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reconciling PER and Win Shares per minute
Posted: Mon Oct 03, 2011 5:03 pm
by Mike G
Some of us still use basketball-reference a lot, and the two 'composite stats' listed for players in the "Advanced Statistics" section are often not in very close agreement. A player may look great in one number and mediocre in the other.
My general take is that PER accounts for pace but not for how good the team is, and thus only accounts for how good a player is per possession, regardless of how much better the opponent is. And Win Shares exaggerate the difference between players for good teams and those with lesser teams.
I grabbed 645 player lines from 2010-11, players with multiple teams being separated into their part-seasons.
http://www.basketball-reference.com/lea ... stats.html
I found the following formula to guess a player's WS/48 based on his PER:
WS/48 = (PER - 4.92)/99.0
This minimizes the sum of differences between player WS and the total 'guessed' WS.
It's very tempting to use the formula
WS/48 = (PER-5)/100 . And doing so yields this conversion:
Code: Select all
PER WS/48
35.0 .300
30.0 .250
25.0 .200
20.0 .150
15.0 .100
10.0 .050
5.0 .000
0.0 -.050
Anyway, of players with >1000 minutes, those whose PER most underestimates their WS/48.
Code: Select all
Player Tm Min PER WS/48 WS ws48? WS? dif dif48
Joel Anthony MIA 1463 7.3 .107 3.3 .024 .7 2.5 .083
James Jones MIA 1549 11.1 .145 4.7 .062 2.0 2.7 .083
Tyson Chandler DAL 2059 18.4 .218 9.4 .136 5.8 3.5 .082
Kurt Thomas CHI 1178 10.0 .131 3.2 .051 1.3 2.0 .080
Keith Bogans CHI 1461 9.0 .118 3.6 .041 1.3 2.3 .077
Ryan Anderson ORL 1424 19.0 .217 6.4 .142 4.2 2.2 .075
Kyle Korver CHI 1649 13.0 .149 5.1 .082 2.8 2.3 .067
Joakim Noah CHI 1576 18.8 .205 6.7 .140 4.6 2.1 .065
J.J. Redick ORL 1513 12.8 .143 4.5 .080 2.5 2.0 .063
Matt Bonner SAS 1432 13.5 .147 4.4 .087 2.6 1.8 .060
Ronnie Brewer CHI 1781 13.8 .147 5.5 .090 3.3 2.1 .057
Hedo Turkoglu ORL 1910 13.5 .143 5.7 .087 3.4 2.2 .056
Nick Collison OKC 1524 10.8 .113 3.6 .059 1.9 1.7 .054
Paul Pierce BOS 2774 19.7 .201 11.6 .149 8.6 3.0 .052
Ray Allen BOS 2890 16.4 .166 10.0 .116 7.0 3.0 .050
All players from very good teams, mostly or entirely with high TS% and low TO rates.
Those whose PER would generally get a much higher WS/48:
Code: Select all
Player Tm Min PER WS/48 WS ws48? WS? dif dif48
Jordan Crawford TOT 1027 11.8 -.026 -.6 .069 1.5 2.0 -.095
Mo Williams CLE 1065 13.8 -.005 -.1 .090 2.0 2.1 -.095
J.J. Hickson CLE 2256 15.6 .032 1.5 .108 5.1 3.6 -.076
DMarcus Cousins SAC 2309 14.6 .022 1.1 .098 4.7 3.6 -.076
Michael Beasley MIN 2361 15.5 .035 1.7 .107 5.3 3.5 -.072
John Wall WAS 2606 15.8 .041 2.2 .110 6.0 3.7 -.069
Andray Blatche WAS 2172 16.9 .053 2.4 .121 5.5 3.1 -.068
Darko Milicic MIN 1686 12.2 .007 .2 .074 2.6 2.3 -.067
Mo Williams TOT 1788 13.9 .026 1.0 .091 3.4 2.4 -.065
Sonny Weems TOR 1413 10.2 -.011 -.3 .053 1.6 1.9 -.064
Andrea Bargnani TOR 2353 16.4 .053 2.6 .116 5.7 3.1 -.063
Linas Kleiza TOR 1032 10.1 -.010 -.2 .052 1.1 1.3 -.062
Tyreke Evans SAC 2107 14.4 .036 1.6 .096 4.2 2.6 -.060
Stephen Jackson CHA 2405 14.6 .039 2.0 .098 4.9 2.9 -.059
Antawn Jamison CLE 1842 16.8 .067 2.6 .120 4.6 2.0 -.053
All players from bad teams, etc.
