I'm just back at home... If you can give me a few hours and accept the data which goes back to 85, I want to send a metric too instead of trying to increase prediction power... Surpassing BPM should be enough for now.
Edit: Well, I'm out then
The debut and popularization of BPM
-
permaximum
- Posts: 416
- Joined: Tue Nov 27, 2012 7:04 pm
Re: The popularization of BPM
@Neil Paine
I'm just back at home... If you can give me a few hours and accept the data which goes back to 85, I want to send a metric too instead of trying to increase prediction power... Surpassing BPM should be enough for now.
Edit: Well, I'm out then
I'm just back at home... If you can give me a few hours and accept the data which goes back to 85, I want to send a metric too instead of trying to increase prediction power... Surpassing BPM should be enough for now.
Edit: Well, I'm out then
-
Neil Paine
- Posts: 73
- Joined: Mon Apr 18, 2011 1:18 am
- Location: Philadelphia
- Contact:
Re: The popularization of BPM
I ended up not having started yet, and another demand came up for tomorrow, so you've got a few days at least, if not more.
-
permaximum
- Posts: 416
- Joined: Tue Nov 27, 2012 7:04 pm
Re: The popularization of BPM
Do you test prediction accuracy using the previous year per min (or per pos) value on the outcome of next season's games or the whole season? Wins or margin? Or SRS if it's season?Neil Paine wrote:I ended up not having started yet, and another demand came up for tomorrow, so you've got a few days at least, if not more.
Re: The popularization of BPM
Here's how Neil did it the last time: http://www.apbr.org/metrics/viewtopic.p ... 343#p15334permaximum wrote:Do you test prediction accuracy using the previous year per min (or per pos) value on the outcome of next season's games or the whole season? Wins or margin? Or SRS if it's season?Neil Paine wrote:I ended up not having started yet, and another demand came up for tomorrow, so you've got a few days at least, if not more.
Re: The popularization of BPM
Have you seen my request regarding the R² for the specific sample (714 players with the most minutes played in the 14yr RAPM set)? I would like to calculate that by myself, but somehow I can't extract the data from your public tableau (it is supposed to show me an export option, but that doesn't show up). Your reported R² (that is possesssion weighted correlation, right?) are based on that 900 player sample you used, though it might be not that different anyway, but I guess the R² would be higher for the somewhat smaller sample.DSMok1 wrote: Here's how Neil did it the last time: http://www.apbr.org/metrics/viewtopic.p ... 343#p15334
I used a combination of multivariat analysis and non-linear regression to get the following results for that 14yr RAPM set (possession weighted R²):
ORAPM: 0.859
DRAPM: 0.683
RAPM: 0.739
Though, currently I'm in the process of redefining the variables going in and trying to make the whole algorithm more applicable to historic data. The algorithm is based on about half of the dataset (5000 to 15000 min played), while then applied to the whole 714 player sample.
Here are the numbers for the players:
Code: Select all
Player Off Def Com
LeBron James 7.83 0.81 8.64
Kevin Garnett 2.34 4.52 6.86
Chris Paul 6.09 0.70 6.80
Manu Ginobili 6.03 0.67 6.69
Tim Duncan 1.71 4.53 6.24
Kobe Bryant 6.35 -0.18 6.17
Tracy McGrady 5.09 0.80 5.89
Shaquille O'Neal 1.95 3.87 5.83
Paul George 2.18 3.55 5.73
Pau Gasol 1.70 3.90 5.61
Marc Gasol 0.42 4.62 5.04
Andrei Kirilenko 1.86 3.14 5.00
Dwyane Wade 4.87 -0.04 4.83
John Stockton 3.60 1.19 4.80
Blake Griffin 2.87 1.83 4.70
Steve Nash 6.47 -1.77 4.69
Kevin Durant 3.69 0.98 4.67
Amir Johnson 1.97 2.60 4.57
