APBRmetrics

schtevie · Joined: 18 Apr 2005 Posts: 413

Let me try to kick off the summer fun by initiating what could be a productive (and almost certainly amusing) discussion on the correctness of the assumptions behind the various the NBA prediction methods employed here and elsewhere.

The motivation is the curious case of the 2008 Boston Celtics. Quite simply, all methods not based on Adjusted +/- failed and failed spectacularly. To such a degree that there is no way to casually explain away the estimation errors. That this is so is, on its face, surprising. The players involved in the beefing up of the Cs were as known quantities as known quantities could be in this league. That their collective effort could (be so misconstrued should be a shot across the bow.

Eyeballing the average error, the consensus of those posting here was that the Celtics would win about 15 fewer games than they actually did (16 in a Pythagorean world) and this figure is actually biased low, given that KG and Ray Allen played fewer minutes and games than (I think) was generally anticipated (certainly, at least, in the case of Bob Cs simulation). And a further bias is that I don't think that any estimate (mine included) explicitly factored in the generally expected age-related diminution of the Big Three's productivity.

So, the question is what is the source of these estimation errors? I think it would be very useful if everyone who played the estimation game reran their Celtics estimate, using actual minutes played, then posted these along with their explanation(s) of the differential. My guess is that the common answer resides in the great statistical void of defense, but maybe there are other truths to be revealed.

So, in the spirit of such self-examination and reflection, let me begin with my own reappraisal. I had based my estimate on incomplete data. I didn't have the 2006-2007 Adj. +/- data at hand, and I didn't have the complete roster either. If I did, I would have presented the following estimates of the Celtics performance based on the reported year's Adjusted +/-:

2003 & 2004 avg.: 24.0
2005: 20.7
2006: 12.2
2007: 16.2

2008 actual: 11.3

In this light, my (actual) estimate based on (year ending) 2006 data looks pretty darn good. Were I to have used 2007 data, my guess would have been less impressive. But then again, fitting a trend would also have led to a very solid estimate.

A brief digression is relevant however on the 2007 datum.

On the one hand, perhaps the unexpected jump up (given the age-profile of the players) reflects the imprecision of the regression results (a known weakness of the approach). On the other hand, the 2007 data is derived from Steve Ilardi's 82games article. His approach then (as opposed to now) was to estimate Adjusted +/- on a 40 minutes per game basis, as opposed to per 100 possessions. To put these numbers to the common basis, I multiplied them, player by player, by approximately 1.37 (1.2 to get them from 40 to 48 minutes, then dividing by approximately .91 to reflect the actual pace of games). Perhaps I am making a scaling error. Perhaps there is something about the per minute regressions. (David Lewin had hinted last fall that his 2007 Adj. +/- numbers indicated that, indeed, time was not on the Big 3's side, and David is far too nice of a guy to intentionally mislead.) Or perhaps the 2007 estimates are correct but imprecise.

This aside, some other commentary is relevant. Given that the story of the Celtics is typically viewed through the prism of the Big 3, let's look at their collective Adj. +/- over these same years. Given 2008 minutes, this would be their estimated contribution to team success:

2003 & 2004 avg.: 34.5
2005: 31.1
2006: 20.0
2007: 29.6
2008 actual: 17.8

Comparing these numbers with the counterparts above, we see that indeed the 3 was Big, but that their collective skills, though still formidable, appear to be waning as expected (again, 2007 being an open question).

Peeling one more layer off the onion, we see that this deterioration is driven by the diminution of Ray Allen, who posted a -0.87 Adj. +/- last year, whereas Paul Pierce and KG have remained remarkably resilient. Will the wheels stay on the bus for another year, however? I don't know if I would bet on that, Ray's in particular, but a related thought in a moment.

A couple other observations about the Adjusted +/- estimate.

As I noted before, my guess is that the superiority of Adjusted +/- in this instance is largely attributable to the measurement of defense in general, and that of Kevin Garnett in particular. Using Eli W's recently posted Adj. +/- numbers, on average, three quarters of the Cs margin of superiority came from defense, and three quarters of that was attributable to KG. A higher fraction still in terms of games played. Phenomenal. By contrast, his contribution to offense was nil. (A similar relative contribution, by the way, as in 2003 and 2004, as estimated by Prof. Rosenbaum.) You miss this part of the story, and there is no hope of being on target.