Re: reconciling PER and Win Shares per minute
Posted: Tue Oct 04, 2011 12:14 am
by Crow
That is a handy general conversion formula.
Only about half the big WS/48 underestimates using PER are for guys with low usages (<15%) and only about the big overestimates are for guys with high usages (near or over 25%). I had expected those rates to be higher.
Other factors are involved. One big factor in WS/48 but not in PER at all is team shot defense.The underestimate list is all players from good teams and almost all good defensive teams (one average defensive team but probably the best defender on that team- Collison). The overestimate list is all players from bad teams and bad defensive teams.
Re: reconciling PER and Win Shares per minute
Posted: Tue Oct 04, 2011 10:35 am
by Mike G
Indeed, the 61-win Bulls have the PER's of a 44-win team with average defense; the 21-win Raptors have PER's of a 39-win team. That seems pretty drastic.
One might "adjust" PER by (Tm DRtg/Lg DRtg)^N -- finding an exponent that best fits team PER-wins (from formula above) to Pythagorean wins (or WS) .
Re: reconciling PER and Win Shares per minute
Posted: Tue Oct 04, 2011 12:15 pm
by Mike G
OK, this is definitely going to be a work in progress for a while.
I'm calling this
PERWins.
PERW = (PER-5)/100 * (Min/48.4)
Now the suggested adjustment to PER.
PER2 = PER * (LgDRtg/TmDRtg)^4
For whatever reason, an exponent of 4.00 makes a better fit than does 3.99 or 4.01 .
Now an adjusted version of PERWins:
PER2W = (PER2 - 5)/100 * (Min/48.4)
Ranked from best to worst teams, the differences from WS, for PERW and PER2W
Code: Select all
West WS perW per2W diff dif2 East WS perW per2W diff dif2
LAL 58.0 46.3 54.3 -11.7 -3.7 CHI 63.1 43.4 63.2 -19.7 0.1
SAS 57.0 46.5 51.0 -10.5 -6.0 MIA 63.1 46.3 56.6 -16.8 -6.5
OKC 54.3 46.5 46.8 -7.7 -7.5 ORL 57.2 40.8 55.2 -16.4 -2.1
DAL 52.9 43.6 49.4 -9.2 -3.4 BOS 56.5 41.8 61.1 -14.7 4.5
DEN 52.2 45.2 45.2 -7.0 -7.0 PHI 46.2 42.2 47.9 -4.0 1.7
HOU 47.6 44.7 40.7 -2.9 -6.9 NYK 43.9 44.4 38.1 0.5 -5.8
MEM 47.3 44.0 49.6 -3.3 2.3 MIL 40.8 35.6 46.9 -5.1 6.1
POR 46.3 42.8 43.3 -3.5 -3.0 ATL 39.4 39.1 39.8 -0.3 0.4
NOH 45.8 41.0 46.0 -4.8 0.3 IND 38.9 37.6 40.5 -1.2 1.7
PHO 39.7 42.6 35.8 2.9 -3.9 DET 32.2 41.3 32.1 9.1 -0.1
UTA 36.5 41.9 35.8 5.4 -0.7 CHA 31.7 36.8 35.7 5.1 4.0
GSW 36.3 42.3 34.9 6.0 -1.4 NJN 26.4 34.9 29.8 8.5 3.4
LAC 32.9 37.5 34.6 4.6 1.7 TOR 25.7 38.6 28.1 12.9 2.4
SAC 28.9 36.1 32.7 7.2 3.7 WAS 23.3 36.2 30.5 13.0 7.2
MIN 24.9 35.7 28.4 10.8 3.5 CLE 18.2 33.7 25.5 15.5 7.3
Denver's DRtg was exactly the league average, so it doesn't change anything.
