Is there diminishing returns to RAPM?

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colts18
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Is there diminishing returns to RAPM?

Post by colts18 » Fri Aug 08, 2014 5:00 pm

If you pair up a few high RAPM players, would their impacts total the combined sum of their RAPM or will there be diminishing returns? I'm asking in regards to the 2015 Cavs. xRAPM is predicting them to win 65 games but I will definitely take the under. I see a small chance at that happening. IIRC RAPM had the 2011 Heat as a 70 win team. I'm not sure you can add to 2 or 3 +5 RAPM players and get a +10 or +15 team. I see it like the usage/efficiency tradeoff.

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DSMok1
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Re: Is there diminishing returns to RAPM?

Post by DSMok1 » Fri Aug 08, 2014 5:18 pm

I think there is a diminishing return, particularly on offense. I've been asking for studies on this--it can be framed at the lineup level, within season (like Eli Witus' diminishing returns in rebounding study). In other words--take your RAPM dataset, and the player RAPM values on O and D. Look at individual lineups and see what the player sum is, and compare with how the lineups actually performed.
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gzchen
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Re: Is there diminishing returns to RAPM?

Post by gzchen » Fri Aug 08, 2014 6:11 pm

Not directly related to your question:
I've seen a few people make various rough projections based on minutes estimates and RPM/RAPM, and I realize Silver mentions the potential impact of injuries briefly, but when making these estimates, people should probably use "total minutes divided by 82" instead of "minutes per games actually played" as their measure for "minutes per game." Sure, that would require more work to estimate accurately, but someone like Varejao definitely should not be projected to play 82 games and this would affect his projected minutes fairly significantly. This along with the likely diminishing returns to RAPM (which, given what DSMok1 suggests, might be especially significant given that, other than Varejao, the main Cavs players all add their value offensively as opposed to defensively) would probably outweigh any potential defensive improvement from guys like Irving, Waiters, and LeBron (either from lower usage or organic growth), and I would definitely take the under on 65 as well.

Crow
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Re: Is there diminishing returns to RAPM?

Post by Crow » Fri Aug 08, 2014 9:19 pm

I believe Jeremias has said that player rapm summed is a pretty accurate forecast on average for judging combined rapm of players playing together and that pair rapm isn't on average that much different than player rapm summed. But I recall the past data did have a number of pairings where the pair rapm was sharply different than the sum.

xkonk
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Re: Is there diminishing returns to RAPM?

Post by xkonk » Fri Aug 08, 2014 9:37 pm

I remembered the same as Crow; assuming the link works it's on page 2 of this thread viewtopic.php?f=2&t=227&hilit=RAPM+pair

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Re: Is there diminishing returns to RAPM?

Post by Bobbofitos » Sat Aug 09, 2014 12:00 am

I think "if perfectly healthy" / those mins are guaranteed, 65 wins really isn't a bad line.

That said, there is no way that team maintains perfect health. I suppose there's a reason to predict the most optimistic projection possible, but I'd rather just aim for the best prediction, period... Which doesn't have Andersen Varejao playing 26 mins a night, for 82 games, for example. (It's been 4 years since he hit that sum, and only has done it twice in his career)

mtamada
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Re: Is there diminishing returns to RAPM?

Post by mtamada » Sat Aug 09, 2014 6:42 pm

This seems like deja vu. When Miami assembled its Big Three there were all sorts of discussions about whether they would break the record for wins in a season. When Boston assembled its Big Three there was similarly a "Boston rolls" thread here in apbrmetrics.

I suspect that a simple summation of Plus-Minus stats (from whatever model we pick) is a good approximation for small changes, but not so good if we're talking about a massive influx such as a pair of all-pro players being added to Cleveland's roster. I.e. for small changes in talent we don't have to worry about diminishing returns, but for big changes we do.

In addition there's regression to the mean. If we take this season's first team all-pro players, regardless of whether we assemble them onto a single team or scatter them across five separate teams, it's unlikely that all five of them will be first team all-pro next season. RAPM of course already has some regression to the mean built into it, but even so to take top outcomes from any process means that we have to expect that those top outcomes will experience regression.

Or yet another way to put it: if we have a model which is predicting 65 wins for an NBA team, that model probably needs to be regressed. Unless the team has assembled a historic level of talent, and even then it's not a guarantee: Boston won 66 in the first year it assembled its Big 3, but Miami famously semi-fell on their face with only 58 wins and a loss in the Finals.

So whether we want to call it diminishing returns or regression to the mean, yeah 65 wins seems like too high a prediction.

AcrossTheCourt
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Re: Is there diminishing returns to RAPM?

Post by AcrossTheCourt » Sat Aug 09, 2014 9:39 pm

First of all, there's a major problem with that projection: Varejao is projected to play more minutes than he has since LeBron was last there, and Irving will play more minutes than he's ever played. It's really optimistic with its minutes distribution. If you use more reasonable estimates you get closer to a "plain" 60 minutes.

I touch on these issues a little on an article I'll have today, but diminishing returns with respect to WHAT? That is the issue.

LeBron and, say, Mutombo would have not diminishing returns because their skills and values do not overlap and interfere.

LeBron and Wade interfere with each other because their values are maximized with the ball in their hands.

By the way, someone ask Nate Silver to show his offensive/defensive splits. I'm pretty sure his prediction would have them near a +10 offense.

edit: By the way, few thought Boston was going to be amazing in 2008. Most predictions were around 50 wins. RAPM liked Boston a lot more of course because of Garnett.

Mike G
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Re: Is there diminishing returns to RAPM?

