Factoring starter minutes into stats (MikeG 2010)
Posted: Fri Apr 15, 2011 2:33 am
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Mike G
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PostPosted: Thu Dec 02, 2010 11:13 am Post subject: Factoring starters' minutes into boxscore-based stats Reply with quote
Since we know a player's minutes per game, games, and games started, we should be able to estimate the percentage of his opponents (and teammates) who have been Starters. We might then adjust his per-minute stats to the relative quality of the competition.
A couple of per-minute summary stats are PER and Win Shares per 48 minutes, both available at basketball-reference.com. Here are some of last year's and this season's numbers for players who have started all (or most) games this year, and who also don't play a lot of minutes. We can assume a high % of their opponents are starters.
Code:
2009-10 2010-11 PER WS/48
player tm G GS mpg G GS mpg 2010 2011 2010 2011
Hawes,Spencer Phi 72 59 26.4 18 18 17.0 13.8 10.2 .054 .005
Mohammed,Nazr Cha 58 29 17.0 17 17 17.6 19.6 16.5 .174 .088
Lopez,Robin Phx 51 31 19.3 9 9 17.8 17.6 11.2 .158 .017
Blair,Dejuan SAS 82 23 18.2 18 18 19.5 17.7 13.0 .147 .085
Williams,Shelden Den 54 0 11.1 17 17 20.4 14.1 12.0 .162 .102
Arroyo,Carlos Mia 72 34 22.0 19 19 22.2 12.3 11.6 .113 .121
Bogans,Keith Chi 79 49 19.7 16 16 21.6 7.7 8.0 .081 .062
McRoberts,Josh Ind 42 3 12.5 17 17 23.5 14.8 14.0 .134 .146
Gooden,Drew Mil 70 33 25.1 16 15 24.8 16.9 14.4 .121 .088
Milicic,Darko Min 32 18 21.4 18 18 27.5 12.8 12.0 .050 -.007
Almost all of these 11 have seen both their PER and their WS/48 drop, even as they have become starters this year. Are they really worse players than before?
Now here are their estimated % of Starter opponents, along with a proposed 'factor' for adjusting their stats, relative to a league standard of 2/3 of opponent minutes being Starters.
Code:
2009-10 2010-11 - PER - - - adj - WS/48 - - - adj
player sta% fac sta% fac 2010 2011 2011 2010 2011 2011
Hawes,Spencer .76 1.07 .88 1.15 13.8 10.2 11.0 .054 .005 .005
Mohammed,Nazr .67 1.00 .88 1.15 19.6 16.5 18.9 .174 .088 .101
Lopez,Robin .71 1.03 .88 1.15 17.6 11.2 12.5 .158 .017 .019
Blair,Dejuan .58 .93 .87 1.14 17.7 13.0 16.0 .147 .085 .104
Williams,Shelden .41 .78 .86 1.14 14.1 12.0 17.4 .162 .102 .148
Arroyo,Carlos .66 .99 .85 1.13 12.3 11.6 13.2 .113 .121 .137
Bogans,Keith .71 1.04 .85 1.13 7.7 8.0 8.7 .081 .062 .068
McRoberts,Josh .45 .83 .84 1.12 14.8 14.0 19.0 .134 .146 .198
Gooden,Drew .66 .99 .81 1.10 16.9 14.4 16.0 .121 .088 .098
Milicic,Darko .69 1.02 .81 1.10 12.8 12.0 13.0 .050 -.007 ---
avg .63 .97 .85 1.13 14.7 12.3 14.6 .119 .071 .087
Note that the 'adjusted' PER and WS/48 are almost all closer than the unadjusted, to last year's values. This adjustment suggests that PER's for these 10 players have not universally plunged since last year, but are on average just about the same.
These adjusted values do not represent anything absolute, but assume last year was 'correct', and then adjust to this year's Starter%.
For most of these guys, last year's PER and WS are probably 'too high', relative to league average (2/3) Starter%.
Sta% = GS/G*(1-1/3*mpg/48.5)+(1-GS/G)*1/3*(1+mpg/48.5)
fac = (Sta%*3/2)^x : for this demonstration, x = 0.5
2011PERadj = 2011fac/2010fac * 2011PER
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Last edited by Mike G on Thu Dec 02, 2010 12:37 pm; edited 2 times in total
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EvanZ
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PostPosted: Thu Dec 02, 2010 12:28 pm Post subject: Re: Factoring starters' minutes into boxscore-based stats Reply with quote
Mike G wrote:
Since we know a player's minutes per game, games, and games started, we should be able to estimate the percentage of his opponents (and teammates) who have been Starters. We might then adjust his per-minute stats to the relative quality of the competition.
But that makes perfect sense! Laughing
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DSMok1
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PostPosted: Thu Dec 02, 2010 12:37 pm Post subject: Reply with quote
That's why MPG is part of SPM and ASPM as a linearly positive factor. If you play 40 MPG, you're playing better competition/have better intangibles.
In fact, I use regressed MPG and team efficiency to create the Bayesian prior onto which I regress single-season ASPM (see the spreadsheets for the details) to create my best-estimate of single-season true production level for ASPM.
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Mike G
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PostPosted: Thu Dec 02, 2010 1:02 pm Post subject: Reply with quote
DSMok1 wrote:
.. If you play 40 MPG, you're playing better competition/have better intangibles...
Intangibles, maybe. But consider the mpg extremes: Going 48 minutes, your opponents have been 2/3 starters. (Starters have for years averaged 32 minutes.) Starting and going just 1 minute, you've likely faced 100% starters in that minute.
Nazr, RLopez, and Hawes start every game and average <18 minutes. The formula given above estimates their competition consists of 88% starters.
According to PER, Tyrus Thomas is the 10th best player in the league. According to WS/48, Brandon Bass is #6, Amir Johnson #16, Shannon Brown is better than Kobe Bryant. But those guys (other than Kobe) do not start, do not play over 20 mpg, and play against only 45-50% starters.
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DSMok1
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PostPosted: Thu Dec 02, 2010 1:56 pm Post subject: Reply with quote
Ah! I see what you mean. I wonder if I can factor that into ASPM...
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EvanZ
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PostPosted: Thu Dec 02, 2010 8:30 pm Post subject: Reply with quote
Assumption: Playing against starters would hurt your stats on offense, but playing with starters would help your stats on offense.
Am I right about that? If so, do these balance out the overall effect for subs?
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Mike G
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PostPosted: Fri Dec 03, 2010 6:05 am Post subject: Reply with quote
Good point, Evan. A player might see some improvement as a starter, in his shooting%, his TO rate, maybe his Ast rate.
But he won't generally get as many scoring opps, or rebounding opps; likely less ball-handling. These are 'volume' stats, and they count as 'productivity' on the floor.