The avg unadjusted absolute difference between WS and PERW is 9.1
Avg diff between WS and PER2W is 3.6
I have noticed that teams averaged 42.2 WS, rather than 41. This seems to have something to do with overtime minutes; perhaps converting from WS/
48, even though teams averaged up to 48.8 mpg (Phx, NJ, Okl) ?
Re: reconciling PER and Win Shares per minute
Posted: Tue Oct 04, 2011 1:08 pm
by Mike G
PER2W are constructed such that they more closely match Win Shares -- which are supposed to match pythagorean Wins.
PER is adjusted by DRtg, in some cases dramatically, to achieve this. The top 10 players in minutes:
Code: Select all
Player Tm Min PER per2 WS perW per2W
Monta Ellis GSW 3227 18.6 16.4 6.0 9.1 7.6
LaMarcus Aldridge POR 3211 21.5 21.7 11.1 10.9 11.1
Luol Deng CHI 3208 15.5 20.3 10.0 7.0 10.1
Dorell Wright GSW 3147 15.0 13.2 5.8 6.5 5.4
Blake Griffin LAC 3112 21.9 20.8 9.9 10.9 10.2
LeBron James MIA 3063 27.3 31.5 15.6 14.1 16.8
Kevin Durant OKC 3038 23.6 23.7 12.0 11.7 11.7
Pau Gasol LAL 3037 23.3 26.1 14.7 11.5 13.2
Derrick Rose CHI 3026 23.5 30.8 13.1 11.6 16.1
Al Jefferson UTA 2940 20.1 18.1 7.8 9.2 8.0
All players with poor defensive teams have had their PER adjusted downward.
LeBron and Rose both now have per2W which exceed their WS.
Here are some players who were with 2 teams for at least 300 minutes each.
On the left are players whose PER changed rather drastically, and it may be explained almost entirely by their changed environment: per2 has changed much less.
Players on the right would seem to offer counter-evidence.
Code: Select all
Player Tm PER per2 ws48 Player Tm PER per2 ws48
J Richardson PHO 19.1 17.0 .118 Vince Carter ORL 16.1 19.9 .153
J Richardson ORL 13.2 16.3 .127 Vince Carter PHO 14.2 12.7 .061
Marcin Gortat ORL 13.7 16.9 .159 Hedo Turkoglu PHO 13.1 11.7 .093
Marcin Gortat PHO 18.8 16.8 .152 Hedo Turkoglu ORL 13.5 16.7 .144
Gilbert Arenas WAS 14.0 12.6 .025 Nenad Krstic OKC 12.5 12.5 .097
Gilbert Arenas ORL 8.6 10.6 .008 Nenad Krstic BOS 14.3 18.7 .171
Marcus Thornton NOH 14.0 15.2 .057 Jeff Green OKC 12.9 12.9 .088
Marcus Thornton SAC 18.2 17.1 .124 Jeff Green BOS 12.9 16.9 .119
Baron Davis LAC 16.3 15.5 .080 Jarrett Jack TOR 12.5 10.3 .003
Baron Davis CLE 19.3 16.4 .087 Jarrett Jack NOH 14.6 15.8 .083
Mickael Pietrus ORL 8.3 10.2 .084 Kendrick Perkins BOS 10.2 13.4 .089
Mickael Pietrus PHO 10.8 9.6 .039 Kendrick Perkins OKC 9.1 9.1 .046
Shane Battier HOU 12.9 12.1 .106 Carl Landry SAC 14.7 13.8 .087
Shane Battier MEM 10.6 11.5 .098 Carl Landry NOH 15.2 16.5 .126
WS/48 is given for corroboration: In almost every case, per2 is more closely related.
