basically his prior, yep.

I have now added up to date single year non-prior-informed RAPM for those interested. Take note that the problems with APM are only diminished when a uniform prior is assumed, as in single year non-prior-informed RAPM.

Are you using a fix prior for first year players, or maybe based on current season stats / college stats / age?