I don't know exactly what to do with the Starter%, so I get this normalized 'factor' and multiply all the production rates by it, uniformly, including fouls and turnovers. So a guy playing a lot with and against subs will have his 'normalized' TO and PF deflated, along with everything else. This is a bit of compensation.
There's also the issue of garbage time. If a player goes over 40 mpg, he's getting some of that. A guy who never starts, and runs under 10 mpg, gets largely garbage time. It's really a stretch to count all minutes (and productions) as being equal.
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EvanZ
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PostPosted: Fri Dec 03, 2010 8:33 am Post subject: Reply with quote
Thanks, Mike. Would you mind running those numbers for Dorell Wright?
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Mike G
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PostPosted: Fri Dec 03, 2010 9:09 am Post subject: Reply with quote
Dorell Wright's Miami line from 2009-10 line, and this year's.
Code:
St% fac tm G Min Eff% Sco Reb Ast PF Stl TO Blk T e484
.48 .89 Mia 72 21 .562 13.2 5.9 1.8 2.2 1.2 1.2 .7 22.0 .81
.73 1.04 GSW 18 39 .520 13.7 4.9 2.3 2.3 1.0 1.7 .7 20.5 .69
The T rate (weighted sum of other columns) and eWins per 484 minute (1.00 is avg, zero = replacement) suggest he was better as a sub.
The ratio of this year's to last year's factors (104/89) is 1.169
Multiply that by last year's PER and WS/48 --
Code:
yr tm PER ws/48
2010 Mia 14.5 .137
2011 GSW 13.2 .059
2011 *1.17 15.4 .069
At least by PER, his starting status would seem to be justified; but the scoring and rebounding pace are both a bit looser in The City.
Oh, last night's game not included.
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Last edited by Mike G on Fri Dec 03, 2010 9:27 am; edited 1 time in total
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EvanZ
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PostPosted: Fri Dec 03, 2010 9:22 am Post subject: Reply with quote
Thanks, Mike! I've been a little bit disappointed with him, but if he can ever get his shooting to be more consistent, he'll be pretty good. He does "all the little things" well, and he's almost certainly the best defender on the Warriors (although that's not saying much right now Laughing Crying or Very sad). Last night he had 10 rebounds, 7 asts, 1 stl, 2 blk and only 1 TOV. But he went 4/13 (.385 TS%).
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Mike G
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PostPosted: Fri Dec 03, 2010 9:28 am Post subject: Reply with quote
Sorry, I just downgraded him in an edit.
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Mike G
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PostPosted: Fri Dec 03, 2010 10:20 am Post subject: Reply with quote
[Now, where was I?]
If I didn't factor in starter/sub percents, I might think Corey Maggette was the 10th best scorer in the league, instead of 34th.
or that Shannon Brown is #12, rather than #36 so far.
or that Tyrus Thomas is our #19 scorer, #26 rebounder, and #9 shotblocker, rather than 38, 41, and 13, respectively. #12 overall player or #30?
Tyler Hansbrough: 86 or 128?
Craig Smith: 89 or 130 ?
Is Mareese Speights 12th-best rebounder or 41st ?
Is JR Smith top-100 in scoring, rebounding, and assists? or in none of these?
Is Marcin Gortat the #8 rebounder or #27? 22nd in blocks or 32nd?
Is Brandon Bass the 35th best player or the 60th?
Matt Barnes #71 or #96?
On the other side of the ticket, players whose Starter% enhances their rankings:
Shaq: 11th Sco and 13 Reb, unadjusted; 6th Sco and 11th Reb adjusted.
Nazr Mohammed: #16 Reb and #14 Blk, vs #10 Reb and #12 Blk
Horford: Sco #29, Reb #31, vs Sco 27 and Reb 23
Hibbert: #13 Blk, #13 overall, vs #14 Blk and 11 overall.
Duncan #15 vs #13 overall ranking
DeJuan Blair #9 Reb vs #4
All in this group are starters who go modest minutes.
All rankings are of players with at least 200 minutes.
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Mogilny
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PostPosted: Fri Dec 03, 2010 6:33 pm Post subject: Reply with quote
Interesting stuff. Amirs stats has been pretty awesome this year, will they decline now when he starts? Charlie Villaneuva is another guy who springs to my mind.
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Mike G
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PostPosted: Sun Dec 05, 2010 8:03 am Post subject: Reply with quote
Amir Johnson is an annual topic of hot discussions about guys whose numbers imply they should be getting a lot more minutes.
Here are his career splits, in raw per36, from
http://www.basketball-reference.com/pla ... 01/splits/
Code:
Amir G mpg FTA OReb Reb Blk TO Pts TS%
Bench 204 14.6 3.3 4.2 10.2 2.5 1.7 11.5 .612
Start 32 22.3 1.8 3.5 8.2 1.8 1.4 11.9 .686
FGA, Ast, Stl rates are roughly equal.
Even with barely half the FTA while starting, his Pts/Min are higher, due to better %.
As of Friday, I've got Amir ranked at #70 in per-minute productivity.
If I alter his line such that he'd started every game (leaving everyone else's the same), he vaults to a tie with Paul Pierce at #27.
I see at b-r.com, he's #40 in PER, #12 in WS/48. About every year, in both metrics, he rates as a star, or Allstar-level.
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Crow
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PostPosted: Sun Dec 05, 2010 3:57 pm Post subject: Reply with quote
Factoring the impact of estimated minutes against starters vs bench into boxscore-based metrics is a valuable enterprise in that segment over not doing it, but at some point it might good to see actual minutes for individual players against starter match-up opponents and maybe the average number of starters faced too (since defense is team and it is also somewhat on offense). If somebody wanted to pull that from play by play for everyone it would probably identify some players whose actual minutes against starters is notably over or under estimated by the standard minutes based method because of how their time is actually used by the coach with the starter / sub issue prominently in mind or not and along with other concerns or not.
And it could also be said that Adjusted +/- handles this issue fully and more simply and maybe better. With some estimated error of course, but without having to make starter assumptions or finding the actual level or making any assumptions about what that this means for defense faced. Very often starters are not that good on defense. I don't know if it is more or less than subs or that much better or worse. It is easier to accept that starters are better on offense than defense. If you are measuring "relative scoring potency" then the opponent's offense matters from that perspective but I am probably more interested in how their defense directly matters for the scoring of the other team.
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BobboFitos
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PostPosted: Sun Dec 05, 2010 3:58 pm Post subject: Reply with quote
I just don't understand why coaches claim "foul rate" about not playing more players more minutes... When they clearly deserve those minutes. Let the players foul out - there's always another game!
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Mike G
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PostPosted: Tue Dec 28, 2010 12:17 pm Post subject: Reply with quote
Amir Johnson update.
