Adjusted Player Pairs

[J.E.]

Thanks you DSMok1 and his suggestion to "Just list all pairs currently on the court as the variables" I was able to compute adjusted player pairs today.
I built pairs for offense only. Offensive lambda was 4000. Defense was done the same way as always. Test set performance was pretty much the same as it was with standard RAPM.

http://stats-for-the-nba.appspot.com/pairs_explained
http://stats-for-the-nba.appspot.com/pair11
http://stats-for-the-nba.appspot.com/pair10
http://stats-for-the-nba.appspot.com/pair09
http://stats-for-the-nba.appspot.com/pair08

Multiyear coming tomorrow or so. Only offensive impact is listed in those ratings. Can't comment on the results right now, need sleep. Have fun

[Crow]

Thanks for sharing this interesting work.

(The 1000 possession cut-off for listing on the result pages would be equal to about 7 minutes per game if the pair played every game.)

[J.E.]

(The 1000 possession cut-off for listing on the result pages would be equal to about 7 minutes per game if the pair played every game.)

Possessions are offense and defense together, so it's ~3.5 MPG.

I think the (extremely obvious) next step would be to use (RatingP1+RatingP2)/4, with RatingPx derived from standard RAPM, as a prior for every pair. If any lambda other than infinity turns out to be optimal it means we improved on test set performance. (Because lambda == infinity would lead to the exact same test-set-prediction-numbers as standard RAPM)

[Crow]

"Possessions are offense and defense together"

Right, in this circumstance I guess. Thanks for the correction.

I can see options for analysis- representation of different combos of perimeter-interior in the rating tails, same for age / NBA experience, offensive / defensive rating "bias", usage, FGAs, FT/FGA, dominant shot location (inside / outside), maybe even dominant play type, etc.

Maybe I'll do some of that later.

Do you plan any such analysis yourself?

Use of a prior would seem like a worthwhile variation to try and see what difference it makes.


(Some sort of blending of a boxscore statistical rating and RAPM would still seem like a worthwhile variation in general and even for pairs and even with a prior.)

[J.E.]

Do you plan any such analysis yourself?

I'll glance over the numbers once and then and look for anything interesting but I won't do any thorough analysis. If you want to do some analysis I would appreciate it. Maybe wait on multiyear numbers or on the numbers with different priors. Those should be a little more helpful. I'll post them in a couple of days.

One thing I found interesting is that James Jones is currently not getting any minutes for the Heat. Is he injured? Why are they playing Mike Miller instead? Jones and Wade are a really good pair, it seems.

[DSMok1]

J.E., I was thinking about this--

Obviously, with player pairs, the multicollinearity is much worse than even with regular APM. What's more, the collinearity is likely more consistent through the season. This could perhaps cause the lambda value to be incorrectly low when validated against same-season data. Do you think this is a valid worry?

I would add that multi-year information for player pair data would probably be more useful than even for individual players--if there is a synergy there, it'll probably be quite consistent. Do you agree?

[Crow]

I might do more later when the multi-year data is available as you suggest.

But to get started, I looked at 28 pair offensive ratings of 1.5 or higher and 3,000 possession or more for perimeter and interior positions and about half were perimeter-interior and half were perimeter-perimeter. None were interior-interior. Maybe the 3,000 possession cutoff I picked hampered that?

Looking at about 135 pairs +1 or better and over 1,000 possession only a very few were full-time PFs & Cs. A few more had a combo forward involved. Scarcity of bigs with a positive offensive impact is probably a good part of this.


Only 4 pairs out of about 135 pairs over +1 involved 2 guys over 25% usage, though there were only 8 such pairs where each guy played over 20+ minutes per game for the season in the league to check. Still it seems notable that just 50% of such high usage pairs were over +1 on Adjusted Pair Rating and the other half less than that.


Of the 28 pair ratings of 1.5 or higher and 3,000 possessions or higher, it looks like 1/3rd of the guys involved were over 30. Almost 1/3rd of the guys involved averaged 5+ FTA/game. I only saw 5 pairs with a guy under 16% usage on this very top performing pair list.

