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schtevie
Joined: 18 Apr 2005 Posts: 412
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Posted: Fri Aug 03, 2007 4:18 pm Post subject: Should we believe what we believe? If so, Celtics roll. |
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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. |
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Mountain
Joined: 13 Mar 2007 Posts: 1527
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Posted: Fri Aug 03, 2007 4:58 pm Post subject: |
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Berri has a post pegging them about around 50 wins. |
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Neil Paine
Joined: 13 Oct 2005 Posts: 774 Location: Atlanta, GA
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Posted: Fri Aug 03, 2007 6:43 pm Post subject: |
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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:
Code: | Pos Player MPG
PG Rajon Rondo 25
PG Eddie House 14
SG Ray Allen 37
SG Tony Allen 20
SG Jackie Manuel 7
SF Paul Pierce 37
SF B. Scalabrine 13
PF Kevin Garnett 39
PF Leon Powe 16
PF Brandon Wallace 5
C K. Perkins 27 |
I can also include the projected stats (not every player had enough minutes for a comp-based projection, so for some I used past performance -- normalized to a lgRtg of 106.3 -- or made an educated guess) to arrive at:
Code: | Pos Player Min/G ORtg %Poss DRtg Min
PG Rajon Rondo 25 101.0 19.7 105.5 2050
PG Eddie House 14 105.6 21.8 108.4 1148
SG Ray Allen 37 114.3 26.6 112.4 3034
SG Tony Allen 20 104.8 20.3 104.8 1640
SG Jackie Manuel 7 99.0 14.0 107.5 574
SF Paul Pierce 37 110.8 26.7 107.4 3034
SF B. Scalabrine 13 97.0 13.7 107.9 1066
PF Kevin Garnett 39 109.2 25.6 100.6 3198
PF Leon Powe 16 108.6 19.5 105.0 1312
PF Brandon Wallace 5 103.0 14.0 101.0 410
C K. Perkins 27 103.3 15.3 104.5 2214 |
However, when I add up the individual possessions, it exceeds the projected total team possessions (let's use last year's total of 7636). That means I have to scale down each player's possession total accordingly... You could actually do this in a number of ways (keep the stars' %Poss the same and downgrade the role players, etc.), but I simply kept the proportions the same and scaled to 7636 team possessions. After doing that, I have:
Code: | Pos Player Min/G Poss %Poss Min
PG Rajon Rondo 25 717 18.0 2050
PG Eddie House 14 444 19.9 1148
SG Ray Allen 37 1433 24.3 3034
SG Tony Allen 20 591 18.6 1640
SG Jackie Manuel 7 143 12.8 574
SF Paul Pierce 37 1438 24.4 3034
SF B. Scalabrine 13 259 12.5 1066
PF Kevin Garnett 39 1453 23.4 3198
PF Leon Powe 16 454 17.8 1312
PF Brandon Wallace 5 102 12.8 410
C K. Perkins 27 601 14.0 2214 |
I can't keep the offensive ratings the same, though, because the usage rates have changed. While some people disagree with this idea, I'm going to go with it until somebody can prove otherwise. I'm going to break down the ORtg sensitivity into three groups: high-usage, normal usage, and low-usage.