Shane Battier 1.34 3.09 4.43
James Harden 5.11 -0.71 4.40
Yao Ming -0.05 4.23 4.19
Russell Westbrook 3.32 0.85 4.17
Chauncey Billups 5.15 -1.04 4.12
Ben Wallace -0.94 5.05 4.11
Patrick Beverley 2.96 1.07 4.03
Andre Iguodala 1.69 2.33 4.02
Dirk Nowitzki 4.00 -0.04 3.95
Jason Kidd 1.64 2.25 3.90
Tyson Chandler -0.57 4.45 3.88
David Robinson -0.73 4.58 3.86
Stephen Curry 4.06 -0.28 3.78
Baron Davis 2.51 1.20 3.71
Vlade Divac -0.91 4.62 3.71
Ricky Rubio 1.42 2.25 3.67
Deron Williams 5.14 -1.49 3.65
Vince Carter 3.51 0.06 3.57
Karl Malone 1.75 1.77 3.51
Gilbert Arenas 3.74 -0.27 3.47
Robert Horry 0.46 2.91 3.38
Kawhi Leonard 2.23 1.14 3.36
Chris Bosh 1.91 1.41 3.32
Kyle Lowry 3.04 0.27 3.31
Chris Webber 1.17 2.11 3.27
Kevin Love 2.99 0.26 3.25
Danny Green 1.53 1.64 3.17
Eddie Jones 0.99 2.11 3.10
Boris Diaw 1.27 1.83 3.10
Josh Childress 1.39 1.69 3.08
Marcus Camby -1.52 4.53 3.01
Paul Millsap 1.31 1.70 3.00
Peja Stojakovic 3.38 -0.38 3.00
Doug Christie 0.90 2.08 2.98
Dwight Howard 0.29 2.67 2.96
Gary Payton 2.05 0.91 2.96
Mike Miller 2.87 0.07 2.94
Danny Granger 1.72 1.19 2.92
Andre Miller 2.61 0.28 2.89
Jermaine O'Neal -1.27 4.12 2.86
Paul Pierce 2.32 0.53 2.86
Lamar Odom 0.43 2.38 2.81
Hedo Turkoglu 1.78 1.02 2.80
Tony Allen -0.45 3.21 2.76
Brent Barry 2.37 0.38 2.75
Aaron McKie 0.17 2.51 2.68
Greg Ostertag -2.07 4.57 2.50
Kerry Kittles 0.78 1.70 2.48
Shawn Bradley -2.91 5.34 2.43
Jason Richardson 2.39 0.02 2.41
Shawn Marion 1.33 1.06 2.39
Antawn Jamison 3.08 -0.70 2.38
Rasheed Wallace 1.37 1.00 2.37
Gerald Wallace -0.46 2.79 2.33
Brad Miller 1.20 1.07 2.27
Ray Allen 3.93 -1.73 2.20
Andrew Bogut -1.31 3.49 2.18
Reggie Miller 3.43 -1.24 2.18
Anthony Tolliver 0.85 1.32 2.17
Josh Smith -0.39 2.55 2.16
Steve Francis 1.24 0.90 2.14
Caron Butler 1.19 0.94 2.13
Serge Ibaka -0.51 2.63 2.12
Draymond Green -0.23 2.35 2.12
Chandler Parsons 1.91 0.21 2.12
Chuck Hayes -0.66 2.75 2.10
Arvydas Sabonis -1.89 3.99 2.10
Carmelo Anthony 3.81 -1.76 2.06
Metta World Peace 0.66 1.39 2.05
Kevin Martin 3.91 -1.86 2.04
Ryan Bowen -0.54 2.59 2.04
Jeff Foster -0.35 2.39 2.04
Jamal Mashburn 1.38 0.62 2.00
Josh Howard 1.43 0.53 1.96
Jae Crowder 0.48 1.45 1.93
Matt Bonner 2.47 -0.54 1.93
Ronnie Brewer -0.42 2.31 1.89
Eric Bledsoe -0.51 2.39 1.88
Brandon Roy 3.35 -1.50 1.85
Terry Porter 0.50 1.35 1.84
Ryan Anderson 2.32 -0.48 1.84
Jason Terry 2.54 -0.73 1.81
Bo Outlaw -1.88 3.68 1.80
Kyrie Irving 2.86 -1.08 1.78
Devin Harris 2.81 -1.07 1.73
Andre Drummond 0.55 1.15 1.70
Brian Cardinal -0.35 2.05 1.70
Scott Padgett 0.39 1.30 1.69
DeAndre Jordan -0.96 2.62 1.66
Michael Redd 3.10 -1.45 1.65
Andris Biedrins -0.90 2.54 1.65
Rashard Lewis 2.33 -0.68 1.65
Ty Lawson 3.20 -1.57 1.64
J.R. Smith 2.21 -0.61 1.60
Rudy Fernandez 1.63 -0.04 1.59
Joakim Noah -0.32 1.90 1.58
Jeremy Lin 1.19 0.38 1.57
Donyell Marshall 0.60 0.95 1.56
Al Horford 0.53 1.01 1.54
Mike Dunleavy 1.31 0.22 1.53
Luol Deng 0.45 1.07 1.53
James Jones 1.55 -0.05 1.50
Anthony Davis 1.16 0.34 1.50
Cuttino Mobley 1.02 0.44 1.46
Jose Calderon 2.64 -1.20 1.44
Jimmy Butler 0.30 1.14 1.44
Joel Przybilla -1.88 3.31 1.43
Erick Dampier -1.07 2.50 1.42
Dikembe Mutombo -1.83 3.25 1.42
Raef LaFrentz 0.67 0.74 1.41
James Posey -0.17 1.49 1.32
Pablo Prigioni 0.75 0.56 1.31
Nene Hilario -1.14 2.38 1.24
Delonte West 0.69 0.56 1.24
Goran Dragic 2.25 -1.04 1.21
DeMarcus Cousins -0.58 1.79 1.21
Reggie Jackson 0.24 0.91 1.15
Nick Collison -0.52 1.64 1.13
Ronny Turiaf -0.61 1.74 1.12
Thaddeus Young 0.48 0.64 1.12
Jon Barry 0.65 0.47 1.12
Derek Fisher 1.04 0.07 1.10
Bryon Russell 0.28 0.81 1.09
DeMarre Carroll 0.38 0.70 1.09
Trevor Ariza 0.10 0.96 1.07
Bryant Stith 0.44 0.62 1.06
Mike Conley 1.11 -0.05 1.06
Roy Hibbert -2.19 3.24 1.06
LaMarcus Aldridge 1.41 -0.38 1.03