Per-36-minutes, data drawn from --
http://www.basketball-reference.com/pla ... lits/2011/
Code:
Amir G mpg FGA FTA OReb DRb Ast Stl Blk TO PF Pts TS%
Bench 16 19.8 9.9 4.9 5.6 4.8 1.0 1.1 1.8 1.8 6.3 15.3 .633
Start 14 26.6 9.3 1.9 3.2 4.9 1.8 1.5 1.6 1.5 5.2 11.9 .587
Coming off the bench, he got 2.5 times as many FTA, leading to 28% more points, and 75% more OReb.
As a starter, more assists and steals.
When I split these into 2 Amirs, it's guessed that Amir1 (off the bench) plays against and with 51% starters; Amir2 (the starter) goes against 79% starters.
Code:
per36 Sco Reb Ast PF Stl TO Blk e484
Amir1 14.3 11.1 1.0 6.1 1.1 1.8 1.7 1.18
Amir2 11.8 9.3 2.0 5.4 1.5 1.7 1.5 .98
Without 'starter compensation', he's a 28% better rebounder off the bench.
With adjustment, the diff is only 19%. About the same as his overall dropoff (e484, average = 1.00).
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BobboFitos
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PostPosted: Tue Dec 28, 2010 4:08 pm Post subject: Reply with quote
Mike, Amir has been battling a bad back his last couple of starts. I'm not sure to what extent that has affected his play, but he was pretty brutal last night vs Memphis... Does change the starter vs reserve numbers somewhat.
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Mike G
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PostPosted: Mon Jan 10, 2011 3:54 pm Post subject: Reply with quote
23 players who have started between 40% and 60% of their games, raw per36 minute averages as starter and as substitute.
Code:
Al-Farouq per 36 minutes, unadjusted
Aminu mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 22.1 .536 11.4 2.2 1.5 4.4 1.5 1.4 .6 3.5 3.3 13.2 19.2
sub 14.9 .528 11.6 3.3 2.5 6.5 1.1 1.4 .4 2.9 3.4 13.8 22.8
Louis
Amundson mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 16.9 .462 10.7 2.7 4.3 5.2 1.2 1.5 1.2 1.5 6.1 11.0 22.9
sub 17.8 .400 10.1 4.3 4.3 5.1 1.0 .8 1.0 2.0 4.3 9.6 19.8
Jose
Calderon mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 32.9 .598 10.7 1.2 .7 2.7 10.7 1.6 .0 2.7 2.4 13.4 26.4
sub 21.7 .482 11.9 2.8 .4 2.9 8.9 1.7 .0 2.4 2.3 12.6 24.1
Wilson
Chandler mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 39.0 .627 13.6 2.6 1.2 5.3 2.1 .7 1.3 1.1 2.9 18.4 28.0
sub 29.3 .533 16.0 3.5 1.8 5.2 1.6 .6 2.0 1.9 4.3 18.7 28.0
Jason
Collins mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 19.0 .458 4.6 1.6 2.0 4.6 1.5 .8 .3 1.6 5.0 4.9 12.5
sub 5.3 .688 5.8 6.8 1.0 5.4 1.0 .0 1.0 3.4 8.3 12.2 17.0
Demarcus
Cousins mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 27.4 .512 16.9 5.8 3.2 7.2 2.7 .8 1.0 2.9 5.5 19.9 32.0
sub 24.0 .430 14.2 5.5 4.2 7.0 1.7 1.3 .7 4.0 6.0 14.3 25.2
Samuel
Dalembert mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 24.7 .465 7.9 2.0 4.2 7.7 1.3 .4 3.1 3.0 4.1 8.2 21.8
sub 15.1 .398 9.7 1.6 4.9 7.9 1.4 .3 2.9 1.7 5.4 8.2 23.9
Baron
Davis mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 30.2 .485 13.0 2.2 .5 2.4 8.2 1.1 .5 2.7 3.2 13.6 23.6
sub 19.9 .389 13.8 3.6 .5 3.8 10.9 2.5 .9 3.8 4.3 12.0 26.7
Austin
Daye mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 22.3 .554 13.2 2.2 1.6 5.4 1.3 .4 .6 1.6 4.1 15.7 23.5
sub 10.6 .394 14.7 1.8 2.3 4.8 1.6 1.6 .5 1.6 3.8 12.2 21.3
Taj
Gibson mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 25.7 .536 12.7 3.0 3.1 6.1 1.7 1.1 2.0 2.1 4.7 15.0 26.9
sub 19.8 .422 11.8 2.4 3.8 5.9 1.0 .6 2.6 1.6 3.4 10.8 23.0
Xavier
Henry mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 20.7 .482 10.3 2.2 .3 2.1 1.7 .5 .3 1.1 3.5 10.9 14.8
sub 12.9 .428 12.8 6.7 1.4 1.9 .5 .9 .0 .7 3.3 13.5 17.4
Serge
Ibaka mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 26.3 .573 10.4 2.4 3.5 5.7 .2 .8 3.0 .6 4.5 13.2 25.7
sub 25.7 .614 9.4 3.8 3.0 6.3 .3 .4 3.3 1.6 4.8 13.6 25.2
Antawn
Jamison mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 36.1 .546 17.1 4.3 .9 5.2 1.3 .8 .6 1.3 2.7 20.7 28.1
sub 25.4 .498 16.0 3.7 2.0 6.1 2.1 .9 .6 1.4 3.2 17.6 27.8
Amir
Johnson mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 27.8 .582 9.5 2.3 3.1 5.1 2.0 1.0 1.5 1.4 5.0 12.3 23.6
sub 19.8 .633 9.9 4.9 5.6 4.8 1.0 1.1 1.8 1.8 6.3 15.3 27.8
Linas
Kleiza mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 30.6 .510 14.7 1.7 1.0 4.8 2.1 .7 .2 2.8 3.7 15.8 21.7
sub 21.1 .509 14.4 3.0 1.9 5.9 .6 .4 .2 2.4 3.3 16.0 22.8
Carl
Landry mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 31.3 .516 13.4 4.9 3.8 3.2 .9 .6 .1 2.0 3.0 16.0 22.7
sub 23.5 .516 12.0 5.5 2.8 3.1 .9 .7 1.3 1.9 3.5 14.8 21.6
Jason
Maxiell mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 21.4 .507 7.9 3.2 2.4 2.8 .6 .7 .8 .8 3.5 9.5 16.0
sub 16.1 .459 6.0 4.2 2.1 3.3 .6 .9 1.5 1.6 4.0 7.1 13.8
O.J.
