APBRmetrics

[schtevie]

I was lazily waiting for someone to (calculate then) say what follows: The result of the trade for KG should be to make the Celtics the odds on favorite to win the NBA championship.

Forecasting team results, by summing "recent" adjusted plus-minus statistics for the relevant players, the 2007-08 Celtics would appear to be a team for the ages. Here are the calculations:


Career Career DLew's DanR's
Avg. Avg. 2004-6 Weighted 2002-4 Weighted
mpg (% of 4 Adj. +/- Results Overall +/- Results

R. Allen 37.5 0.78 6.43 5.02 8.5 6.64
T. Allen 18.9 0.39 8.18 3.22 8.18* 3.22
KG 38.3 0.80 8.78 7.01 16.2 12.93
M. Olowok. 26.3 0.55 -8.00 -4.38 -7.6 -4.16
K. Perkins 16.6 0.35 -4.18 -1.45 -4.18* -1.45
P. Pierce 37.8 0.79 10.16 8.00 6.8 5.36
B. Scalabr. 15.1 0.31 2.27 0.71 -4.1 -1.29
Other* 49.5 1.03 -7.7* -7.94 -7.7* -7.94

TEAM TOTAL 10.20 13.30

This table is, I think, reasonably self-explanatory. The primary assumptions (besides the validity of Adjusted +/- itself) are as follows:

(1) All Celtics players will play their career average minutes.

(2) Roster players not having estimated Adjusted +/-s are given the value of replacement players from Dan's 2002-04 estimates.

(3) Similarly, Tony Allen and Kendrick Perkins have imputed 2004-06 values for the 2002-2004 calculation, when they weren't in the league.

And what is the bottom line?

Well, that the Celtics will outscore their opponents by between 10 and 13 points per 100 possessions, which would put them in the same league as the greatest Bulls team, which had the highest margin of all time (around 12, if I recall correctly).

Is this a reasonable estimate? If we believe in Adjusted +/- it is.

There are two basic caveats though.

(1) One or more of the Big and Old Three may completely break down. This is true, but catastrophe could afflict any team in the league; the Celtics are just a little more susceptible.

(2) One or more of the Big Three could face a discernible degradation of their skills. This is true, but this effect is by definition marginal, albeit increasingly likely and significant over time. Given historical averages however, next year performance shouldn't be much worse. (It is noted, though, that last year's numbers were not included, so if David Lewin has the 2006-07 data in his pocket, these would be interesting to add.)

These two points aside, there is also an argument that the calculations above are biased downwards.

First and foremost, there is no reason to believe that the Celtics will fill out its roster with replacement level players as there will be an incentive for decent veterans, looking for a ring, to come along for the ride. Also, it was assumed that the current remaining youngsters only had replacement value, and I suspect (at least in the case of Rajon Rondo's) that this isn't the case.

Secondly, it may be the case that using Adjusted +/- calculations in the "non-marginal" manner above underestimates players' productivity. In particular, it will be very difficult for team's to successfully double-team the Big Three, and this will likely raise their shooting percentages. Against this, however, is the fact that someone has to take the below-average shots at the end of the shot clock. How these offsetting effects cut, one can only guess.

Regardless, the 5/1 odds of the Celtics winning the title seem rather low....if we believe what we believe.

That is all.

[Mountain]

Berri has a post pegging them about around 50 wins.

[Neil Paine]

Okay, let's put to the test a theoretical procedure to predict team performance... For every player, I have projected an ORtg, %Poss, and DRtg for the upcoming season. Using these projections, and predicting minutes per game, one can give a prediction for team offensive and defensive ratings, which in turn can project winning % through the pythagorean formula.

Using HoopsHype's depth charts, I constructed a theoretical Celtics lineup for 2007-08:

[schtevie]

Yeesh, what a mess I made.

Here is what the column headers of the "self-explanatory" table were supposed to say. Left to right:

(1) Career Average Minutes per Game.
(2) Those minutes per game divided by 48, reflecting the fraction of position time played.
(3) David Lewin's Adjusted +/- averaged over the 2004 to 2006 season.
(4) Column (2) times Column (3), reflecting the Adjusted +/- per player.
(5) Dan Rosenbaum's Preferred Adjusted +/- for the 2002-2004 season.
(6) Column (2) times Column (5), reflecting the corresponding +/- per player.

The summation of these individual player contributions equals the expected team +/-. Then the TEAM TOTAL is the summation of these contributions.