Finally, looking forward rather than back, I hope and trust, as a nominal Celtics fan, that the contribution of James Posey is well understood. There has been too much hagiography written about his contribution to the team's success, and it was disturbing to see Danny Ainge being quoted words to the effect that signing him was very important to the Celtics future. (Then again, there is now expressed formal interest in Corey Magette, and I just can't imagine him taking the required championship discount, so perhaps all the talk is all just noise.)

James Posey may be a good spot-up three point shooter, a good locker room influence, and a good man defender at times, but according to +/- and contrary to advertisement, he is not the guy who does all the little things well. The last time he made a positive contribution to a team was 2003 & 2004 (an average +/- of 3.0) and alarmingly, last years contribution was by far his worst, dipping down to -7.25 which Eli W tells us was all negative effect on offense with no discernible effect on defense.

If Danny invests his MLE in an aging, below-average player, barring great advances in the Celtic youth, I fear that there will be no two-peat, what with the expected deterioration of the Big 3.

Pssst. Na-je-ra.

(I am sure that DeanO won't notice he is gone.)

I look forward to a lively discussion.

thref23 · Joined: 13 Aug 2007 Posts: 90

jmethven · Joined: 16 May 2005 Posts: 51

I'd be really curious (once the off-season transactions have cooled down a bit) to try and predict win-loss records for each team using adjusted plus-minus. I've already taken a stab at this on my blog, reacting to the recent signing of Baron Davis by the Clippers. My (very) rough estimation says that the Clippers, getting full, productive seasons from Davis and Brand, will have an efficiency margin of +3.45, putting them around 50 wins. I think this estimate has face validity at the least and I'm really curious to see how this method will do going forward.

For those who don't want to click, my projection looks like this:

Baron Davis 35.5 mpg, +7.02
Cuttino Mobley 37.0 mpg, -1.42
Al Thornton 27.3 mpg, -4.43
Elton Brand 38.3 mpg, +5.91
Chris Kaman 29.1 mpg, -2.00

Tim Thomas 21.7 mpg, -0.33
Brevin Knight 16.3 mpg, +1.18
Quinton Ross 16.1 mpg, -2.33
Eric Gordon 18.7 mpg, -2.85

Ben · Joined: 13 Jan 2005 Posts: 266 Location: Iowa City

The Lakers with Bynum and Gasol are an interesting candidate for this method.

Mike G

supersub15 · Joined: 21 Sep 2006 Posts: 273

jmethven · Joined: 16 May 2005 Posts: 51

dquinn1575 · Joined: 03 Jun 2008 Posts: 12

[quote]Baron Davis 35.5 mpg, +7.02
Cuttino Mobley 37.0 mpg, -1.42
Al Thornton 27.3 mpg, -4.43
Elton Brand 38.3 mpg, +5.91
Chris Kaman 29.1 mpg, -2.00

Tim Thomas 21.7 mpg, -0.33
Brevin Knight 16.3 mpg, +1.18
Quinton Ross 16.1 mpg, -2.33
Eric Gordon 18.7 mpg, -2.85

How did you reach the +3.45 number from the posted P/M? I couldn't figure it out. Thanks.[/quote]

Take each minutes played by rate per minute (for Davis 35.5 * 7.02 = 249.21) Sum the total to get 165.149 - Take that divided by 48 minutes to get 3.44

I'm thinking this method would do well to compare teams, but you are omitting minutes outside of the top 9 players - for example for the 07-08 Clippers that would equal about 62 mpg ~ 15% of all minutes played. I would think you should have a baseline of a certain amount of minutes played with low contribution to reflect the remainder of the bench.