Allen Iverson 2.19 -1.17 1.02
Bobby Jackson 0.57 0.45 1.02
Chris Andersen -1.71 2.73 1.01
Scottie Pippen -0.27 1.26 0.99
Thabo Sefolosha -0.41 1.39 0.97
Jamaal Tinsley -0.15 1.12 0.97
Brendan Haywood -1.62 2.58 0.96
Damian Lillard 2.66 -1.73 0.93
C.J. Watson 0.38 0.53 0.91
George Hill 1.17 -0.27 0.90
Isaiah Thomas 2.59 -1.70 0.89
Darrell Armstrong -0.13 1.02 0.88
Klay Thompson 1.65 -0.76 0.88
Kyle Korver 1.33 -0.49 0.85
Derrick Rose 2.43 -1.58 0.85
Dan Majerle -0.08 0.93 0.85
Brandon Jennings 1.95 -1.10 0.84
Matt Barnes 0.50 0.32 0.82
Danilo Gallinari 0.33 0.48 0.82
Bonzi Wells 0.37 0.44 0.82
Anthony Parker 0.37 0.43 0.80
Carlos Delfino 0.92 -0.15 0.77
Rudy Gay 0.94 -0.18 0.76
Zaza Pachulia -1.77 2.52 0.76
Horace Grant 0.21 0.49 0.70
Josh McRoberts 0.24 0.42 0.66
Rajon Rondo 0.35 0.30 0.66
Austin Croshere 0.52 0.12 0.64
Wesley Matthews 2.06 -1.42 0.64
Rasho Nesterovic -1.44 2.08 0.64
Ersan Ilyasova 0.93 -0.30 0.64
Joe Johnson 1.79 -1.17 0.62
Anderson Varejao -0.06 0.66 0.61
Luc Mbah a Moute -1.07 1.67 0.61
Eric Piatkowski 0.95 -0.35 0.60
Vladimir Radmanovic 0.35 0.25 0.59
Bruce Bowen -1.61 2.20 0.59
Kenyon Martin -1.55 2.12 0.58
George Lynch -0.92 1.46 0.53
Walter McCarty -0.03 0.56 0.53
Richard Jefferson 0.38 0.15 0.52
Jodie Meeks 0.50 0.00 0.51
Mehmet Okur 1.11 -0.62 0.49
Tiago Splitter -1.55 2.04 0.49
Jameer Nelson 2.23 -1.75 0.48
Tim Thomas 0.48 -0.01 0.47
Sam Cassell 2.08 -1.63 0.45
Daniel Gibson 0.68 -0.23 0.45
Adrian Griffin -1.20 1.65 0.44
Hasheem Thabeet -2.65 3.09 0.44
Raymond Felton 0.99 -0.56 0.43
Kurt Thomas -1.54 1.96 0.42
Zydrunas Ilgauskas -1.34 1.76 0.42
Jumaine Jones 0.26 0.15 0.42
Grant Hill -0.23 0.63 0.39
Amare Stoudemire 0.62 -0.24 0.38
P.J. Tucker -0.10 0.47 0.38
Brook Lopez 0.27 0.09 0.36
Jared Dudley 0.51 -0.15 0.36
Eduardo Najera -0.60 0.95 0.35
Renaldo Balkman -2.20 2.53 0.33
Eric Snow -0.78 1.10 0.32
Sasha Vujacic 1.85 -1.53 0.32
Robert Traylor -0.74 1.06 0.31
Stephon Marbury 1.96 -1.66 0.30
Shareef Abdur-Rahim 0.30 -0.01 0.30
Greg Monroe -0.43 0.72 0.29
Derek Anderson 0.71 -0.42 0.29
Ime Udoka -0.35 0.63 0.28
Damon Jones 1.87 -1.60 0.27
Antoine Walker -0.23 0.47 0.23
Christian Laettner -1.33 1.56 0.23
Omer Asik -1.52 1.76 0.23
David West 0.04 0.17 0.21
Mike Bibby 1.59 -1.39 0.20
Keith Bogans -0.25 0.44 0.19
Toney Douglas 0.70 -0.52 0.18
Antonio Daniels 1.77 -1.59 0.17
Jerome Williams -1.98 2.14 0.16
Andrew Bynum -1.23 1.38 0.15
Jared Sullinger -0.14 0.28 0.14
Larry Sanders -2.87 3.01 0.14
Avery Bradley -0.82 0.96 0.13
Omri Casspi 0.22 -0.10 0.12
Nicolas Batum 1.70 -1.59 0.11
Kirk Hinrich 0.01 0.08 0.08
Jarron Collins -2.55 2.61 0.05
Quentin Richardson 0.22 -0.18 0.05
Corie Blount -1.57 1.60 0.03
Lance Stephenson -0.71 0.74 0.03
Martell Webster -0.25 0.27 0.02
Michael Kidd-Gilchrist -1.09 1.10 0.01
Tayshaun Prince -0.56 0.57 0.01
Devean George -0.67 0.67 0.00
Reggie Evans -1.49 1.49 0.00
John Wall 0.84 -0.85 -0.01
Marko Jaric -0.94 0.92 -0.02
Nick Van Exel 1.47 -1.50 -0.03
Nate Robinson 1.59 -1.62 -0.03
DeMar DeRozan 0.28 -0.31 -0.04
Eric Williams -0.76 0.72 -0.04
Dale Davis -0.63 0.57 -0.06
Kenneth Faried -0.14 0.05 -0.09
Brian Grant -1.26 1.17 -0.09
Zach Randolph 0.56 -0.65 -0.10
Charlie Villanueva 1.44 -1.54 -0.10
Terrence Jones 0.88 -0.98 -0.11
Louis Williams 1.51 -1.61 -0.11
Elton Brand 0.56 -0.67 -0.11
Tony Delk -0.38 0.26 -0.12
James Anderson -0.29 0.17 -0.12
Al Harrington -0.13 0.00 -0.13
Toni Kukoc 1.17 -1.30 -0.14
Keon Clark -2.35 2.20 -0.14
Kendrick Perkins -2.41 2.27 -0.14
Bobby Simmons 0.11 -0.26 -0.15
Erick Strickland -0.39 0.23 -0.17
Luther Head -0.11 -0.07 -0.19
Luke Walton -0.29 0.09 -0.21
Shelvin Mack -0.40 0.19 -0.21
Rick Fox -0.65 0.43 -0.22
Greg Buckner 0.02 -0.24 -0.22
Marcus Morris -0.34 0.12 -0.23
