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New Adjusted Plus-Minus Ratings for 2007-2008
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Mountain



Joined: 13 Mar 2007
Posts: 1527

PostPosted: Wed Nov 12, 2008 10:56 am    Post subject: Reply with quote

Thanks for the follow-up.

"Define high usage players using a median split (07-08, mp >= 1000). "

19.5 from results at basketball-reference.com for 254 player sample
http://www.basketball-reference.com/fc/tiny.cgi?id=L1457

"Within that group define high and low ORTG players with another median split."

Per b-r 108.8.


"The correlation b/t offensive apm and usage is the same across efficiency levels (r = .43)."

Not sure what you mean by this, especially the "b/t". Using your choices (which would be?) you already this?


Last edited by Mountain on Wed Nov 12, 2008 11:25 am; edited 1 time in total
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Brian M



Joined: 25 Nov 2006
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PostPosted: Wed Nov 12, 2008 11:09 am    Post subject: Reply with quote

b/t = between, sorry.

I mean that within the high usage, low efficiency group, the correlation between offensive apm and usage is .43. In the high usage, high efficiency group, the correlation between offensive apm and usage is also .43. So the relationship between usage and offensive apm is not modulated by ORTG, as also suggested by the weak interaction effect in the regression analysis.
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Mountain



Joined: 13 Mar 2007
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PostPosted: Wed Nov 12, 2008 11:27 am    Post subject: Reply with quote

Ok on the b/t.

So you defined high/low usage and efficiency previously to answer that issue? How did your values compare to these medians I looked up? The same?
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Ilardi



Joined: 15 May 2008
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Location: Lawrence, KS

PostPosted: Wed Nov 12, 2008 5:04 pm    Post subject: Reply with quote

Brian M wrote:
I took a look at correlating the adjusted +/- data to 2007-08 PER for players with >= 1000 minutes played. (I suppose it would be more appropriate to take a weighted average PER over several seasons mirroring the apm data, but alas.)

correlations of PER with:
total apm: r = .50
off apm: r = .58
def apm: r = .05

Regressing total apm onto PER:

apm = .4954 * PER - 7.5031

So a rough but simple rule of thumb appears to be apm ~= (PER-15)/2, though the estimate is rather noisy (std dev of residuals = 3.4) because PER does not capture any variation in defensive apm.

The correlations between ORTG and off apm (r = .48 ) and DRTG and def apm (-.49) are pretty solid. Interestingly, usage rate correlates with offensive apm (r = .44) but not ORTG (r = .02), consistent with the hypothesis that usage has offensive value. (Though alternatively, perhaps players get higher usage in virtue of whatever they do offensively above and beyond what shows up in ORTG.) Doing a partial correlation to control for differences in offensive apm, a negative correlation between ORTG and usage emerges (r = -.24, p = .0001)

Taking the average of zscore(ORTG) and -zscore(DRTG) gives correlation with apm r = .5. apm correlates with win shares slightly but perhaps not significantly better than PER (r = .55)


Thanks for this very useful information. As I suspected, PER is almost completely unrelated to defensive APM. It's also encouraging to learn that offensive APM, while overlapping considerably with PER, also has some unique variance (part of which is shared with usage).

I wonder: would you be willing to make your spreadsheet for these analyses available? There are some additional analyses I'd love to do when time permits (including some with metrics like eFG% allowed, Defensive Composite Score, etc.), but it would be fantastic not to have to enter all the data from scratch!
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Mike G



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PostPosted: Wed Nov 12, 2008 6:21 pm    Post subject: Reply with quote

davis21wylie2121 wrote:
... a team's total efficiency differential (ORtg-DRtg) is equal to the minute-weighted average of its players' adjusted +/- scores.
..

If Team A consists of 1 player whose APM is +10, and he plays the whole game; and other players who net zero APM ...
And Team B is entirely average (zero APM) ...
And the game goes 100 possessions ...

Will Team A tend to beat Team B by 10 points? Or by 2 pts?
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Ilardi



Joined: 15 May 2008
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Location: Lawrence, KS

PostPosted: Wed Nov 12, 2008 7:16 pm    Post subject: Reply with quote

Mike G wrote:
davis21wylie2121 wrote:
... a team's total efficiency differential (ORtg-DRtg) is equal to the minute-weighted average of its players' adjusted +/- scores.
..

If Team A consists of 1 player whose APM is +10, and he plays the whole game; and other players who net zero APM ...
And Team B is entirely average (zero APM) ...
And the game goes 100 possessions ...

Will Team A tend to beat Team B by 10 points? Or by 2 pts?