Of 36 such traded players, the average PER change (absolute) was 2.75, and per2 change was 2.70
Re: reconciling PER and Win Shares per minute
Posted: Tue Oct 04, 2011 5:31 pm
by Mike G
Here are the top 20 PER and PER2 from last season; minimum 1000 minutes.
Code: Select all
Player Tm PER ws48 Player Tm per2 ws48 per2w48 WS per2W
LeBron James MIA 27.3 .246 Dwi Howard ORL 32.1 .238 .271 14.4 16.4
Dwi Howard ORL 26.0 .238 LeBron James MIA 31.5 .246 .265 15.6 16.8
Dwyane Wade MIA 25.6 .220 Derrick Rose CHI 30.8 .210 .258 13.1 16.1
Kevin Love MIN 24.3 .212 Dwyane Wade MIA 29.6 .220 .246 12.8 14.3
Kobe Bryant LAL 23.9 .180 Ke Garnett BOS 27.0 .196 .220 9.0 10.1
Chris Paul NOH 23.7 .234 Kobe Bryant LAL 26.8 .180 .218 10.4 12.5
Kevin Durant OKC 23.6 .191 Pau Gasol LAL 26.1 .234 .211 14.7 13.2
R Westbrook OKC 23.6 .160 Paul Pierce BOS 25.8 .203 .208 11.6 11.9
Derrick Rose CHI 23.5 .210 Chris Paul NOH 25.6 .234 .206 13.9 12.3
D Nowitzki DAL 23.4 .215 D Nowitzki DAL 25.5 .215 .205 11.1 10.6
Pau Gasol LAL 23.3 .234 Ca Boozer CHI 24.6 .150 .196 5.8 7.6
A Stoudemire NYK 22.7 .135 Joakim Noah CHI 24.6 .207 .196 6.7 6.4
Z Randolph MEM 22.6 .187 Za Randolph MEM 24.6 .187 .196 10.5 11.0
De Williams UTA 22.1 .160 Kevin Durant OKC 23.7 .191 .187 12.0 11.7
Bl Griffin LAC 21.9 .153 Ru Westbrook OKC 23.7 .160 .187 9.4 11.0
Tim Duncan SAS 21.9 .172 Andrew Bynum LAL 23.6 .212 .186 6.6 5.8
Ma Ginobili SAS 21.7 .197 Ry Anderson ORL 23.5 .219 .185 6.4 5.4
L Aldridge POR 21.5 .167 Tim Duncan SAS 23.3 .172 .183 7.7 8.2
Kevin Martin HOU 21.4 .176 Ma Ginobili SAS 23.1 .197 .181 9.9 9.1
Ca Anthony DEN 21.2 .128 Chris Bosh MIA 22.4 .178 .174 10.3 10.1
Kevin Love (per2 = 21.1) would be the highest from a bad team.
Re: reconciling PER and Win Shares per minute
Posted: Tue Oct 04, 2011 6:02 pm
by Crow
I compared Mike's per2W values to “Win Shares" using the values on this chart
http://dberri.files.wordpress.com/2011/07/untitled9.png for the top 10 minute guys and the average absolute difference was about 3 wins. That is substantial and probably related to how these metrics vary on treatment of usage and scoring efficiency.
I then compared “Wins Produced Combined” (which gives more individualized defensive ratings to players than traditional Wins Produced by looking at presumptive based on boxscore opponent performance against a particular player) to per2W and the average absolute difference was just a bit more than 1 win. Still apples and oranges and this is just a small sample. The closer similarity is probably just coincidence, but I mention it anyways, mainly to get to the next suggestion.