Chris Kaman -2.94 2.70 -0.24
Jerry Stackhouse 1.39 -1.66 -0.26
David Lee 0.33 -0.60 -0.27
Glenn Robinson 0.72 -0.99 -0.28
Markieff Morris -0.43 0.15 -0.28
Nikola Vucevic -1.44 1.15 -0.29
Charlie Ward -1.22 0.92 -0.29
Walt Williams 0.67 -0.99 -0.32
Aaron Gray -1.37 1.05 -0.32
Kemba Walker 0.56 -0.89 -0.33
Kyle Singler -0.85 0.51 -0.34
Derrick Brown -0.78 0.45 -0.34
Stephen Jackson 0.85 -1.19 -0.35
Morris Peterson 0.49 -0.84 -0.35
Maurice Evans -0.10 -0.27 -0.37
Al Jefferson 0.12 -0.49 -0.37
John Salmons -0.26 -0.12 -0.38
Dorell Wright 0.49 -0.88 -0.39
Tim Hardaway 0.57 -0.97 -0.40
Tony Parker 1.32 -1.72 -0.40
Alonzo Mourning -2.06 1.67 -0.40
Danny Ferry -0.64 0.25 -0.40
Terrence Ross 0.53 -0.94 -0.41
Kelvin Cato -2.66 2.24 -0.41
Andrew DeClercq -1.74 1.31 -0.42
Matt Harpring 0.78 -1.21 -0.43
Carlos Boozer -0.39 -0.05 -0.43
Jamario Moon -0.20 -0.23 -0.44
Corey Maggette 0.86 -1.30 -0.44
Wally Szczerbiak 1.22 -1.66 -0.44
Bill Walker 0.32 -0.77 -0.45
Michael Jordan 0.03 -0.48 -0.45
Brian Scalabrine -1.81 1.35 -0.46
Popeye Jones 0.24 -0.71 -0.47
Antonio McDyess -1.48 1.02 -0.47
Lucious Harris 0.27 -0.77 -0.50
Bradley Beal -0.02 -0.51 -0.52
Shaun Livingston -1.01 0.48 -0.54
Derrick Favors -1.65 1.08 -0.56
Shawne Williams -1.03 0.46 -0.57
Beno Udrih 1.08 -1.64 -0.57
Derrick Coleman -1.01 0.44 -0.57
Moochie Norris -0.49 -0.08 -0.57
Corey Brewer 0.08 -0.66 -0.57
Tyreke Evans 0.65 -1.23 -0.58
Fabricio Oberto -1.25 0.66 -0.59
Anthony Peeler -0.37 -0.23 -0.60
Keith Van Horn 0.25 -0.86 -0.61
JaVale McGee -2.09 1.45 -0.64
Jordan Farmar -0.14 -0.50 -0.64
Marquis Daniels -0.50 -0.14 -0.64
Jason Thompson -1.30 0.65 -0.65
Todd MacCulloch -1.26 0.59 -0.67
Pat Garrity 0.35 -1.02 -0.67
Rick Brunson -0.74 0.05 -0.69
Nenad Krstic -1.40 0.71 -0.69
Patrick Mills 1.06 -1.77 -0.71
Jason Collins -4.33 3.62 -0.71
Alonzo Gee -1.41 0.69 -0.72
Allan Houston 0.97 -1.71 -0.73
Ruben Patterson 0.86 -1.60 -0.75
Darius Songaila -0.77 0.02 -0.75
Theo Ratliff -3.83 3.07 -0.75
Mike James 1.02 -1.79 -0.78
Danny Fortson -0.33 -0.46 -0.79
Hakeem Olajuwon -2.01 1.21 -0.80
Jonas Valanciunas -1.20 0.39 -0.81
Mo Williams 0.96 -1.77 -0.82
Ed Davis -1.47 0.64 -0.83
Courtney Lee 0.17 -1.01 -0.83
Monta Ellis 0.57 -1.41 -0.84
J.J. Redick 1.16 -2.00 -0.84
Clifford Robinson -0.71 -0.14 -0.84
Wilson Chandler -0.66 -0.19 -0.85
Anthony Johnson 0.01 -0.86 -0.86
Taj Gibson -2.05 1.19 -0.86
Channing Frye -0.16 -0.69 -0.86
Michael Finley 1.47 -2.33 -0.86
Linas Kleiza -0.13 -0.75 -0.87
Eddie House -0.68 -0.19 -0.87
Jarvis Hayes 0.26 -1.13 -0.88
Jrue Holiday -0.48 -0.40 -0.88
P.J. Brown -1.56 0.66 -0.91
Al-Farouq Aminu -1.82 0.91 -0.91
Patrick Patterson 0.44 -1.35 -0.91
Steve Blake 0.25 -1.16 -0.91
Greivis Vasquez 0.80 -1.72 -0.92
Casey Jacobsen -2.02 1.10 -0.92
Marcus Thornton 0.26 -1.18 -0.92
Raja Bell 0.47 -1.41 -0.94
Brian Shaw -1.35 0.39 -0.96
Ryan Hollins -2.38 1.42 -0.96
Rodney Stuckey 0.72 -1.69 -0.97
Dion Waiters 0.46 -1.43 -0.97
Darren Collison 0.41 -1.40 -0.99
Fred Hoiberg -0.49 -0.51 -1.00
Iman Shumpert -2.19 1.19 -1.00
Kwame Brown -3.09 2.07 -1.03
Alec Burks -0.36 -0.67 -1.03
Landry Fields -1.15 0.11 -1.04
Richard Hamilton 0.82 -1.87 -1.04
Julian Wright -1.78 0.74 -1.04
Antonio Davis -2.08 1.01 -1.07
Gordon Hayward 0.57 -1.64 -1.07
Leandro Barbosa 1.59 -2.66 -1.08
Roger Mason 1.03 -2.12 -1.10
Samuel Dalembert -2.37 1.27 -1.10
Brian Cook -0.48 -0.62 -1.10
Jared Jeffries -1.26 0.16 -1.11
Brandan Wright -0.31 -0.81 -1.12
Marcus Williams -0.03 -1.09 -1.12
Robin Lopez -1.07 -0.06 -1.13
DeSagana Diop -3.41 2.28 -1.13
Quincy Pondexter -1.40 0.26 -1.14
Carl Landry -0.16 -0.99 -1.15
Kelenna Azubuike -0.10 -1.06 -1.16
Mario Chalmers -1.86 0.69 -1.16
Greg Stiemsma -3.72 2.53 -1.19
