### Adjusted Lineup Rankings

Recently, 82games put up some pages listing the top five-man lineups from this past regular season in terms of plus/minus and points scored and allowed per possession. You can find similar rankings on BasketballValue. I wanted to go a step further and adjust each lineup’s ranking based on the quality of the opposing lineups that it faced during the season.

To do this I started with lineup data from BasketballValue. To adjust each lineup’s offensive rating, I calculated a weighted average of the season defensive ratings of all the opposing lineups that that lineup faced. These defensive ratings were weighted by the number of possessions the original lineup played against that defensive lineup. This meant that for each lineup I had its offensive rating and its average opponents’ defensive rating. I subtracted the second from the first to get an adjusted measure of the lineup’s offensive production. So if a lineup had a good offensive rating but played against poor defensive lineups, its rating was decreased, while if a lineup had a poor offensive rating but played against good defensive lineups, its rating was increased.

The adjustments I made were only one level deep. In college football ranking systems you sometimes see similar multi-level adjustments for strength of schedule that take into account a team’s record, its opponents’ records, and its opponents’ opponents’ records. The same thing could be done here - I’m adjusting each team’s offensive ratings for their opponents’ defensive ratings, but I could first adjust the opponents’ defensive ratings for *their* opponents’ offensive ratings. Theoretically, one could do this infinitely, and I think the results would ultimately be similar to what you’d get from a regression-based method like Dan Rosenbaum uses for his adjusted plus/minus. But I’m just going to do one level of adjusting, partly because it can be calculated pretty quickly with some pivot tables in Excel, and partly because you just don’t gain that much the deeper you go. This is because over the course of a season, things tend to even out, and most lineups end up facing a similar mix of good and bad opposing lineups. The variance in opponents’ defensive ratings is a lot less than the variance in lineup offensive ratings, and the variance in opponents’ opponents’ offensive ratings would be even smaller.

Below are the adjusted rankings for offensive rating, defensive rating, and point differential. I excluded lineups that played together for less than 200 offensive possessions (or 200 defensive possessions). “ORtg” is the lineup’s offensive rating (points per 100 possessions), “oppDRtg” is the weighted average of the defensive ratings of the opposing lineups faced. “offDiff” is the additional points scored per 100 possessions over what would be expected based on the quality of the defenses faced. “DRtg”, “oppORtg”, and “defDiff” are the defensive counterparts to those stats. “totDiff” is the sum of “offDiff” and “defDiff”, which represents the additional point differential per 100 possessions over what would be expected based on the quality of the offenses and defenses faced.

#### Best and Worst Offensive Lineups:

#### Best and Worst Defensive Lineups:

#### Best and Worst Overall Lineups:

#### The Data

I uploaded a table containing every lineup’s offensive and defensive numbers to Swivel (it was too big for Google Spreadsheets). You can view it here or download it in CSV form here.

Thanks very much.

For some reason I am not seeing a team column at google spreadsheets or in the csv file.

Will study the file a bit before commenting on the data but clearly this represents a great leap forward beyond the raw 5 man lineup data as you show that the quality of lineups faced varies significantly.

Comment by Mountain — April 25, 2008

Yeah, there isn’t a team column. I didn’t put it in basically out of laziness - it wasn’t in the original BasketballValue data, and I didn’t feel like writing a formula to insert it. But it wouldn’t take much time, so I’ll try to go back and add it some time soon.

Comment by Eli — April 25, 2008

Wow, amazing stuff.

Some observations:

- A lineup with Steve Nash among the top defensive teams? Shawn Marion must have been good.

- It doesn’t seem to be Marbury’s fault that NY sucked so much.

- Nash and Stoudemire really make PHX’s offense tick.

- Denver’s new strategy is trying to beat LAL with one of the worst lineups in the NBA. If they’re indeed an OK defensive team, it is because of Kenyon Martin.

Comment by Jacob — April 25, 2008

This is very interesting work, something I’ve played around with in my head but never tried to actually do anything with it.

That said, the next level in my thinking is: can you isolate player performance based on who they’re playing with and who they’re playing against?

Since you’ve already put the data together, are there enough combinations of say Nash without the “other guys” to determine how much the “other guys” contribute to his performance and vice-versa?

Comment by Ryan J. Parker — April 25, 2008

What you’re describing is basically Dan Rosenbaum’s adjusted plus/minus. As for whether there are “enough combinations,” the answer is probably not if all you have is one season’s worth of data.

BasketballValue calculates adjusted plus/minus for the current season here:

http://basketballvalue.com/topplayers.php?year=2007-2008

And you can find a lot more links on the topic in the “Dan Rosenbaum’s adjusted plus/minus” section here:

http://www.countthebasket.com/statlinks.htm

Comment by Eli — April 25, 2008

Yeah I have read his work on the topic before, although for some reason (at the time at least) it didn’t seem to do what I was looking for.

I’ll look again. :)

Comment by Ryan J. Parker — April 25, 2008

Adjusted player pairs and triplets would be another interesting revelation.

Comment by Mountain — May 4, 2008

I now realize that Adjusted player pairs and triplets could be found - by this method- by manually sorting and summing the appropriate 5 man lineups. I might try that for a few pairs but if you do a global sort or perhaps add a search function to speed it up that would be cool.

Comment by Mountain — May 4, 2008

I cannot thank you enough for the blog.Thanks Again. Much obliged.

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