Perhaps it might be worth comparing
net counterpart per2w to Wins Produced Combined so that both metrics use the net counterpart basis. Though this is getting pretty twisted and might not interest many, especially not the purists. Adjusting for team defensive performance and counterpart performance might be too much or in a roundabout way might balance those weights and fit with a perspective that shot defense occurs at counterpart and team levels and perhaps should be evaluated at both rather than just one.
Comparison to some form of APM could be added, if inclined. I generally think viewing and considering the pattern of ratings across metrics is more helpful than focusing on just one.
Re: reconciling PER and Win Shares per minute
Posted: Fri Oct 21, 2011 8:15 pm
by Crow
Of the top 20 on PER, only 60% were in a lineup that was in the league's top 20 for minutes used and was positive on raw and / or Adjusted +/-.
5 were on negative performing lineups- D. Williams, Westbrook & Durant (both on the court and the lineup is rated negative? I guess Thabo, Green and Krstic wasn't a good idea as the by far most used lineup for 2+ cumulative seasons), Love and Aldridge. 3 (Anthony, Griffin and Nowitski) were not in a top 20 for minutes used lineup.
Is it that hard to find a good big minute lineup for 40% of the league's top 20 on PER? Some of these players may be tough cases to work well at lineup level, some are missed coaching opportunities (or a different philosophy, intention or not).
WS per 48 for bigger minute players did somewhat better. 75% of them appear in a lineup that was in the league's top 20 for minutes used and was positive on raw and / or Adjusted +/-.
Re: reconciling PER and Win Shares per minute
Posted: Sat Oct 22, 2011 7:21 pm
by Crow
The top 20 on 1 year RAPM appear on positive lineups within the top 20 on minutes played, slightly more than the top 20 on PER but a bit less than the top 20 on WS/48.
But would need to check multi-season to see if that was a stable pattern. WS/48 benefits from having team-based shot defense included instead of just individual stats and that could affect which lineups are positive and which lineups are allowed to get big minutes.
Maybe that is worth something. Never know til you check and think about it.
Re: reconciling PER and Win Shares per minute
Posted: Wed Nov 30, 2011 11:12 am
by Mike G
This is a bit tangential. I got to checking trends in league dominance by various positions, and why some rather mediocre players got into lots of All-Star games while some really good ones did not.
This isn't at all an in-depth study, but just breaking it down to decades -- the '90s being 1990-1999, for example -- the median PER and WS/48 of All-Star seasons, by position, via:
http://bkref.com/tiny/BPAZy\
Code: Select all
position: Guards Forwards Centers all All-Stars
decade PER ws48 PER ws48 PER ws48 PER ws48
'50s 15.9 .119 20.6 .177 22.5 .158 19.1 .150
'60s 16.9 .134 18.7 .138 19.3 .178 18.1 .144
'70s 18.4 .125 18.5 .138 21.7 .178 19.1 .141
'80s 19.2 .148 21.6 .168 20.4 .168 20.4 .160
'90s 19.9 .170 20.4 .172 22.9 .178 20.7 .172
'00s 21.4 .162 22.2 .179 22.6 .194 22.0 .175
'10s 21.2 .171 22.6 .182 20.3 .181 21.6 .177
Recall that PER and ws/48 tend to be related by ws/48 = (PER-5)/100
That is, a PER of 15 predicts a WS/48 = .100; 20 = .150
Knowing, too, that WS/48 are generally higher (relative to PER) for players with winning teams, the table corroborates the perception that players from better teams are also more likely to be selected to All-Star lineups, over players with similar stats for weaker teams.
The only examples breaking this pattern are centers in the '50s and guards in the '70s.
In all other instances, WS/48 are higher than expected, given the PER's.
The link above is for '70s guards. Pete Maravich was a '79 AllStar with PER 13.4 and .004 WS/48.
Re: reconciling PER and Win Shares per minute
Posted: Mon Dec 05, 2011 10:10 am
by huevonkiller
The problem with PER is usage rate.
The problem with WS/48 is team defense of course. Both are very helpful figures once you understand their flaws.