Eric Gordon 1.81 -3.01 -1.20
Tyrone Nesby -1.27 0.07 -1.20
Brevin Knight -3.20 2.00 -1.20
Troy Murphy -0.44 -0.77 -1.21
Damon Stoudamire 0.35 -1.57 -1.22
Terrell Brandon -0.14 -1.08 -1.22
Udonis Haslem -1.24 -0.01 -1.25
Khris Middleton 0.52 -1.77 -1.25
Chris Singleton -3.14 1.89 -1.25
Elden Campbell -2.44 1.18 -1.26
James Singleton -1.00 -0.28 -1.28
Joe Smith -1.83 0.54 -1.30
Jalen Rose 0.42 -1.72 -1.30
Austin Daye -1.20 -0.10 -1.30
Mikki Moore -2.18 0.88 -1.30
Jarrett Jack 0.48 -1.78 -1.30
Larry Hughes -0.05 -1.25 -1.31
Stacey Augmon -1.98 0.64 -1.34
Ian Mahinmi -2.87 1.52 -1.35
Andray Blatche -1.44 0.09 -1.35
Nikola Pekovic -0.35 -1.03 -1.38
Lindsey Hunter -2.20 0.81 -1.38
Emanual Davis -1.97 0.59 -1.39
T.J. Ford -0.38 -1.01 -1.39
Mookie Blaylock -2.89 1.50 -1.39
DerMarr Johnson -1.72 0.31 -1.41
Trevor Booker -0.91 -0.51 -1.42
Jan Vesely -2.80 1.37 -1.42
Jamaal Magloire -2.77 1.35 -1.43
Trenton Hassell -1.25 -0.18 -1.43
Fred Jones -0.51 -0.92 -1.43
Viktor Khryapa -1.49 0.05 -1.44
Speedy Claxton -2.16 0.72 -1.45
Chase Budinger 0.52 -1.97 -1.45
Arron Afflalo -0.01 -1.44 -1.45
Yakhouba Diawara -0.69 -0.77 -1.46
David Wesley -1.07 -0.40 -1.47
Steve Smith 0.38 -1.86 -1.48
Chris Duhon -0.73 -0.75 -1.48
Jahidi White -2.32 0.83 -1.48
Clarence Weatherspoon -1.04 -0.44 -1.48
Charlie Bell -0.35 -1.14 -1.50
Alan Anderson -0.75 -0.76 -1.51
Mark Jackson -0.35 -1.18 -1.54
Scot Pollard -2.41 0.86 -1.54
D.J. Augustin 0.35 -1.89 -1.54
Glen Rice 0.28 -1.83 -1.56
Corliss Williamson -1.05 -0.51 -1.56
DeJuan Blair -1.20 -0.37 -1.57
Malik Rose -1.27 -0.30 -1.57
Anfernee Hardaway -2.63 1.06 -1.57
Jake Voskuhl -2.63 1.06 -1.57
Alexey Shved -1.71 0.13 -1.58
Ervin Johnson -2.83 1.24 -1.59
Marcin Gortat -1.82 0.22 -1.60
Earl Watson -1.88 0.27 -1.61
Darrell Arthur -2.49 0.88 -1.62
Juwan Howard -1.53 -0.09 -1.62
Mickael Pietrus -2.47 0.85 -1.62
Tristan Thompson -1.45 -0.17 -1.62
C.J. Miles -0.04 -1.60 -1.64
Gerald Henderson -0.60 -1.07 -1.67
Dante Cunningham -1.47 -0.21 -1.68
Craig Smith -0.66 -1.02 -1.68
Ben Gordon 1.06 -2.75 -1.69
Michael Ruffin -3.35 1.66 -1.69
Leon Powe -1.37 -0.32 -1.69
Jamal Crawford 1.28 -2.98 -1.69
Jerryd Bayless 1.04 -2.74 -1.70
Andres Nocioni 0.26 -1.96 -1.70
Evan Turner -2.42 0.70 -1.72
Charles Oakley -1.56 -0.16 -1.72
Travis Diener 0.83 -2.57 -1.73
Antoine Wright -1.17 -0.57 -1.74
Sarunas Jasikevicius -2.20 0.46 -1.74
Rodney Carney -1.72 -0.02 -1.74
Cartier Martin -0.83 -0.94 -1.76
Bob Sura -0.59 -1.18 -1.77
Voshon Lenard -0.34 -1.43 -1.77
Rod Strickland -0.51 -1.27 -1.78
Nick Young -0.07 -1.71 -1.79
Jonas Jerebko -0.42 -1.38 -1.80
Jason Williams 0.76 -2.56 -1.80
Ira Newble -1.32 -0.48 -1.80
Lamond Murray -1.19 -0.61 -1.81
Luis Scola -1.39 -0.42 -1.81
Smush Parker -0.71 -1.10 -1.81
O.J. Mayo -0.41 -1.40 -1.81
MarShon Brooks -0.63 -1.19 -1.82
Donte Greene -1.84 0.02 -1.82
Jeff McInnis 0.83 -2.65 -1.82
Rashad McCants -0.59 -1.24 -1.83
Tyler Zeller -2.18 0.33 -1.86
Lorenzen Wright -2.69 0.83 -1.86
Shammond Williams -0.77 -1.10 -1.87
Timofey Mozgov -2.37 0.49 -1.87
Emeka Okafor -1.60 -0.30 -1.90
Chucky Atkins 0.40 -2.30 -1.90
Ramon Sessions 0.18 -2.09 -1.91
Carlos Arroyo -0.20 -1.73 -1.93
Ekpe Udoh -3.79 1.86 -1.94
Darvin Ham -2.21 0.27 -1.94
Vin Baker -2.08 0.14 -1.94
Michael Beasley -0.86 -1.09 -1.96
Dan Gadzuric -2.93 0.96 -1.97
Shandon Anderson -1.60 -0.38 -1.98
Reggie Williams 0.42 -2.40 -1.98
Luke Ridnour -0.83 -1.15 -1.98
Anthony Morrow -0.07 -1.92 -1.99
Stephen Graham -2.18 0.19 -2.00
John Henson -2.42 0.41 -2.00
Ricky Davis -0.38 -1.64 -2.02
David Harrison -4.12 2.10 -2.03
Drew Gooden -1.53 -0.51 -2.03
Mickael Gelabale -0.26 -1.77 -2.04
Jim Jackson -2.25 0.21 -2.04
Tony Battie -2.37 0.33 -2.04
Rodney Rogers -1.44 -0.62 -2.06
Alvin Williams -0.89 -1.18 -2.07