[J.E.]

Do you think this is a valid worry?

I think this is a valid worry.

I would add that multi-year information for player pair data would probably be more useful than even for individual players--if there is a synergy there, it'll probably be quite consistent. Do you agree?

I would agree. I'll try to get the optimal lambda value for multi-year analysis in a couple of hours. Do you have any other ideas to attack this problem, other than using multiple years?

Crow, thanks for the analysis. If you want to do further analysis I think it may be more important to look for the difference in rank between "rank of pair" vs "rank from summed individual numbers". The fact that Nowitzki+Terry or Bosh+Wade are good offensive pairs doesn't tell us anything new, put their standard RAPM numbers together and you see the same thing. Only when there is a big difference in rank we can see whether a certain pair performed way above/below what we would have expected anyway.

Multi-year should be available in a couple of hours. Defensive pairs in a couple of days

[bbstats]

Maybe it would be (more) beneficial to show (Adj.Pair.Value - SumRapm(p1,p2)) ? So that its telling us something new...

[Crow]

I agree with the value of looking at the difference in rank between "rank of pair" vs "rank from summed individual numbers". I calculated the difference as a column but in the rush to post something I left that part unused yet.

This is one perspective: "Only when there is a big difference in rank we can see whether a certain pair performed way above/below what we would have expected anyway."

Still, there is another perspective to these 2 numbers and their relationship. Standard RAPM numbers for players are for the player with and without the other. Why introduce what a player does without a specific player if you want to know what he does with a specific player? It could cloud the main issue with other player relationships (probably at a specific position or at least a general role). The pair numbers are all the minutes of the pair together and nothing else. Couldn't that be considered enough on its own, at least for one perspective, uncluttered by without the player, which is not the primary focus of this number?

The aggregate player exists off the court and on paper, but the "aggregate player" doesn't ever play as the aggregate player, only as the player with or without the other specific player. If they are different that is of course interesting, but if you want to know what he does with a player, the with the player pair rating gives an answer.

You can go further of course and I would to try to understand what is actually happening with / without but with / without is a different issue than just "with". I'd look at player pairs alone and the differences of player pairs with the sum of overall player ratings (and probably calculate without the other player ratings too) but I think the pair rating has value on its own that is uniquely targeted and valuable.


Looking briefly at difference in pair rank sum of individual ranks for the top 28 (and recognizing that this is a small sample and only a starting place), the best half of that top group are still about half were perimeter-interior and half were perimeter-perimeter. Guys over 30 years and guys with 5+ FTAs/game are much less common in this top of the top subset based on ranking difference than they were among the full 28 pairs over 1.5. So maybe these facets are not as important in sparking big additional positive impact as their higher frequency of appearance in the top 28 performing pairs might have suggested.


But I'll wait for the multi-season offensive data to do any further analysis with probably a larger part of the dataset. And I will look forward to the defensive data as well.

[Crow]

If possible, it would be handy to have team identifiers on the multi-season pair list (or any list) for sorting.

[J.E.]

If possible, it would be handy to have team identifiers on the multi-season pair list (or any list) for sorting.

With a quick hack I can put a team name in front of the player names, but the team name could be any team the player has played for in the last 4 years, not necessarily the team the player has played for in 2011. Would that be enough?

[Crow]

Yes, that would be fine. Making some manual adjustments is easier than fitting team names to the whole database. Thanks for the assistance.

[J.E.]

http://stats-for-the-nba.appspot.com/defensive_pairs

2008 to 2011. Didn't actually do any crossvalidation, just assumed a defensive lambda of 4000. Might not be perfect but should be really close.
Jose Calderon is part of the 8th best pair (with Amir Johnson) and he's also part of the 2nd worst pair (with, you guessed it, Andrea Bargnani).

Multiyear offensive pairs and triplets are being computed right now

[Crow]

Thanks for the data.

And the team identifier. I can work with that some to make additional columns and get the ability to sort by team.

Also, on the defensive pair list the first column is currently labeled Offense per 100. I assume it should be Defense per 100.