Mayo mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 36.0 .512 14.2 2.3 .6 2.9 2.4 1.1 .5 2.1 2.3 15.6 21.0
sub 24.0 .518 14.7 3.7 .6 2.5 2.4 .9 .4 1.6 2.2 16.9 22.3
Jodie
Meeks mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 28.3 .548 10.1 4.3 .2 2.1 1.0 .7 .1 1.4 1.5 13.2 16.0
sub 17.3 .606 10.8 3.1 .2 1.2 1.5 1.7 .0 .6 1.5 14.8 18.7
Jamario
Moon mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 25.7 .493 8.5 .5 .9 5.7 2.5 .8 .4 .6 1.8 8.6 18.2
sub 12.1 .370 8.7 .4 .2 3.8 1.5 1.9 .9 1.3 1.7 6.6 13.6
Andres
Nocioni mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 26.6 .615 10.1 3.2 .7 6.5 1.7 .8 .5 1.8 4.0 14.2 22.5
sub 14.7 .501 12.8 1.6 1.0 5.9 1.4 .4 1.0 1.7 3.5 13.5 21.6
Jason
Thompson mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 25.2 .533 11.4 4.1 2.9 6.7 1.0 .2 .6 2.0 3.8 14.1 23.4
sub 14.6 .489 10.1 5.8 3.7 7.2 2.1 .4 1.0 1.9 5.1 12.3 24.9
Evan
Turner mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 28.5 .451 8.5 3.7 .6 5.8 2.4 .9 .3 1.6 2.9 9.2 17.7
sub 22.6 .437 11.2 1.9 .9 5.6 2.7 1.0 .2 2.0 3.3 10.6 19.0
X is just sum of Pts+Reb+Ast+Stl+Blk-TO
Averages for these 23 players:
Code:
all mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 27.7 .537 11.8 2.9 1.8 4.7 2.4 .8 .9 1.8 3.5 14.0 22.8
sub 19.0 .494 12.2 3.6 2.3 5.0 2.0 .9 1.1 2.0 3.8 13.6 22.9
St/Sub 1.46 1.09 .97 .81 .79 .94 1.23 .91 .76 .93 .91 1.03 .99
Almost all players get (and likely receive) more assists in games they've started. Shooting tends to be less frequent but better.
We'd expect players to get starting nods when they're perceived to be playing well; back to the bench when their play suffers.
So, the almost identical 'X' rate (total productivity) may be just a coincidence, and that certain rates -- FTA, OReb, Blk -- are more indicative of 'easier' stats off the bench.
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Italian Stallion
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PostPosted: Thu Jan 13, 2011 4:45 pm Post subject: Reply with quote
Very enjoyable thread guys. Very Happy
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PostPosted: Thu Jan 13, 2011 8:24 pm Post subject: Re: Factoring starters' minutes into boxscore-based stats Reply with quote
Hi, I am new to this site but I wanted to throw my hat in the ring in terms of this little statistical experiment. Firstly, I think this adjustment process is a great idea for helping to weight a player's performance based on opponent and teammate quality. It's relatively simple and yet gets at the gist of the problem. One thing to note of interest is that the variance the players' PERs for 2011 dropped quite a bit relative to 2010. I'd be curious as to whether this phenomenon exists for a larger sample of players who transitioned from role player to starter and whether it relates to the decrease in the players' Sta%.
Mike G wrote:
These adjusted values do not represent anything absolute, but assume last year was 'correct', and then adjust to this year's Starter%.
For most of these guys, last year's PER and WS are probably 'too high', relative to league average (2/3) Starter%.
2011PERadj = 2011fac/2010fac * 2011PER
A minor statistical critique if you don't mind...
As you keenly noted, the tool you created is useful only for comparing 2010 vs. 2011 given the adjustment calculations. Devising a standardized metric so that we can compare all players to each other is pertinent to both evaluating their relative value and especially whether one should start over another. Shouldn't we aim to adjust all PERs and WS's to some agreed level of Sta%?
I would suggest the standard Sta% = 1/1*(1-(1/3)*32/48.5) = 77.7%. That is, the percentage of time spent facing other starters for a player who starts every game and plays 32 minutes. Though I'd love to hear alternative ideas.
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Mike G
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PostPosted: Fri Jan 14, 2011 9:14 am Post subject: Reply with quote
Thank you for the feedback.
From your special case of the Sta% formula, I get .780 (not .777).
This is a rather high standard for the whole league, since the average starter goes about 2/3 of the game, which is .667 .
Just 46 players -- barely 10% of all who have played -- are above .780 Sta%
The median of all players is .545 -- 225 players above and below that mark.
Low-mpg players tend toward the lower end. Half of all NBA minutes are with players above (and below) .732 Sta%.
Right around the minutes-weighted NBA average of .667 Sta% --
Code:
Sta% player tm GS G mpg StFac
.678 Bynum,Andrew LAL 8 15 23.0 1.002
.676 Collins,Jason Atl 14 27 12.6 1.002
.667 Graham,Joey Cle 8 16 19.3 1.000
.667 Barron,Earl Phx 6 12 15.2 1.000
.663 Jamison,Antawn Cle 17 35 30.6 .999
.659 Ibaka,Serge Okl 18 38 26.1 .998
.655 Nocioni,Andres Phi 16 34 20.4 .998
.654 Landry,Carl Sac 16 35 27.9 .998
The final column, 'Starter Factor' is designed such that 1.00 is average. It is --
StFac = (St%*(3/2))^N
And currently I have N = .135
The top of the list, and some from near the bottom (ranked by sta%) --
Code:
Sta% player tm GS G mpg StFac
.878 Bogans,Keith Chi 37 37 17.7 1.038
.876 Ming,Yao Hou 5 5 18.0 1.038
.875 Martin,Kenyon Den 8 8 18.1 1.037
.865 Mohammed,Nazr Cha 29 30 17.6 1.036
.863 Blair,Dejuan SAS 38 38 19.9 1.036
Sta% player tm GS G mpg StFac
.397 Thabeet,Hasheem Mem 0 28 9.2 .932
.395 Martin,Cartier Was 0 27 9.0 .932
.392 Johnson,Armon Por 0 26 8.5 .931
.390 Marks,Sean Por 0 21 8.3 .930
.387 Mbenga,D.J. NOH 0 25 7.8 .929
.385 Walton,Luke LAL 0 23 7.5 .929
.383 Wafer,Von Bos 0 31 7.2 .928
The exponent .135 is responsible for the rather small range of factors applied. The least-used players still get credit for 92% of their productions. Those whose stats are compiled against almost 90% starters are given a bonus of not quite 4%.
I do think these (or similar) factors could be applied to PER. If there's a replacement level to be subtracted for a stat like Win Shares, apply such a factor before that subtraction.
The bigger issue, though, is finding an appropriate factor for each statistic. A smallish sample upthread suggests that some productions come more easily vs (and with) starters : namely, assists and high% shots.