Latrell Sprewell -0.36 -1.72 -2.08
Marco Belinelli 0.07 -2.19 -2.12
Marcus Banks -1.96 -0.17 -2.13
Kosta Koufos -2.33 0.19 -2.14
Tobias Harris -0.79 -1.37 -2.16
Matt Carroll -0.98 -1.19 -2.17
Dion Glover -1.80 -0.39 -2.18
Rafer Alston -0.89 -1.30 -2.18
Tyrus Thomas -2.88 0.69 -2.20
Stromile Swift -2.51 0.31 -2.20
Wesley Person 0.46 -2.68 -2.22
Lavoy Allen -2.68 0.43 -2.25
Jeff Teague -0.48 -1.76 -2.25
Francisco Garcia -1.70 -0.56 -2.26
Michael Carter-Williams -0.88 -1.39 -2.26
Sasha Pavlovic -1.75 -0.52 -2.27
Damien Wilkins -0.94 -1.36 -2.30
Adonal Foyle -3.70 1.39 -2.32
Devin Brown -0.49 -1.83 -2.32
Aaron Williams -2.91 0.58 -2.33
Monty Williams -2.05 -0.30 -2.36
Kenny Anderson -2.50 0.15 -2.36
Anthony Carter -3.11 0.73 -2.37
Scott Williams -3.21 0.83 -2.38
Chris Mihm -3.19 0.81 -2.38
Wesley Johnson -1.61 -0.78 -2.38
Jiri Welsch -1.59 -0.80 -2.39
Mark Blount -1.97 -0.44 -2.41
Hubert Davis -0.78 -1.65 -2.43
Eric Maynor -0.44 -2.01 -2.45
Wayne Ellington -0.87 -1.58 -2.45
Gary Neal 0.40 -2.86 -2.46
Jason Smith -2.75 0.28 -2.46
Randy Foye -0.54 -1.93 -2.46
Michael Dickerson -0.76 -1.72 -2.47
Von Wafer -1.18 -1.30 -2.48
Garrett Temple -2.18 -0.30 -2.48
Terrence Williams -2.42 -0.08 -2.50
Kirk Snyder -0.27 -2.24 -2.51
Chris Douglas-Roberts -1.66 -0.86 -2.52
Brandon Knight -0.35 -2.18 -2.53
Gordan Giricek -0.92 -1.62 -2.53
Jake Tsakalidis -3.29 0.76 -2.54
Spencer Hawes -1.32 -1.24 -2.56
Kendall Gill -3.49 0.91 -2.58
Steve Novak -0.37 -2.21 -2.58
Travis Best -1.66 -0.97 -2.63
Calbert Cheaney -2.58 -0.05 -2.63
Jerome James -3.80 1.15 -2.65
Jeff Green -1.41 -1.25 -2.66
Maurice Taylor -2.72 0.04 -2.67
Mark Madsen -2.48 -0.20 -2.68
Glen Davis -2.19 -0.51 -2.71
Marvin Williams -0.94 -1.77 -2.71
Primoz Brezec -1.85 -0.87 -2.72
Gerald Green -1.02 -1.70 -2.72
Solomon Jones -3.15 0.40 -2.75
Quinton Ross -2.80 0.05 -2.76
Stanislav Medvedenko -2.48 -0.31 -2.79
John Starks -0.92 -1.88 -2.80
Hilton Armstrong -2.98 0.18 -2.80
Rodrigue Beaubois -2.17 -0.64 -2.81
Ronald Murray -1.14 -1.67 -2.81
Chris Wilcox -1.84 -0.97 -2.82
Brandon Bass -1.92 -0.90 -2.82
Greg Anthony -1.88 -0.94 -2.83
Louis Amundson -2.48 -0.35 -2.83
Jose Barea -0.24 -2.60 -2.84
Loren Woods -3.04 0.18 -2.86
Brandon Rush -1.76 -1.11 -2.87
Dan Dickau -0.62 -2.25 -2.87
Andrea Bargnani 0.18 -3.06 -2.88
Tyrone Hill -2.69 -0.19 -2.89
Marreese Speights -2.89 -0.01 -2.90
Brian Roberts -0.24 -2.66 -2.90
Jordan Hill -2.58 -0.32 -2.90
Etan Thomas -2.76 -0.17 -2.93
Ronnie Price -2.51 -0.46 -2.97
Lee Nailon -1.92 -1.05 -2.97
Willie Green -0.76 -2.22 -2.98
Chris Whitney -0.95 -2.04 -2.98
Darko Milicic -3.88 0.89 -2.98
LaPhonso Ellis -3.56 0.57 -2.99
Daequan Cook -0.82 -2.18 -3.00
Gary Trent -2.28 -0.73 -3.01
Johnny Newman -1.59 -1.43 -3.02
A.J. Price -1.55 -1.51 -3.06
Eddie Robinson -1.14 -1.93 -3.06
Bostjan Nachbar -1.94 -1.13 -3.06
Tyronn Lue -0.39 -2.68 -3.07
Al Thornton -1.69 -1.46 -3.15
DeShawn Stevenson -0.21 -2.95 -3.16
Joel Anthony -3.15 0.00 -3.16
Kevin Ollie -2.62 -0.55 -3.16
Rasual Butler -1.58 -1.59 -3.17
Zeljko Rebraca -3.55 0.37 -3.18
Jimmer Fredette 0.26 -3.45 -3.19
Steve Kerr -1.21 -1.99 -3.20
Mike Sweetney -2.64 -0.58 -3.22
Calvin Booth -4.02 0.80 -3.22
Austin Rivers -0.73 -2.51 -3.24
Kevin Seraphin -3.56 0.32 -3.24
Jason Maxiell -2.46 -0.79 -3.25
Sonny Weems -1.68 -1.57 -3.25
Will Bynum -1.27 -1.98 -3.25
Shelden Williams -2.77 -0.49 -3.26
Maurice Harkless -2.64 -0.62 -3.26
Eddy Curry -2.73 -0.54 -3.27
Dominic McGuire -3.55 0.28 -3.27
Sam Young -1.95 -1.33 -3.29
Othella Harrington -2.49 -0.80 -3.29
Johan Petro -3.84 0.54 -3.29
Shannon Brown -1.42 -1.89 -3.31
Jason Kapono -0.94 -2.40 -3.34
Sergio Rodriguez -1.63 -1.73 -3.37
Jason Caffey -3.02 -0.37 -3.38
Troy Hudson 0.29 -3.69 -3.39