I believe that this exercise is within the acceptable bounds of the adjusted +/- framework (again, recognizing that the estimate is not based on the most recent year's data).

Accordingly, and in rhetorical defense of same, it would seem to me that Berri's alleged estimates of 50 wins and davis21wylie2121 estimates of 48 wins seems a bit low.

Said another way, how can it be that you take three of the top 20 players in the league, each playing distinctly different positions (though admittedly perhaps slightly past their prime) and you only get a 48 to 50 win team? What would be the analogous antecedent that would bolster this case? Name a Big Three of any time that only won 48 games.

[Neil Paine]

[Mountain]

Someone compared this big 3 to 98-99 Rockets with Barkley, Pippen and Olujuwon. It is was the lockout shortened season but that team won about 60% or roughly 48-50 wins in a regular season. 5th on offense, 18th on defense. Something similar could happen in Boston. Boston was 18th on defense last year. Garnett's Wolves were 22nd and only that because they didnt foul. Boston did a lot of fouling last year and I'd guess will next season too. If team defensive efficiency is in 20s then I don't think Boston does any better than 50 wins. If Garnett and whatever supporting cast assembled can get defense ranking below 15 then they will be more powerful and perhaps closer to your expectations. I am not high of Doc Rivers but I don't know him well.

[schtevie]

This is why I titled my remarks "Should we believe..."

As to whether the estimate provided based on Adjusted +/- results is plausible is open to debate. As noted, the fact of the matter is that last year's estimates are not publicly known. Perhaps they reflect a dimunition in the productivity of the key players. But there would have to be a big change, or the method would have to be rather unreliable to undo the estimated contributions of the Big Three.

That said, in estimating this upcoming year's record, it should be noted that three of the most productive Celtics had last year marred by injury: Allen, Pierce, and West. That, and the fact that the team may have been playing for the lottery, suggests that last years squad, at "ordinary" health, was better than their record indicated. The assumption of a return to career norms is the basis of the calculations.

At the end of the day however, the Adjusted +/- regressions say what they say (assuming I am listening correctly, and that the key players are still as productive as they were over the four years before last) and this is that the sum of Ray Allen, Paul Pierce, and Kevin Garnett add 20+ net points per 100 possessions. And that is a lot of wins over 41.

I look forward to the year as a nice experiment.

[Brian M]

Is it a property of adjusted +/- that taking the minute-weighted sum of a team's players' adjusted +/-s equals the expected team point differential? I don't see any obvious a priori reason why this should be the case and I have not seen it demonstrated elsewhere, either formally or empirically.

[DLew]

The minute weighted sum of a team's adjusted plus-minus will be roughly equal to the team's point differential given that there are no trades. In-season player movement messes up this property if players change their performance when they change teams (which they always do to some degree) because the model assumes player performance is constant for the year.

Schtevie, I would say that the problem with your calculations is that adjusted plus-minus, like almost any statistic, exhibits diminishing marginal returns. Also, I think we all know that KG, Ray Allen, and Paul Pierce are not as good as they were 2002-2006. I can't comment specifically on their adjusted plus-minus numbers last year, but I will say that all three are on the wrong side of 30.

[Mountain]

Schtevie, it should be a good experiment indeed like B Wallace to Chicago and Kobe without Shaq and some of the other notable roster changes.

When I see your adjusted +/- data, my gut immediately expects shrinkage when all three play mainly from sharing limited shots and limited called or good situation, high on the pecking order shots. Maybe the adjusted +/- scores could be scaled, with a bit of estimation of importance of shooting to their adj. +/- to the new level of shots they are likely to get if that is less than less season? Davis estimated their shots to go down by about 15%. Does this seem about right to you?

Looking at the 4 factor data for these guys could be worthwhile but I am not sure how much it will transfer from one situation to another.

Davis, your estimates make a nice rough cut. If you feel like sharing any other team estimates later that would be interesting too.

[Brian M]

[mtamada]

[bchaikin]

It'd be interesting to see others' estimates, e.g. what does BobC's simulation project?

give me a listing of minutes played for each player (per game), in increments of 4 minutes, and i'll run the sim. wildcards are of course PF glen davis and PG gabe pruitt - to estimate them choose nba players whose games you think would best reflect davis and pruitt as rookies...

[Mike G]

There are a wide range of plausibilities. Supposing the 8 Celts (currently known) can play 82 games each, keeping their eWins/minute constant.

[NickS]