10 pts
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Neil Paine



Joined: 13 Oct 2005
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PostPosted: Wed Nov 12, 2008 7:59 pm    Post subject: Reply with quote

So Steve, are you saying that a team's efficiency differential is not equal to the minute-weighted average of its players' adjusted +/- scores, but rather the minute-weighted sum? This is something I've always wondered and I've seen comments that suggest both, so I'm glad someone is willing to set the record straight.
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Ilardi



Joined: 15 May 2008
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Location: Lawrence, KS

PostPosted: Wed Nov 12, 2008 8:36 pm    Post subject: Reply with quote

davis21wylie2121 wrote:
So Steve, are you saying that a team's efficiency differential is not equal to the minute-weighted average of its players' adjusted +/- scores, but rather the minute-weighted sum? This is something I've always wondered and I've seen comments that suggest both, so I'm glad someone is willing to set the record straight.


Yes, essentially. Once you know the team's minutes-weighted mean (average) adjusted plus-minus value on a per-possession basis, you can then derive the team's overall efficiency differential as equal to 5 times the mean per-possession APM value (since there are always 5 players on the court at a time) times the mean number of team possessions per game.
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Mike G



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PostPosted: Wed Nov 12, 2008 9:09 pm    Post subject: Reply with quote

Ilardi wrote:
Once you know the team's minutes-weighted mean (average) adjusted plus-minus value on a per-possession basis, you can then derive the team's overall efficiency differential as equal to 5 times the mean per-possession APM value (since there are always 5 players on the court at a time) times the mean number of team possessions per game.

I'm still unclear. Are the APM values per 100 poss, or per 48 min? Is the eff-diff per game or per 100?

Also confusing, when I see a Yahoo!sports boxscore of a game in progress, I might see that after 8 minutes, 5 Lakers have played 8 minutes, they lead by 6 points, and all 5 players have a +6 in the +/- column.

If all 5 starters go the full 48 min, and they win by 10, presumably they all have a +10 in the +/- column. But they didn't win by 50, only by 10.

Based on just this sample, would Adjusted +/- simply divide by 5 to give each of 5 guys a +2 APM ? I presume so; and realize that the Adjustment doesn't just re-allocate pt-diff, but also divides by 5. On average.

Sorry to be so elementary. My brain only gets to things whenever it does.
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Brian M



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PostPosted: Wed Nov 12, 2008 9:39 pm    Post subject: Reply with quote

Ilardi wrote:
I wonder: would you be willing to make your spreadsheet for these analyses available?


http://spreadsheets.google.com/pub?key=pSGB2cjdx_ok5R5E1l0RQFw

I should note that my original spreadsheet had a small error because a few rows were misaligned. This has been corrected in the above sheet. The analyses I described before change very slightly using the corrected data-- for instance some correlations change by .01 or so-- but the difference is pretty much negligible.
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deepak



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PostPosted: Wed Nov 12, 2008 9:55 pm    Post subject: Reply with quote

Mike G wrote:
If all 5 starters go the full 48 min, and they win by 10, presumably they all have a +10 in the +/- column. But they didn't win by 50, only by 10.

Based on just this sample, would Adjusted +/- simply divide by 5 to give each of 5 guys a +2 APM ? I presume so; and realize that the Adjustment doesn't just re-allocate pt-diff, but also divides by 5. On average.

Sorry to be so elementary. My brain only gets to things whenever it does.


The sum of all the APMs should approximately equal the final scoring margin. That's the basic assumption behind it, I think. So, in that example, if that starting 5 played a perfectly average opponent, then they each get 1/5th the credit for the final margin.

If the opponents APM summed to, say, +5, and this starting 5 won by 10, then they each would get +1 APM, I think.

I hope I'm not butchering it. I have a hard time grasping this concept as well.
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Neil Paine



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PostPosted: Wed Nov 12, 2008 11:25 pm    Post subject: Reply with quote

Ilardi wrote:
Yes, essentially. Once you know the team's minutes-weighted mean (average) adjusted plus-minus value on a per-possession basis, you can then derive the team's overall efficiency differential as equal to 5 times the mean per-possession APM value (since there are always 5 players on the court at a time) times the mean number of team possessions per game.

Thanks, Steve. I don't know why I always assumed it was a weighted mean and not a sum, but for some reason that thought always stuck with me.

On a related note, have you done any research on diminishing returns? Or would we really expect that a lineup of Baron Davis, Manu Ginobili, LeBron James, Kevin Garnett, and Brad Miller would outscore 5 average NBA players by 48.2 points per 100 possessions?
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Mountain



Joined: 13 Mar 2007
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PostPosted: Thu Nov 13, 2008 12:37 am    Post subject: Reply with quote

Adjusted +/- is done in the context of teams with roles to some degree.

