Plus or Minus? Khris Middleton and Zaza Pachulia headline who helped (and hurt) the 14/15 Milwaukee Bucks

Khris Middleton's real plus-minus (RPM) may have been the most-cited stat of the Milwaukee Bucks' breakthrough 14/15 season, a fact as encouraging as it was bizarre. Seriously: how often do you get to hear Sidney Moncrief talking about stats derived from ridge regression models?

Novelty aside, Middleton finished the season an impressive 10th in the entire NBA with a +6.1 RPM, which basically means that having Middleton on the court was worth about six points per 100 possessions relative to a league-average player. And yes, that's really, really good. You can read a lot more about what RPM is here and here, though at a high level it's essentially a way to take the raw +/- data you now find in box scores and (using a huge, complicated regression model) strip out the biases that come from playing with different teammates and against opponents of varying quality. It's also intended to be predictive, though glancing at the data from the past two years suggests it can swing considerably over time. And so it goes.

In short, no one will claim RPM is perfect, or for that matter simple. ESPN doesn't provide standard errors for its RPM estimates, and for guys with low minute totals they would likely be quite high (possibly to the point that their RPM figures are mostly worthless). It's also somewhat abstract; a couple analytics guys who are far smarter than I am told me at the Sloan conference in March that RPM isn't something they would regularly cite in conversations with a GM -- though outlier situations such as Middleton's are always worth mentioning. In that regard raw on/off data is still an easier concept for most to grasp, and by netting out how a player does compared to his team without him we can at least implement some crude method of control.

Since there's no place that conveniently organizes team RPM and allows you to compare it against "regular" plus-minus data, I thought it would be of interest to pull the Bucks' data and present it in a single place. First, let's look at a table showing both, with better performers on offense and defense highlighted in green. For raw plus-minus, I included on-court, off-court and net differential.

Because RPM also breaks down symmetrically into offense and defense, we can also think about it graphically -- note that the further a player is towards the top and right, the better.

The Bucks' best players by RPM standards rated similarly well in raw plus-minus terms, with Middleton and Zaza Pachulia the Bucks' best in aggregate. Speaking of which: Zaza ranked 15th overall and second among all centers in RPM (behind DeMarcus Cousins), which speaks volumes about how well he's fit in with Jason Kidd's system. The only downside is that I have a hard time imagining Pachulia replicating those results next year (RPM's predictive powers be damned), though the reality is that the same is likely true of any higher profile big man the Bucks might sign this summer. Can anyone live up to the standards of 2015 Zaza Pachulia? Did anyone think we'd ever ask that question?

Both Middleton and Pachulia made huge gains from a year ago, with Middleton in particular seeing his defensive RPM make a complete turnaround -- from a horrendous -3.50 last season to +4.11 this year. It's difficult to explain how his numbers could swing that wildly (especially given the priors methodology of RPM), though the results also underscore how a team's defensive system can play a huge role in player performance. In case you were under a rock for the last two years, the Bucks were indeed terrible under Larry Drew and excellent under the Sean Sweeney-led system implemented by Jason Kidd, so it shouldn't be shocking that a number of Bucks players saw major gains in terms of their DRPM.

That group includes John Henson, who posted an inexplicably bad -2.35 DRPM last year (among the worst for all centers) and jumped to a very respectable +1.32 this season. The latter still wouldn't paint him as an elite defender, though it's more than respectable and jives with the Bucks' strong defensive efficiency with him on the court (97.6 pts/100 allowed). Less encouraging is Henson's offensive RPM, which went from a terrible -3.42 last year to an unsightly -4.16 this year. No shocker there -- the Bucks were generally terrible offensively when Henson was on the court, with his 96.2 pts/100 rating the worst among any regular rotation player.

The most interesting divergence between RPM and raw point differential is at point guard, where both Michael Carter-Williams and Kendall Marshall helped the Bucks outscore opponents by a wide margin despite looking below average by RPM standards. Note that ESPN doesn't provide pre- and post-trade estimates of RPM, though we do know that MCW's ORPM at the time of the trade was an ugly -3.28 and it improved modestly after he landed in Milwaukee. The strange part is that the Bucks were really good with MCW on the court, especially on the offensive end, where you would think his brick-laying, non-floor-spacing ways would be especially harmful. Maybe his style meshed better with the other Bucks than we might expect, or maybe (as the RPM data would suggest) it's just a quirk of sharing the court with a starting five that played really well in spite of him. Stay tuned -- next season will likely tell us plenty about how good the Bucks can be with MCW running the show, though for now we can take some solace in the team's post-trade lineup data.

On the less promising side, the Bucks' rookies may want to shield their eyes of virtually any plus-minus metric. Lineups featuring Jabari Parker were notably poor on both ends, with Johnny O'Bryant's season a disaster no matter what type of stat you're using. As for Parker, we knew he would face a steep learning curve on the defensive end, though it's tough to figure out how much of the starters' early season issues were related to his problems vs. a general lack of cohesion. We also don't know how much he would have improved as the season wore on, which is yet another unfortunate byproduct of the torn ACL he suffered in December. Of the Bucks' eight most frequently-used lineups, only one had a negative point differential and it featured both Parker and Larry Sanders (and it was really negative). Via NBA.com:

Interestingly, Sanders' presence did little to stop the defensive bleeding of the Knight/Mayo/Giannis/Parker lineup that got an extended look in the first two months of the season, though small sample caveats (137 minutes isn't a ton) do apply. And while you'd expect Parker would have improved over the course of this season if he hadn't gone down with his ACL injury, it also raises obvious questions about how much Parker can actually help the Bucks when he first returns next season. I'm all for giving him big minutes when he's ready to play, but he'll still be a guy with limited NBA experience on top of the usual challenges of coming back from a major knee injury. So calibrate your expectations accordingly.