Code: | Initial %Poss Sensitivity
---------------------------
<18% +/- 0.8
18-23% +/- 0.6
>23% +/- 0.4 |
All this means is that low-usage players will see wilder swings in ORtg when their usage changes (penalties for increases, bonuses for decreases) than higher-usage players. Using this method, here are the new projections:
Code: | Pos Player Min/G ORtg %Poss PProd Min
PG Rajon Rondo 25 102.0 18.0 731 2050
PG Eddie House 14 106.7 19.9 474 1148
SG Ray Allen 37 115.2 24.3 1651 3034
SG Tony Allen 20 105.8 18.6 626 1640
SG Jackie Manuel 7 100.0 12.8 143 574
SF Paul Pierce 37 111.7 24.4 1606 3034
SF B. Scalabrine 13 97.9 12.5 254 1066
PF Kevin Garnett 39 110.1 23.4 1600 3198
PF Leon Powe 16 109.6 17.8 498 1312
PF Brandon Wallace 5 104.0 12.8 106 410
C K. Perkins 27 104.3 14.0 627 2214 |
Tallying up the points produced, we can project the Celtics to score 8315 points, for an offensive rating of 108.9. Now, defense... While DRtg is a crude measure, it will have to do for our purposes here. Since we have no "Defensive %Poss" metric (nor would I even know what its implications would be if it did exist), I'm going to assume that each player affects 1/5 of defensive possessions while on the court. Clearly, this is not necessarily true, but remember that this is a very rough projection right now. More detail can be added later, if one so chooses. Here is the final 2007-08 Boston projection:
Code: | Pos Player Min/G Min ORtg %Poss PProd DRtg
PG Rajon Rondo 25 2050 102.0 18.0 731 105.5
PG Eddie House 14 1148 106.7 19.9 474 108.4
SG Ray Allen 37 3034 115.2 24.3 1651 112.4
SG Tony Allen 20 1640 105.8 18.6 626 104.8
SG Jackie Manuel 7 574 100.0 12.8 143 107.5
SF Paul Pierce 37 3034 111.7 24.4 1606 107.4
SF B. Scalabrine 13 1066 97.9 12.5 254 107.9
PF Kevin Garnett 39 3198 110.1 23.4 1600 100.6
PF Leon Powe 16 1312 109.6 17.8 498 105.0
PF Brandon Wallace 5 410 104.0 12.8 106 101.0
C K. Perkins 27 2214 104.3 14.0 627 104.5 |
These Celtics would post a defensive rating of 106.1 (a hair under the league average). With a team ORtg of 108.9 and a team DRtg of 106.1, we can expect them to win about 58.9% of their games, for 48 wins next season.
And there you have it... A crash course in how I project team performance. |
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schtevie
Joined: 18 Apr 2005 Posts: 412
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Posted: Fri Aug 03, 2007 7:38 pm Post subject: |
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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. |
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Neil Paine
Joined: 13 Oct 2005 Posts: 774 Location: Atlanta, GA
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Posted: Fri Aug 03, 2007 7:55 pm Post subject: |
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schtevie wrote: |
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. |
I would counter by saying that even a 50-win season for Boston would represent a 26-win improvement from last year... That would mean that adding essentially no one but Allen and Garnett, and subtracting Jefferson/Gomes/West/etc., would add almost 30 wins to the team! Berri estimates the departed players as being worth ~ 14.5 wins; DeanO's pW pegs them at ~ 17 wins... Are you telling me that taking a 24-win team, subtracting something like 16 wins from that, and then adding Allen + Garnett (and maybe 8 more wins from a healthy Pierce, depending on whose rating system you look at) adds up to 55+ wins? This is a much cruder analysis than what I did a few posts above, and it still doesn't see this team as much more than a 45-50-win squad, pending further moves. And I'm a Celtics fan. But apparently I'm not drinking the Kool-Aid as much as everyone else is. |
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Mountain
Joined: 13 Mar 2007 Posts: 1527
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Posted: Fri Aug 03, 2007 10:27 pm Post subject: |
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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. |
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schtevie
Joined: 18 Apr 2005 Posts: 412
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Posted: Fri Aug 03, 2007 10:43 pm Post subject: |
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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. |
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Brian M
Joined: 25 Nov 2006 Posts: 40
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Posted: Fri Aug 03, 2007 10:54 pm Post subject: |
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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. |
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DLew
Joined: 13 Nov 2006 Posts: 224
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Posted: Fri Aug 03, 2007 11:36 pm Post subject: |
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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. |
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Mountain
Joined: 13 Mar 2007 Posts: 1527
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Posted: Fri Aug 03, 2007 11:41 pm Post subject: |
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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. |
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Brian M
Joined: 25 Nov 2006 Posts: 40
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Posted: Sat Aug 04, 2007 1:00 am Post subject: |
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DLew wrote: | 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. |
I assume you have investigated this in your own work then? Are there any good, formally specified reasons for anticipating that a team's point differential should roughly equal the minute weighted sum of its players' adjusted +/-s? Or is this just something that so far has been established observationally? |
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mtamada
Joined: 28 Jan 2005 Posts: 377
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Posted: Sat Aug 04, 2007 1:26 am Post subject: |
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schtevie wrote: | 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. |
I think the estimates of 48 and 50 wins are right on. Barring injury, the Celtics will be right in the race for the Eastern title -- but I don't think they'll win it, and I don't think they'll win the championship.