Sean Rooks -3.68 0.28 -3.40
Michael Doleac -3.75 0.35 -3.40
Tom Gugliotta -3.29 -0.12 -3.41
Francisco Elson -3.78 0.36 -3.42
Nazr Mohammed -3.19 -0.23 -3.43
Kareem Rush -1.54 -1.89 -3.43
Ryan Gomes -1.72 -1.72 -3.43
Steven Hunter -3.34 -0.11 -3.45
Jacque Vaughn -2.64 -0.82 -3.47
Josh Boone -2.41 -1.06 -3.47
Jason Hart -2.92 -0.58 -3.50
Dahntay Jones -2.25 -1.25 -3.50
Mardy Collins -2.57 -0.95 -3.51
Eddie Griffin -3.33 -0.19 -3.52
Sebastian Telfair -1.33 -2.19 -3.53
Aaron Brooks 0.38 -3.91 -3.53
Kenny Thomas -2.33 -1.20 -3.54
Desmond Mason -2.20 -1.38 -3.58
Bismack Biyombo -3.76 0.15 -3.61
Anthony Mason -1.83 -1.79 -3.63
Shawn Kemp -3.59 -0.05 -3.64
Keyon Dooling -1.01 -2.63 -3.64
Michael Olowokandi -4.75 1.11 -3.64
Darius Miles -3.97 0.29 -3.69
Victor Oladipo -2.74 -0.95 -3.69
E'Twaun Moore -2.54 -1.16 -3.69
Jannero Pargo -1.67 -2.03 -3.70
Joey Graham -2.35 -1.40 -3.75
Rodney White -3.80 0.00 -3.80
James Johnson -3.70 -0.12 -3.82
Jordan Crawford -0.36 -3.51 -3.87
Juan Dixon -1.53 -2.35 -3.87
Samaki Walker -3.47 -0.41 -3.88
Predrag Drobnjak -2.66 -1.26 -3.92
Brian Skinner -3.53 -0.39 -3.92
Yi Jianlian -2.98 -0.95 -3.93
Donnell Harvey -3.25 -0.68 -3.93
Travis Outlaw -1.29 -2.64 -3.93
Acie Law -2.41 -1.60 -4.01
John Lucas -2.91 -1.12 -4.03
Malik Allen -3.90 -0.20 -4.10
Tyler Hansbrough -2.08 -2.03 -4.11
Earl Boykins -0.20 -3.93 -4.13
Ike Diogu -2.28 -1.94 -4.22
Hakim Warrick -1.75 -2.49 -4.24
Grant Long -5.62 1.38 -4.24
Vitaly Potapenko -2.89 -1.36 -4.25
J.J. Hickson -2.78 -1.48 -4.25
Norris Cole -2.59 -1.69 -4.28
Marcus Fizer -3.13 -1.19 -4.32
Anthony Randolph -3.19 -1.16 -4.35
Royal Ivey -2.89 -1.49 -4.38
Chris Childs -4.81 0.40 -4.41
George McCloud -2.39 -2.05 -4.44
Tony Massenburg -4.00 -0.46 -4.46
Howard Eisley -2.31 -2.22 -4.53
Xavier Henry -2.71 -1.83 -4.54
Jelani McCoy -3.78 -0.79 -4.57
Keith McLeod -3.43 -1.15 -4.58
Chris Gatling -2.82 -1.76 -4.58
Milt Palacio -3.73 -0.85 -4.59
Melvin Ely -4.00 -0.60 -4.60
Patrick Ewing -4.52 -0.09 -4.60
Chris Quinn -1.46 -3.17 -4.63
Kris Humphries -3.52 -1.15 -4.67
Rodney Buford -2.07 -2.66 -4.73
Marc Jackson -2.82 -1.91 -4.73
Enes Kanter -3.05 -1.70 -4.75
Junior Harrington -5.45 0.66 -4.79
Ron Mercer -3.75 -1.05 -4.80
Adam Morrison -1.25 -3.56 -4.80
Andrew Nicholson -3.19 -1.71 -4.91
Kevin Willis -4.02 -0.93 -4.95
Salim Stoudamire -1.15 -3.91 -5.06
Courtney Alexander -2.12 -3.02 -5.14
Avery Johnson -2.59 -2.65 -5.23
Byron Mullens -2.16 -3.12 -5.27
Alan Henderson -3.20 -2.23 -5.43
Harrison Barnes -3.64 -1.80 -5.44
Hanno Mottola -4.37 -1.39 -5.77
Derrick Williams -3.99 -1.79 -5.79
Bimbo Coles -4.32 -1.79 -6.11
Vladimir Stepania -5.01 -1.29 -6.30
Jonathan Bender -4.78 -1.82 -6.60
Jonny Flynn -2.12 -4.52 -6.64
Michael Curry -6.89 -0.01 -6.90
Josh Powell -4.89 -2.42 -7.30
John Amaechi -6.09 -1.56 -7.65
Earl Clark -6.44 -2.65 -9.09
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Re: The popularization of BPM
I would suggest he do same season also, to make sure the metric is actually, at the VERY least, compiling correctly at the team level for the season it's supposed to be measuring. Like I've said before, I did this with PER & it failed pretty bad, higher paced teams came out on top more so than the BEST teams. All the metrics should be pretty darn close to 1.00, or what's the point?DSMok1 wrote:Here's how Neil did it the last time: http://www.apbr.org/metrics/viewtopic.p ... 343#p15334permaximum wrote:Do you test prediction accuracy using the previous year per min (or per pos) value on the outcome of next season's games or the whole season? Wins or margin? Or SRS if it's season?Neil Paine wrote:I ended up not having started yet, and another demand came up for tomorrow, so you've got a few days at least, if not more.