If you get 85% at 3.44 and 15% at -2, you get 2.62 for example.

supersub15 · Joined: 21 Sep 2006 Posts: 273

Thanks for the answers. Now, I'm checking the Adjusted P/M for the Clippers here, and it shows different results for Mobley, Thornton, etc. Is your source different or am I missing something concerning the minutes?

jmethven · Joined: 16 May 2005 Posts: 51

supersub15 · Joined: 21 Sep 2006 Posts: 273

According to the Adjusted P/M, a team composed of Chris Paul (-0.06), Jose Calderon (-5.47), Ray Allen (-0.87), Rip Hamilton (-2.57) Richard Jefferson (-6.16), Carmello Anthony (-4.79), Udonis Haslem (-8.61), Emeka Okafor (-4.76) and Yao Ming (-0.82) would be a losing team. Is this a limitation of this tool?

**Ilardi** · Joined: 15 May 2008 Posts: 265 Location: Lawrence, KS

Mountain · Joined: 13 Mar 2007 Posts: 1527

I assumed Garnett, Allen and Posey were important to improving the geometry of the offensive threat and thus to helping teammate shooting efficiency but the case is mixed in the player pairs. Playing beside Garnett helped the young bigs but really others. Allen helped Pierce a little. Posey on court was associated with decline in teammate FG%s in most cases and the bigs often by large amounts.

Garnett and Thibodeau enhanced the defensive game. Ainge and Rivers knew who knows defense and went out and got them.

They also showed attention to balance.
According to Eli's article, Rondo and Allen made their adjusted +/- contribution on offense. Pierce was the 2-way helpful core piece. Garnett and Perkins made their contribution on the defensive side and playing inside had the most opportunity to do so. Pretty straightforward, solid design. Garnett gave enough post player offense that is wasn't an impediment.

The Spurs were built to be strong on defense inside and have offensive firepower on perimeter too but they managed to have 3 2way helpful players.

The Pistons mixed up the perimeter offense / interior defense design some- Billups and McDyess provided primarily positive offensive adjusted +/- while Hamilton and Prince primarily contributed on defensive adjusted +/- and Wallace was the 2way helpful core.

For the Lakers adjusted +/- suggests Fisher was a dual liability but mainly on defense (age/weight). Kobe was a very strong offensive player with only a small positive defensive impact and not really-right now- 2 way core. Gasol balanced him and was the opposite with surprisingly a modest positive adjusted defensive +/- impact and just a small one on offense.

Radmanovic and Vujacic were helpful on offense but Vujacic was a much bigger and harder to justify defensive liability. Odom was a positive contributor on defense but nearly gave it all back on offense. Turiaf mildly helpful on defense. Walton mildly negative on offense. More of a jumble than a simple / good balance like these other leading contenders. But Bynum was a modest 2 way positive player and maybe will become more.

Can you win a title without a clearcut 2-way strong core piece?

You probably can but when was the last time? 80s Pistons or did Joe Dumars play that role? If you need one, adjusted +/- offensive/defensive splits say that the Hornets are "relying" on Peja. The Rockets' closest was Battier. Utah doesn't have a strong 2way player - unless you count marginal Ronnie Price. Denver had Iverson and Najera as dual positive contributors but strong on one side and just above +1 on the other side like Bryant/Gasol. Phoenix doesn't. Dallas has Nowitski / Kidd / Howard. The Cavs don't have a 2way player. The Magic clearly do with Howard. Toronto has Bosh and Moon. Washington has Jamison. Philly has Thaddeus Young.

anarcholis · Joined: 12 Jun 2007 Posts: 19

bchaikin · Joined: 27 Jan 2005 Posts: 689 Location: cleveland, ohio

Other than Okafor and Haslem, I'm not sure any of these players are considered above average defenders.

over the past 5 seasons the houston rockets have averaged the 4th best/lowest points allowed per team defensive possession in the league, they have the lowest FG% allowed (42.5%), the 2nd lowest eFG% allowed (46.2%), and the lowest 2pt FG% allowed (44.2%)...

yao ming has played the most minutes of any rockets players during this time, has almost double the defensive rebounds of any other rockets player, and over twice as many blocked shots as any other rockets player. if you look at ming's counterpart production at www.82games.com from 03-04 to 07-08, you'll see rockets opposing Cs have done poorly when ming was on the floor...

i'd say all that puts yao ming in some elite defensive territory...