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Mike G
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PostPosted: Thu Dec 02, 2010 11:13 am Post subject: Factoring starters' minutes into boxscore-based stats Reply with quote
Since we know a player's minutes per game, games, and games started, we should be able to estimate the percentage of his opponents (and teammates) who have been Starters. We might then adjust his per-minute stats to the relative quality of the competition.
A couple of per-minute summary stats are PER and Win Shares per 48 minutes, both available at basketball-reference.com. Here are some of last year's and this season's numbers for players who have started all (or most) games this year, and who also don't play a lot of minutes. We can assume a high % of their opponents are starters.
Code:
2009-10 2010-11 PER WS/48
player tm G GS mpg G GS mpg 2010 2011 2010 2011
Hawes,Spencer Phi 72 59 26.4 18 18 17.0 13.8 10.2 .054 .005
Mohammed,Nazr Cha 58 29 17.0 17 17 17.6 19.6 16.5 .174 .088
Lopez,Robin Phx 51 31 19.3 9 9 17.8 17.6 11.2 .158 .017
Blair,Dejuan SAS 82 23 18.2 18 18 19.5 17.7 13.0 .147 .085
Williams,Shelden Den 54 0 11.1 17 17 20.4 14.1 12.0 .162 .102
Arroyo,Carlos Mia 72 34 22.0 19 19 22.2 12.3 11.6 .113 .121
Bogans,Keith Chi 79 49 19.7 16 16 21.6 7.7 8.0 .081 .062
McRoberts,Josh Ind 42 3 12.5 17 17 23.5 14.8 14.0 .134 .146
Gooden,Drew Mil 70 33 25.1 16 15 24.8 16.9 14.4 .121 .088
Milicic,Darko Min 32 18 21.4 18 18 27.5 12.8 12.0 .050 -.007
Almost all of these 11 have seen both their PER and their WS/48 drop, even as they have become starters this year. Are they really worse players than before?
Now here are their estimated % of Starter opponents, along with a proposed 'factor' for adjusting their stats, relative to a league standard of 2/3 of opponent minutes being Starters.
Code:
2009-10 2010-11 - PER - - - adj - WS/48 - - - adj
player sta% fac sta% fac 2010 2011 2011 2010 2011 2011
Hawes,Spencer .76 1.07 .88 1.15 13.8 10.2 11.0 .054 .005 .005
Mohammed,Nazr .67 1.00 .88 1.15 19.6 16.5 18.9 .174 .088 .101
Lopez,Robin .71 1.03 .88 1.15 17.6 11.2 12.5 .158 .017 .019
Blair,Dejuan .58 .93 .87 1.14 17.7 13.0 16.0 .147 .085 .104
Williams,Shelden .41 .78 .86 1.14 14.1 12.0 17.4 .162 .102 .148
Arroyo,Carlos .66 .99 .85 1.13 12.3 11.6 13.2 .113 .121 .137
Bogans,Keith .71 1.04 .85 1.13 7.7 8.0 8.7 .081 .062 .068
McRoberts,Josh .45 .83 .84 1.12 14.8 14.0 19.0 .134 .146 .198
Gooden,Drew .66 .99 .81 1.10 16.9 14.4 16.0 .121 .088 .098
Milicic,Darko .69 1.02 .81 1.10 12.8 12.0 13.0 .050 -.007 ---
avg .63 .97 .85 1.13 14.7 12.3 14.6 .119 .071 .087
Note that the 'adjusted' PER and WS/48 are almost all closer than the unadjusted, to last year's values. This adjustment suggests that PER's for these 10 players have not universally plunged since last year, but are on average just about the same.
These adjusted values do not represent anything absolute, but assume last year was 'correct', and then adjust to this year's Starter%.
For most of these guys, last year's PER and WS are probably 'too high', relative to league average (2/3) Starter%.
Sta% = GS/G*(1-1/3*mpg/48.5)+(1-GS/G)*1/3*(1+mpg/48.5)
fac = (Sta%*3/2)^x : for this demonstration, x = 0.5
2011PERadj = 2011fac/2010fac * 2011PER
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EvanZ
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PostPosted: Thu Dec 02, 2010 12:28 pm Post subject: Re: Factoring starters' minutes into boxscore-based stats Reply with quote
Mike G wrote:
Since we know a player's minutes per game, games, and games started, we should be able to estimate the percentage of his opponents (and teammates) who have been Starters. We might then adjust his per-minute stats to the relative quality of the competition.
But that makes perfect sense! Laughing
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DSMok1
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PostPosted: Thu Dec 02, 2010 12:37 pm Post subject: Reply with quote
That's why MPG is part of SPM and ASPM as a linearly positive factor. If you play 40 MPG, you're playing better competition/have better intangibles.
In fact, I use regressed MPG and team efficiency to create the Bayesian prior onto which I regress single-season ASPM (see the spreadsheets for the details) to create my best-estimate of single-season true production level for ASPM.
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Mike G
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PostPosted: Thu Dec 02, 2010 1:02 pm Post subject: Reply with quote
DSMok1 wrote:
.. If you play 40 MPG, you're playing better competition/have better intangibles...
Intangibles, maybe. But consider the mpg extremes: Going 48 minutes, your opponents have been 2/3 starters. (Starters have for years averaged 32 minutes.) Starting and going just 1 minute, you've likely faced 100% starters in that minute.
Nazr, RLopez, and Hawes start every game and average <18 minutes. The formula given above estimates their competition consists of 88% starters.
According to PER, Tyrus Thomas is the 10th best player in the league. According to WS/48, Brandon Bass is #6, Amir Johnson #16, Shannon Brown is better than Kobe Bryant. But those guys (other than Kobe) do not start, do not play over 20 mpg, and play against only 45-50% starters.
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DSMok1
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PostPosted: Thu Dec 02, 2010 1:56 pm Post subject: Reply with quote
Ah! I see what you mean. I wonder if I can factor that into ASPM...
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EvanZ
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PostPosted: Thu Dec 02, 2010 8:30 pm Post subject: Reply with quote
Assumption: Playing against starters would hurt your stats on offense, but playing with starters would help your stats on offense.
Am I right about that? If so, do these balance out the overall effect for subs?
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Mike G
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PostPosted: Fri Dec 03, 2010 6:05 am Post subject: Reply with quote
Good point, Evan. A player might see some improvement as a starter, in his shooting%, his TO rate, maybe his Ast rate.
But he won't generally get as many scoring opps, or rebounding opps; likely less ball-handling. These are 'volume' stats, and they count as 'productivity' on the floor.
I don't know exactly what to do with the Starter%, so I get this normalized 'factor' and multiply all the production rates by it, uniformly, including fouls and turnovers. So a guy playing a lot with and against subs will have his 'normalized' TO and PF deflated, along with everything else. This is a bit of compensation.
