Chicago76 wrote:Long post, so bear with me:
I've been thinking a bit about RAPM lately. Specifically, how RAPM is essentially a linear solution to a non-linear problem and how that can impact value estimates. We know that lineup A vs. lineup B won't necessarily have a close outcome with respect to the RAPM values estimated. Players aren't robots. We also know lineups are non-randomized and limited as are player minutes. This means player rotations can often complicate the system's ability to identify which player is responsible for the relative outcome vs. another lineup. This is the mathematical error portion and people who are much better versed in the nuts and bolts of the mathematics can run circles around me (and the rest of us) on this part.
When I refer to a non-linear problem, the issues I'm trying to wrap my head around relate to redundancies, synergies, team construction philosophy, and team quality. These issues could suppress or exaggerate a player's RAPM outside of mathematical error/deviation computations.
Team quality is the most intuitive, with the two core issues here being diminishing returns and coasting. Adding a +5 RAPM player to a good lineup is not likely to produce incremental improvement equivalent to adding the same player to a bad team, all else equal. As the quality of teammates increases, a player's incremental impact should decrease. This is the direct RAPM player impact of a good team. Indirectly, good teams are also prone to coasting on leads more frequently, which would suggest that the Ortg-Drtg differential of a good team is to some extent suppressed. If you're up by 15 with 9 minutes left in the game, a team doesn't need to keep their foot down to destroy someone by 25. They just need to play a low-risk/low energy style that will maintain their probability of a W while conserving energy for the demands of the rest of the season. Intuitively, this makes sense to me, although to test it someone would need to look at NPI changes when high impact players face substantial teammate quality changes season over season. There are exceptions (Garnett being a good one w BOS). There is also the issue that high impact players frequently change teams when they are being underutilized and/or their attitude is negatively affecting their play, which would suggest an RAPM bounce the post-team change. Generally though, I would expect this principle to hold true.
What is interesting is comparing RAPM MIN Garnett vs. Duncan over the same period and grouping them according to how good their respective teams were when both were off (simple +/- per 100). 2002-07, MIN had 4 years of -10 per 100 or worse without Garnett. His average normalized RAPM (from Doc's spreadsheet) in those years was 9.8. For the other two years where MIN posted better off-Garnett numbers (-4.2 and +1), his RAPM was only +6.0. Duncan’s Spurs always had better off-Duncan numbers. He was +8 the two years the Spurs posted solid off-Duncan numbers (+2.5 or higher) and Duncan was +9.5 in the other 5 years, four of which were years the team was around 0 to -1 with Duncan on the bench. This still doesn’t explain BOS Garnett though.
The other component I'm thinking about is the more complicated issues of synergies/redundancies and team construction philosophy. This is on a team level. I'm not looking at this from a player characteristic or portability angle. If we suspend reality for a moment and assume that all teams are equal with respect to talent evaluation, drafting, wheeling/dealing, FA acquisition, every player is paid in accordance with their production, and every team spends the exact same amount of money, then every team in the league is mediocre and talent/ability is perfectly distributed across the league. There is a continuum of construction strategy ranging from high risk/high reward to low risk/low reward. The high risk and reward team would be assembled in a way that everyone had a very specific role they performed very well. Players are compartmentalized with respect to skill set and the team relies upon discrete skill sets feeding others to create a perfectly synergistic and additive RAPM output with no redundancies. This team would win a lot until one of those pieces either gets hurt or slumps. Then they would suck horribly. The low risk/low reward team would feature built in redundancies. This team would never hit the same level of play as the first team, but they'd be able to hum along with an insurance policy against injury or a player slump.
The low risk strategy is the Spurs in a nutshell, except they are obviously far above average from a talent evaluation and personnel management standpoint. They were remarkably consistent, regardless of who might have missed stretches of the season with injury. Duncan played at least 33mpg in his first 11 non-CBA shortened seasons. Apart from a 63-win season, they never won more than 60 games, but they always won at least 53. They hit 56-58 wins more than half the time, with the other seasons not too far off (53, 54, 59, 60). In Duncan’s first 10 years, they weren’t superlatively dominant in the way that many dynasties are where they can reel off consecutive titles or finals appearances. They never even went to the WCF in consecutive years. They were consistently good and over the long run they were able to win a title every 2-3 years with reasonably deep bench play and a variety of players who rose to the occasion in key moments. This is what redundant teams do. They maintain a consistent level of play, and quite likely individual player RAPMs among many of their most important players were suppressed a bit. BOS was a bit more compartmentalized w/ Allen, Rondo, and Garnett in particular. They didn’t have a way of playing around the issue of Garnett being on the bench quite as easily as the Spurs did with Duncan. Part of that may be that Garnett offers an extremely rare skill set that happens to be valuable. But another part might be construction or Popovich’s ability to do things with alternate lineups Rivers couldn’t.
Curious to hear what others think of my little theory. Re: Garnett v. Duncan, I think you can make a reasonable case for either. Their respective RAPMs are close enough, due to statistical error and the issues I mentioned, that the case isn’t made or lost for either on the basis of RAPM. Someone’s selection of one over the other will be determined more by what the selector places importance upon rather than a clear cut statistical case.
Not even getting into the math, but just philosophically, there is a very interesting interpretation to be made from your post. RAPM was never conceived to measure who the best basketball player is...it is intended to be a measure of how much a player contributes to their team's success.
So if your argument that you're making above turns out to hold water, you're essentially making a reasonably compelling argument that over the bulk of their careers Duncan didn't have to impact the games as much for his team to be successful. This wouldn't necessarily prove that Garnett or Duncan were better, but it would indicate that Duncan wasn't as vital to his team's fortunes through the years as Garnett.
And what makes that a really interesting argument, is that it's the EXACT argument that Garnett supporters have been making since the 90s. That Duncan is an AMAZING player, but that he's been blessed to be on a team with excellent materials and a great system. This in no way knocks Duncan at all. But what it does is provide context to the comparison. Because if the root of the case for Duncan over Garnett is based on team success...and if we're honest, that's the ENTIRE basis for the majority of people...then it is hugely vital to acknowledge that Duncan's teams were designed and executed such that he didn't have to be relied on so heavily for the team's success.
You can't get carried away too far in either direction with that particular line of logic. But it is definitely food for thought