Using Brian's useful file what can we note about the usage part of context?

With a few exceptions guys who achieved a +5 or better on offensive +/- had a 20+% usage rate. The exceptions were Jason Kidd, Chris Quinn and Peja barely while the other 11 had it and average was a 24.3 usage rate.

51 players over 1000 minutes had a 24.3+ usage rate so under 22% achieved this +5 adjusted +/- goal. The average is about +2.5 offensive adjusted with a 26.7 usage rate. If you are yielding less on adjusted +/- with this level of usage you should be evaluated very carefully.

You could look at individual adjusted/usage ratios. The average for this group was about offensive adjusted /usage= 9%. The top guys were Paul (at 36%), Bryant (28.5%), James (27.5%) then Garnett (26%).

Iverson is at a fine 19%. Yao was a zero.

The lowest in this group were Nick Young (-17%), Jermaine O'Neal, David West, Charlie V. and Durant (-5%).

The average defensive adjusted is a -0.2 so proibably half or more of the guys are offensively biased. 2 way players are the way to go as much as possible.

5 teams had 3 guys in this group, 9 more had 2. So remaining teams had about 1 each. With one exception all the guys who were negative were on teams with multiples such players and maybe that is a factor- team inability to optimize offensive adjusted for those 2. But others manage to do it ok.

The next 60 guys on usage return almost no offensive adjusted / usage ratio, at just a tiny fraction above 0. Should secondary scorers by this criteria yielding nothing on offensive adjusted on average should make offense lower priority or a more frantic hunt?

The best in the group are Devin Haris, Jason Terry, Billups and Raashard Lewis and they are the few standouts. The very worst are Curry, Kaman, Warrick, Nachbar and surprising to me Farmar. Stuckey at -10%.

The average defensive adjusted is -0.77. Seems to me you'd want to get better than group average on defense wherever possible even if they weren't as prominent a choice from perception of their offensive ability. Again 2 way players have 2 chances to add up to a good contribution worthy of a moderate or bigger salary.

Of the 108 between 15-20% usage the average adjusted offensive return ratio is -5%. If you can find a guy who is neutral on offensive adjusted to be your third guy or better you've done well. Jason Kidd, Sasha Vujacic, Chris Quinn and Vlade Radmanovic are the runaway kings of the third tier.

Among the every worst are Brandon Bass,, Jacque Vaughn Odom, Yi, Pavolovic Haslem, Rondo.Blatche, Jack, Blount, Cook and Mohammed. The average defensive adjusted -0.15. So on average they aren't hurting much on D.

The best combo of offensive and defensive adjusted up to zero or occasionally better is the goal. Some of the best overall are Mike Miller, Peja, Tony Allen, Kidd, Brewer, B Miller, T Young, KMart, Songaila, Dickau, Kirilenko, Maxiell (Utah knows this tier) Radmanovic, Chandler and Moon.
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Mountain



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PostPosted: Thu Nov 13, 2008 3:03 am    Post subject: Reply with quote

The APM values are per 100 possessions at basketballvalue and the most recent multi-year study. Steve's 06-07 dataset was per 40 minutes. Dan Rosenbaum and Dave Lewin's prior work was per 100 possessions.


I did the math on last season's Sonics and it works as a sum.
Durant cost the team -500 some points during his season's actual possessions.
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Mike G



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PostPosted: Thu Nov 13, 2008 6:40 am    Post subject: Reply with quote

Mountain wrote:
The APM values are per 100 possessions at basketballvalue and the most recent multi-year study. Steve's 06-07 dataset was per 40 minutes. Dan Rosenbaum and Dave Lewin's prior work was per 100 possessions.

That's good to know, thanks. Sometimes it doesn't seem to matter, but ...
Quote:
I did the math on last season's Sonics and it works as a sum.
Durant cost the team -500 some points during his season's actual possessions.

This is where we should be careful when wielding metrics in which the average NBA usage is worth zero. That 0 represents a standard which is pretty freaking good.

KD's TS% was .519, a whisker below league avg. The few Sonics higher than that either had lower Ast%, higher TO%, or both. The rookie's .129 TO% was better than NBA avg.

The Sonics were outscored by 718 pts. Jeff Green scored 52% as many pts as Durant. Who on this team is likely to double his scoring to make up for Durant, and do it better?

I realize this is an 'adjusted +/-' thread, and that Durant was very low in this measure. Somewhere I saw that a baseline performance is something like -2.7 . Is that a median? For rookies?
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