There's also the issue of garbage time. If a player goes over 40 mpg, he's getting some of that. A guy who never starts, and runs under 10 mpg, gets largely garbage time. It's really a stretch to count all minutes (and productions) as being equal.
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EvanZ
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PostPosted: Fri Dec 03, 2010 8:33 am Post subject: Reply with quote
Thanks, Mike. Would you mind running those numbers for Dorell Wright?
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Mike G
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PostPosted: Fri Dec 03, 2010 9:09 am Post subject: Reply with quote
Dorell Wright's Miami line from 2009-10 line, and this year's.
Code:
St% fac tm G Min Eff% Sco Reb Ast PF Stl TO Blk T e484
.48 .89 Mia 72 21 .562 13.2 5.9 1.8 2.2 1.2 1.2 .7 22.0 .81
.73 1.04 GSW 18 39 .520 13.7 4.9 2.3 2.3 1.0 1.7 .7 20.5 .69
The T rate (weighted sum of other columns) and eWins per 484 minute (1.00 is avg, zero = replacement) suggest he was better as a sub.
The ratio of this year's to last year's factors (104/89) is 1.169
Multiply that by last year's PER and WS/48 --
Code:
yr tm PER ws/48
2010 Mia 14.5 .137
2011 GSW 13.2 .059
2011 *1.17 15.4 .069
At least by PER, his starting status would seem to be justified; but the scoring and rebounding pace are both a bit looser in The City.
Oh, last night's game not included.
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EvanZ
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PostPosted: Fri Dec 03, 2010 9:22 am Post subject: Reply with quote
Thanks, Mike! I've been a little bit disappointed with him, but if he can ever get his shooting to be more consistent, he'll be pretty good. He does "all the little things" well, and he's almost certainly the best defender on the Warriors (although that's not saying much right now Laughing Crying or Very sad). Last night he had 10 rebounds, 7 asts, 1 stl, 2 blk and only 1 TOV. But he went 4/13 (.385 TS%).
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PostPosted: Fri Dec 03, 2010 9:28 am Post subject: Reply with quote
Sorry, I just downgraded him in an edit.
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Mike G
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PostPosted: Fri Dec 03, 2010 10:20 am Post subject: Reply with quote
[Now, where was I?]
If I didn't factor in starter/sub percents, I might think Corey Maggette was the 10th best scorer in the league, instead of 34th.
or that Shannon Brown is #12, rather than #36 so far.
or that Tyrus Thomas is our #19 scorer, #26 rebounder, and #9 shotblocker, rather than 38, 41, and 13, respectively. #12 overall player or #30?
Tyler Hansbrough: 86 or 128?
Craig Smith: 89 or 130 ?
Is Mareese Speights 12th-best rebounder or 41st ?
Is JR Smith top-100 in scoring, rebounding, and assists? or in none of these?
Is Marcin Gortat the #8 rebounder or #27? 22nd in blocks or 32nd?
Is Brandon Bass the 35th best player or the 60th?
Matt Barnes #71 or #96?
On the other side of the ticket, players whose Starter% enhances their rankings:
Shaq: 11th Sco and 13 Reb, unadjusted; 6th Sco and 11th Reb adjusted.
Nazr Mohammed: #16 Reb and #14 Blk, vs #10 Reb and #12 Blk
Horford: Sco #29, Reb #31, vs Sco 27 and Reb 23
Hibbert: #13 Blk, #13 overall, vs #14 Blk and 11 overall.
Duncan #15 vs #13 overall ranking
DeJuan Blair #9 Reb vs #4
All in this group are starters who go modest minutes.
All rankings are of players with at least 200 minutes.
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Mogilny
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PostPosted: Fri Dec 03, 2010 6:33 pm Post subject: Reply with quote
Interesting stuff. Amirs stats has been pretty awesome this year, will they decline now when he starts? Charlie Villaneuva is another guy who springs to my mind.
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Mike G
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PostPosted: Sun Dec 05, 2010 8:03 am Post subject: Reply with quote
Amir Johnson is an annual topic of hot discussions about guys whose numbers imply they should be getting a lot more minutes.
Here are his career splits, in raw per36, from
http://www.basketball-reference.com/pla ... 01/splits/
Code:
Amir G mpg FTA OReb Reb Blk TO Pts TS%
Bench 204 14.6 3.3 4.2 10.2 2.5 1.7 11.5 .612
Start 32 22.3 1.8 3.5 8.2 1.8 1.4 11.9 .686
FGA, Ast, Stl rates are roughly equal.
Even with barely half the FTA while starting, his Pts/Min are higher, due to better %.
As of Friday, I've got Amir ranked at #70 in per-minute productivity.
If I alter his line such that he'd started every game (leaving everyone else's the same), he vaults to a tie with Paul Pierce at #27.
I see at b-r.com, he's #40 in PER, #12 in WS/48. About every year, in both metrics, he rates as a star, or Allstar-level.
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Crow
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PostPosted: Sun Dec 05, 2010 3:57 pm Post subject: Reply with quote
Factoring the impact of estimated minutes against starters vs bench into boxscore-based metrics is a valuable enterprise in that segment over not doing it, but at some point it might good to see actual minutes for individual players against starter match-up opponents and maybe the average number of starters faced too (since defense is team and it is also somewhat on offense). If somebody wanted to pull that from play by play for everyone it would probably identify some players whose actual minutes against starters is notably over or under estimated by the standard minutes based method because of how their time is actually used by the coach with the starter / sub issue prominently in mind or not and along with other concerns or not.
And it could also be said that Adjusted +/- handles this issue fully and more simply and maybe better. With some estimated error of course, but without having to make starter assumptions or finding the actual level or making any assumptions about what that this means for defense faced. Very often starters are not that good on defense. I don't know if it is more or less than subs or that much better or worse. It is easier to accept that starters are better on offense than defense. If you are measuring "relative scoring potency" then the opponent's offense matters from that perspective but I am probably more interested in how their defense directly matters for the scoring of the other team.
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BobboFitos
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PostPosted: Sun Dec 05, 2010 3:58 pm Post subject: Reply with quote
I just don't understand why coaches claim "foul rate" about not playing more players more minutes... When they clearly deserve those minutes. Let the players foul out - there's always another game!
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Mike G
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PostPosted: Tue Dec 28, 2010 12:17 pm Post subject: Reply with quote
Amir Johnson update.
Per-36-minutes, data drawn from --
http://www.basketball-reference.com/pla ... lits/2011/
Code:
Amir G mpg FGA FTA OReb DRb Ast Stl Blk TO PF Pts TS%
Bench 16 19.8 9.9 4.9 5.6 4.8 1.0 1.1 1.8 1.8 6.3 15.3 .633
Start 14 26.6 9.3 1.9 3.2 4.9 1.8 1.5 1.6 1.5 5.2 11.9 .587
Coming off the bench, he got 2.5 times as many FTA, leading to 28% more points, and 75% more OReb.