Most sports statistics, in particular most basketball statistics, are extremely nonlinear. Putting two 15 rebound per game players on the same squad doesn't mean they'll average 30 rebounds between them. Ditto plus-minus.
As for your final question, here's a team which comes close: the late 1960s Los Angeles Lakers, who'd already had two of the best players of all time in Elgin Baylor and Jerry West (forget about mere Top 20 current players: at that time those two were probably, at worst, the second-best forward and second-best guard of ALL TIME).
And in 1969 they added Wilt Chamberlain, even now at worst the 3rd best center of all time and a plurality or even majority of fans would probably vote him the best center of all time.
The Lakers won 55 games.
Which is more than 48 or 50, but hey, Wilt >> Garnett, Baylor >> Pierce, and West >> Allen.
And 55 >> 48, so 48 or 50 sounds about right.
My intuition says about 50.
I really like seeing Davis's worked out numbers, showing how he derived his estimate of 48. That procedure, and that number, looks sensible to me.
It'd be interesting to see others' estimates, e.g. what does BobC's simulation project? |
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bchaikin
Joined: 27 Jan 2005 Posts: 689 Location: cleveland, ohio
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Posted: Sat Aug 04, 2007 1:53 am Post subject: |
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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... |
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Mike G
Joined: 14 Jan 2005 Posts: 3604 Location: Hendersonville, NC
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Posted: Sat Aug 04, 2007 5:12 am Post subject: |
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There are a wide range of plausibilities. Supposing the 8 Celts (currently known) can play 82 games each, keeping their eWins/minute constant.
Code: | 2007 2008 max
boston celtics G Min eW Eff% G2 Min2 eW2
Kevin Garnett 76 39 12.0 .536 82 40 13.2
Paul Pierce 47 37 6.0 .558 82 40 11.3
Ray Allen 55 40 6.8 .556 82 40 10.1
Tony Allen 33 24 1.9 .581 82 32 6.2
Rajon Rondo 78 23 3.1 .462 82 32 4.5
Kendrick Perkins 72 24 1.9 .508 82 28 2.5
Leon Powe 61 16 1.1 .530 82 16 1.5
Brian Scalabrine 54 16 .4 .533 82 12 0.5
total 33.1 49.8
| I've given players (2008) minutes in 4-minute increments, just to be consistent. This is the most optimistic scenario as far the health of these 8, but anyone may improve on last year's rates. Consider Scalabrine a 'replacement' player (interchangeable), as well as any rookies.
If players don't improve, while missing as many games as last year; and their minutes are taken by replacement types; then 33 eW suggests (66-41=) 25 wins this year. The 50 eW 'max' scenario provides 59 wins.
I threw in Eff% (a shade lower than TS%) just for reference. Since all of these guys were with basically dysfunctional teams last year, they could all improve. (The Big 3 have all been much better.)
KG seems to be nearly indestructible. Three years of purgatory were probably wearing on him. I expect a major resurgeance and an MVP run. _________________ `
36% of all statistics are wrong |
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NickS
Joined: 30 Dec 2004 Posts: 384
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Posted: Sat Aug 04, 2007 11:09 am Post subject: |
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davis21wylie2121 wrote: |
These Celtics would post a defensive rating of 106.1 (a hair under the league average). With a team ORtg of 108.9 and a team DRtg of 106.1, we can expect them to win about 58.9% of their games, for 48 wins next season.
And there you have it... A crash course in how I project team performance. |
*applause*
Very nice, an impressive use of the Ortg and Drtg stats.
Intuitively I feel like the estimate for Ortg looks convincing, but I would expect a better defensive rating. I feel like Allen and Pierce aren't as bad at defense as they look having played on terrible defensive teams last season. Just working off intuition I'd expect to see a defensive rating about a point lower than your estimate.
Of course, this doesn't include injuries, so I suspect 48-50 is a decent estimate, but if they're healthy I could see 50-52 wins for the team (matching what Detroit did last season). |
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