Post by Mike G » Tue Aug 12, 2014 3:26 pm

AcrossTheCourt wrote:...
LeBron and, say, Mutombo would have not diminishing returns because their skills and values do not overlap and interfere.
...
edit: By the way, few thought Boston was going to be amazing in 2008. Most predictions were around 50 wins. RAPM liked Boston a lot more of course because of Garnett.
RAPM would not have predicted that between 2007 and 2008 Rondo would become an amazing player, or that Perkins would suddenly develop/peak.
Glen Davis, James Posey, Eddie House came along and piled on some wins.
Leon Powe just kicked ass.
Garnett, Pierce, and Ray were all at least as good as they'd been the year before.

So it may actually be that player PM did not quite add up in a linear fashion. If not for a bunch of unanticipated contributions, they'd have lost several more games.

Crow
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Re: Is there diminishing returns to RAPM?

Post by Crow » Tue Aug 12, 2014 3:51 pm

Coaching / lineup synergy impacts remain fairly lightly researched and understood. 2007-8 Celtics starting unit was best performing regular season lineup used over 250 minutes and 3rd most used lineup.
In playoffs they had 2 of 7 best performing lineups used over 50 minutes.

David Sparks and his player and lineup type analysis had not been brought into Boston's shop before the title but they apparently had common interests. Should re-do that work using a stronger set of inputs. Advanced stats, perhaps including or exclusively rapm factors and not just core box score stats.

schtevie
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Re: Is there diminishing returns to RAPM?

Post by schtevie » Tue Aug 12, 2014 4:44 pm

Mike G wrote:
AcrossTheCourt wrote:...
LeBron and, say, Mutombo would have not diminishing returns because their skills and values do not overlap and interfere.
...
edit: By the way, few thought Boston was going to be amazing in 2008. Most predictions were around 50 wins. RAPM liked Boston a lot more of course because of Garnett.
RAPM would not have predicted that between 2007 and 2008 Rondo would become an amazing player, or that Perkins would suddenly develop/peak.
Glen Davis, James Posey, Eddie House came along and piled on some wins.
Leon Powe just kicked ass.
Garnett, Pierce, and Ray were all at least as good as they'd been the year before.

So it may actually be that player PM did not quite add up in a linear fashion. If not for a bunch of unanticipated contributions, they'd have lost several more games.
OK. This is a bit weird. To begin, let's keep things in chronological order. There was no RAPM in 2007. The R had not yet gotten there (at least publicly). But it is true that few (hmmm, were there even that many?) thought that Boston was going to be amazing, and this despite more than ample, public +/- evidence to support the point. Furthermore, as a matter of history, it is the Garnett trade that "popularized" the notion that basketball can best be understood in +/- terms.

But this aside, Mike, I simply don't recognize the reality suggested by your "RAPM would not have recognized..." remark.

We know for a fact that, ex post, RAPM did not say that Rondo became an amazing player between 2006-07 and 2007-08. Taking Jeremias' numbers, he went from 1.4 to 0.6. Similarly, Glen Davis, James Posey, and Eddie House, didn't come in and pile on wins, at least in as much as they had negative ratings, -2.1, -1.5, and -1.4, respectively. Then Leon Powe's ass kicking was only to the tune of +0.5.

The point is that you can see what the minutes-prorated pre- and retrodictions of RAPM were, compared to actual offensive and defensive efficiency/rating/whatever, and what you see is that the offensive pre-and retrodictions are very accurate, whereas the defensive contributions significantly underestimate actual performance.

So, no diminishing returns on offense and increasing returns on defense? Or is the latter more plausibly the unattributed Thibodeau effect.

But to the larger point, there is no particular reason to believe, a priori, that all hypothetical player combination will exhibit diminishing returns. (Kind of) contra Daniel's claim, this is because there is no theoretical basis to generally exclude constant or increasing returns; the outcome depends on the specific, hypothetical player/skill combinations in question.

Mike G
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Re: Is there diminishing returns to RAPM?

Post by Mike G » Tue Aug 12, 2014 5:25 pm

RAPM would not have predicted that between 2007 and 2008 Rondo would become an amazing player, or that Perkins would suddenly develop/peak.
Glen Davis, James Posey, Eddie House came along and piled on some wins.
Leon Powe just kicked ass.
Garnett, Pierce, and Ray were all at least as good as they'd been the year before.
Quoting myself^^!
Assumed "would not have predicted..." implies "...had it existed". Sorry if the brevity was misleading.
It's a possibility that players can improve most or all of their efficiencies and still 'lose' in RAPM. Rondo shot .496 eFG% in 2008, up from .424 the year before. ORtg, DRtg, TO% all way better; Usg% and Ast% also stronger.
http://www.basketball-reference.com/pla ... ora01.html

I don't know who's ass Mr Powe was kicking, perhaps a bunch of subs; but by both PER and WS/48, he was the 2nd strongest player on the team.

Code: Select all

2008                              2007
Celts    mpg   PER   WS/48     PER    WS/48
Pierce   36   19.6   .207      21.7   .148
R Allen  33   16.4   .177      21.6   .136
Garnett  29   25.3   .265      24.1   .171
Rondo    29   15.6   .150      13.1   .064
Perkins  24   13.3   .156       9.5   .042
Posey    23   12.0   .164      12.7   .130
House    19   13.0   .127      15.0   .094
T Allen  18   10.7   .093      17.0   .111
Davis    12   11.3   .128         
Powe     11   20.9   .256      14.6   .116
Both PER and ws/48 are suspect, for rather opposite reasons. A reduction in offense may account for PER dropoffs by Pierce, Ray, House, and especially Tony Allen.
All players (other than TA) had much improved WS/48, due to the team-defense influence on that stat.

A below-NBA-avg player off the bench is still making contributions. Opponent bench players are also below-avg, y'know.
Contributions = more wins.

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