As a starter, more assists and steals.
When I split these into 2 Amirs, it's guessed that Amir1 (off the bench) plays against and with 51% starters; Amir2 (the starter) goes against 79% starters.
Code:
per36 Sco Reb Ast PF Stl TO Blk e484
Amir1 14.3 11.1 1.0 6.1 1.1 1.8 1.7 1.18
Amir2 11.8 9.3 2.0 5.4 1.5 1.7 1.5 .98
Without 'starter compensation', he's a 28% better rebounder off the bench.
With adjustment, the diff is only 19%. About the same as his overall dropoff (e484, average = 1.00).
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BobboFitos
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PostPosted: Tue Dec 28, 2010 4:08 pm Post subject: Reply with quote
Mike, Amir has been battling a bad back his last couple of starts. I'm not sure to what extent that has affected his play, but he was pretty brutal last night vs Memphis... Does change the starter vs reserve numbers somewhat.
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PostPosted: Mon Jan 10, 2011 3:54 pm Post subject: Reply with quote
23 players who have started between 40% and 60% of their games, raw per36 minute averages as starter and as substitute.
Code:
Al-Farouq per 36 minutes, unadjusted
Aminu mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 22.1 .536 11.4 2.2 1.5 4.4 1.5 1.4 .6 3.5 3.3 13.2 19.2
sub 14.9 .528 11.6 3.3 2.5 6.5 1.1 1.4 .4 2.9 3.4 13.8 22.8
Louis
Amundson mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 16.9 .462 10.7 2.7 4.3 5.2 1.2 1.5 1.2 1.5 6.1 11.0 22.9
sub 17.8 .400 10.1 4.3 4.3 5.1 1.0 .8 1.0 2.0 4.3 9.6 19.8
Jose
Calderon mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 32.9 .598 10.7 1.2 .7 2.7 10.7 1.6 .0 2.7 2.4 13.4 26.4
sub 21.7 .482 11.9 2.8 .4 2.9 8.9 1.7 .0 2.4 2.3 12.6 24.1
Wilson
Chandler mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 39.0 .627 13.6 2.6 1.2 5.3 2.1 .7 1.3 1.1 2.9 18.4 28.0
sub 29.3 .533 16.0 3.5 1.8 5.2 1.6 .6 2.0 1.9 4.3 18.7 28.0
Jason
Collins mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 19.0 .458 4.6 1.6 2.0 4.6 1.5 .8 .3 1.6 5.0 4.9 12.5
sub 5.3 .688 5.8 6.8 1.0 5.4 1.0 .0 1.0 3.4 8.3 12.2 17.0
Demarcus
Cousins mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 27.4 .512 16.9 5.8 3.2 7.2 2.7 .8 1.0 2.9 5.5 19.9 32.0
sub 24.0 .430 14.2 5.5 4.2 7.0 1.7 1.3 .7 4.0 6.0 14.3 25.2
Samuel
Dalembert mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 24.7 .465 7.9 2.0 4.2 7.7 1.3 .4 3.1 3.0 4.1 8.2 21.8
sub 15.1 .398 9.7 1.6 4.9 7.9 1.4 .3 2.9 1.7 5.4 8.2 23.9
Baron
Davis mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 30.2 .485 13.0 2.2 .5 2.4 8.2 1.1 .5 2.7 3.2 13.6 23.6
sub 19.9 .389 13.8 3.6 .5 3.8 10.9 2.5 .9 3.8 4.3 12.0 26.7
Austin
Daye mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 22.3 .554 13.2 2.2 1.6 5.4 1.3 .4 .6 1.6 4.1 15.7 23.5
sub 10.6 .394 14.7 1.8 2.3 4.8 1.6 1.6 .5 1.6 3.8 12.2 21.3
Taj
Gibson mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 25.7 .536 12.7 3.0 3.1 6.1 1.7 1.1 2.0 2.1 4.7 15.0 26.9
sub 19.8 .422 11.8 2.4 3.8 5.9 1.0 .6 2.6 1.6 3.4 10.8 23.0
Xavier
Henry mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 20.7 .482 10.3 2.2 .3 2.1 1.7 .5 .3 1.1 3.5 10.9 14.8
sub 12.9 .428 12.8 6.7 1.4 1.9 .5 .9 .0 .7 3.3 13.5 17.4
Serge
Ibaka mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 26.3 .573 10.4 2.4 3.5 5.7 .2 .8 3.0 .6 4.5 13.2 25.7
sub 25.7 .614 9.4 3.8 3.0 6.3 .3 .4 3.3 1.6 4.8 13.6 25.2
Antawn
Jamison mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 36.1 .546 17.1 4.3 .9 5.2 1.3 .8 .6 1.3 2.7 20.7 28.1
sub 25.4 .498 16.0 3.7 2.0 6.1 2.1 .9 .6 1.4 3.2 17.6 27.8
Amir
Johnson mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 27.8 .582 9.5 2.3 3.1 5.1 2.0 1.0 1.5 1.4 5.0 12.3 23.6
sub 19.8 .633 9.9 4.9 5.6 4.8 1.0 1.1 1.8 1.8 6.3 15.3 27.8
Linas
Kleiza mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 30.6 .510 14.7 1.7 1.0 4.8 2.1 .7 .2 2.8 3.7 15.8 21.7
sub 21.1 .509 14.4 3.0 1.9 5.9 .6 .4 .2 2.4 3.3 16.0 22.8
Carl
Landry mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 31.3 .516 13.4 4.9 3.8 3.2 .9 .6 .1 2.0 3.0 16.0 22.7
sub 23.5 .516 12.0 5.5 2.8 3.1 .9 .7 1.3 1.9 3.5 14.8 21.6
Jason
Maxiell mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 21.4 .507 7.9 3.2 2.4 2.8 .6 .7 .8 .8 3.5 9.5 16.0
sub 16.1 .459 6.0 4.2 2.1 3.3 .6 .9 1.5 1.6 4.0 7.1 13.8
O.J.
Mayo mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 36.0 .512 14.2 2.3 .6 2.9 2.4 1.1 .5 2.1 2.3 15.6 21.0
sub 24.0 .518 14.7 3.7 .6 2.5 2.4 .9 .4 1.6 2.2 16.9 22.3
Jodie
Meeks mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 28.3 .548 10.1 4.3 .2 2.1 1.0 .7 .1 1.4 1.5 13.2 16.0
sub 17.3 .606 10.8 3.1 .2 1.2 1.5 1.7 .0 .6 1.5 14.8 18.7
Jamario
Moon mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 25.7 .493 8.5 .5 .9 5.7 2.5 .8 .4 .6 1.8 8.6 18.2
sub 12.1 .370 8.7 .4 .2 3.8 1.5 1.9 .9 1.3 1.7 6.6 13.6
Andres
Nocioni mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 26.6 .615 10.1 3.2 .7 6.5 1.7 .8 .5 1.8 4.0 14.2 22.5
sub 14.7 .501 12.8 1.6 1.0 5.9 1.4 .4 1.0 1.7 3.5 13.5 21.6
Jason
Thompson mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 25.2 .533 11.4 4.1 2.9 6.7 1.0 .2 .6 2.0 3.8 14.1 23.4
sub 14.6 .489 10.1 5.8 3.7 7.2 2.1 .4 1.0 1.9 5.1 12.3 24.9
Evan
Turner mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 28.5 .451 8.5 3.7 .6 5.8 2.4 .9 .3 1.6 2.9 9.2 17.7
sub 22.6 .437 11.2 1.9 .9 5.6 2.7 1.0 .2 2.0 3.3 10.6 19.0
X is just sum of Pts+Reb+Ast+Stl+Blk-TO
Averages for these 23 players:
Code:
all mpg TS% FGA FTA OReb DRb Ast Stl Blk TO PF Pts X
start 27.7 .537 11.8 2.9 1.8 4.7 2.4 .8 .9 1.8 3.5 14.0 22.8
sub 19.0 .494 12.2 3.6 2.3 5.0 2.0 .9 1.1 2.0 3.8 13.6 22.9
St/Sub 1.46 1.09 .97 .81 .79 .94 1.23 .91 .76 .93 .91 1.03 .99
Almost all players get (and likely receive) more assists in games they've started. Shooting tends to be less frequent but better.
We'd expect players to get starting nods when they're perceived to be playing well; back to the bench when their play suffers.
So, the almost identical 'X' rate (total productivity) may be just a coincidence, and that certain rates -- FTA, OReb, Blk -- are more indicative of 'easier' stats off the bench.
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Italian Stallion
Joined: 04 Mar 2009
Posts: 112
PostPosted: Thu Jan 13, 2011 4:45 pm Post subject: Reply with quote
Very enjoyable thread guys. Very Happy
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Scoreboard415
Joined: 12 Jan 2011
Posts: 1
Location: Columbus
PostPosted: Thu Jan 13, 2011 8:24 pm Post subject: Re: Factoring starters' minutes into boxscore-based stats Reply with quote
Hi, I am new to this site but I wanted to throw my hat in the ring in terms of this little statistical experiment. Firstly, I think this adjustment process is a great idea for helping to weight a player's performance based on opponent and teammate quality. It's relatively simple and yet gets at the gist of the problem. One thing to note of interest is that the variance the players' PERs for 2011 dropped quite a bit relative to 2010. I'd be curious as to whether this phenomenon exists for a larger sample of players who transitioned from role player to starter and whether it relates to the decrease in the players' Sta%.
Mike G wrote:
These adjusted values do not represent anything absolute, but assume last year was 'correct', and then adjust to this year's Starter%.
For most of these guys, last year's PER and WS are probably 'too high', relative to league average (2/3) Starter%.
2011PERadj = 2011fac/2010fac * 2011PER
A minor statistical critique if you don't mind...
As you keenly noted, the tool you created is useful only for comparing 2010 vs. 2011 given the adjustment calculations. Devising a standardized metric so that we can compare all players to each other is pertinent to both evaluating their relative value and especially whether one should start over another. Shouldn't we aim to adjust all PERs and WS's to some agreed level of Sta%?
I would suggest the standard Sta% = 1/1*(1-(1/3)*32/48.5) = 77.7%. That is, the percentage of time spent facing other starters for a player who starts every game and plays 32 minutes. Though I'd love to hear alternative ideas.
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Mike G
Joined: 14 Jan 2005
Posts: 3574
Location: Hendersonville, NC
PostPosted: Fri Jan 14, 2011 9:14 am Post subject: Reply with quote
Thank you for the feedback.
From your special case of the Sta% formula, I get .780 (not .777).
This is a rather high standard for the whole league, since the average starter goes about 2/3 of the game, which is .667 .
Just 46 players -- barely 10% of all who have played -- are above .780 Sta%
The median of all players is .545 -- 225 players above and below that mark.
Low-mpg players tend toward the lower end. Half of all NBA minutes are with players above (and below) .732 Sta%.
Right around the minutes-weighted NBA average of .667 Sta% --
Code:
Sta% player tm GS G mpg StFac
.678 Bynum,Andrew LAL 8 15 23.0 1.002
.676 Collins,Jason Atl 14 27 12.6 1.002
.667 Graham,Joey Cle 8 16 19.3 1.000
.667 Barron,Earl Phx 6 12 15.2 1.000
.663 Jamison,Antawn Cle 17 35 30.6 .999
.659 Ibaka,Serge Okl 18 38 26.1 .998
.655 Nocioni,Andres Phi 16 34 20.4 .998
.654 Landry,Carl Sac 16 35 27.9 .998
The final column, 'Starter Factor' is designed such that 1.00 is average. It is --
StFac = (St%*(3/2))^N
And currently I have N = .135
The top of the list, and some from near the bottom (ranked by sta%) --
Code:
Sta% player tm GS G mpg StFac
.878 Bogans,Keith Chi 37 37 17.7 1.038
.876 Ming,Yao Hou 5 5 18.0 1.038
.875 Martin,Kenyon Den 8 8 18.1 1.037
.865 Mohammed,Nazr Cha 29 30 17.6 1.036
.863 Blair,Dejuan SAS 38 38 19.9 1.036
Sta% player tm GS G mpg StFac
.397 Thabeet,Hasheem Mem 0 28 9.2 .932
.395 Martin,Cartier Was 0 27 9.0 .932
.392 Johnson,Armon Por 0 26 8.5 .931
.390 Marks,Sean Por 0 21 8.3 .930
.387 Mbenga,D.J. NOH 0 25 7.8 .929
.385 Walton,Luke LAL 0 23 7.5 .929
.383 Wafer,Von Bos 0 31 7.2 .928
The exponent .135 is responsible for the rather small range of factors applied. The least-used players still get credit for 92% of their productions. Those whose stats are compiled against almost 90% starters are given a bonus of not quite 4%.
I do think these (or similar) factors could be applied to PER. If there's a replacement level to be subtracted for a stat like Win Shares, apply such a factor before that subtraction.
The bigger issue, though, is finding an appropriate factor for each statistic. A smallish sample upthread suggests that some productions come more easily vs (and with) starters : namely, assists and high% shots.