Will he maybe going into the future, using previous ratings (ie using 2002 to predict 03, 04, etc correlations)? It seems that would take out bias any metric that regresses previous seasons would have in this specific test. Of course, now that I think about it, metrics that use previous seasons might very well be fluid and change all seasons results every time it is worked (using the "new" data) - I've never looked close enough to see.
Re: The popularization of BPM
@ Mystic:
It looks like my R^2 for BPM, done as you are showing, would be 0.658 overall, 0.779 for offense, and 0.622 for defense, using possessions for weighting and the top 714 minutes players.
Note, however, that in my derivation, I used the sqrt(possessions) for my weighting, which I believe is the correct approach.
It looks like my R^2 for BPM, done as you are showing, would be 0.658 overall, 0.779 for offense, and 0.622 for defense, using possessions for weighting and the top 714 minutes players.
Note, however, that in my derivation, I used the sqrt(possessions) for my weighting, which I believe is the correct approach.
Re: The popularization of BPM
Ok, thanks. As expected higher than those reported on bbr.DSMok1 wrote:@ Mystic:
It looks like my R^2 for BPM, done as you are showing, would be 0.658 overall, 0.779 for offense, and 0.622 for defense, using possessions for weighting and the top 714 minutes players.
Note, however, that in my derivation, I used the sqrt(possessions) for my weighting, which I believe is the correct approach.
For sqrt(possessions) weighted I get the following R²:
Offense: 0.846
Defense: 0.667
Overall: 0.725
Based on those numbers I might be onto something and the whole work wasn't just a waste of time ... Now I really need to make the whole thing more applicable in order to test that for historic season.
Re: The popularization of BPM
Interesting! Those are good numbers. I look forward to seeing what you come up with!
Re: The popularization of BPM
Yes, interesting it is, but those are purely in-sample numbers, which puts an asterix on it, naturally.DSMok1 wrote:Interesting!
The values I posted for those 714 players are solely based on player boxscore data, no team data or +/- based stuff was used. But it is still prelim testing, just to see whether the direction is worth pursuing further. So, thanks again for your answer, that helped me a lot.
-
permaximum
- Posts: 416
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Re: The popularization of BPM
I really wonder why did you use sqrt weighting instead of normal weighting? I really need some info on this oneDSMok1 wrote:Note, however, that in my derivation, I used the sqrt(possessions) for my weighting, which I believe is the correct approach.
Re: The popularization of BPM
Hmmm... It appears I might have been wrong to use that weighting schema. I should be using the reciprocal of the variance of the measurement; variance for the RAPM is probably proportional to 1/n (I had thought proportional to 1/sqrt(n)), though I'm not sure what the collinearity and regression to the mean is doing to that. I perhaps should account for # of teams or # of seasons somehow in the n weighting also (since a player who plays a lot in one team-season will have more error than one who plays in many team seasons the same # of possessions).permaximum wrote:I really wonder why did you use sqrt weighting instead of normal weighting? I really need some info on this oneDSMok1 wrote:Note, however, that in my derivation, I used the sqrt(possessions) for my weighting, which I believe is the correct approach.
Thoughts?
Re: The popularization of BPM
Some stats make a 'team adjustment' that forces the stat to precisely equal team performance. Of course, this correlation means nothing by itself: You could just make everyone 1.00, then adjust to team strength. But this wouldn't perform well in subsequent seasons, as players move from team to team.Statman wrote: I would suggest he do same season also, to make sure the metric is actually, at the VERY least, compiling correctly at the team level for the season it's supposed to be measuring. ... All the metrics should be pretty darn close to 1.00, or what's the point?
Will he maybe going into the future, using previous ratings (ie using 2002 to predict 03, 04, etc correlations)? It seems that would take out bias any metric that regresses previous seasons would have in this specific test...
My big bugaboo is that from east to west there's about 1 ppg difference in SOS. Players going E to W, or W to E, experience a different level of competition. I could correct for it, but I just don't feel like it. Even correcting for team MOV almost feels like cheating.
Re: The popularization of BPM
Progress in perfecting statistical PM (a praiseworthy endeavor) aside, let me return with a comment on a more literal interpretation of the thread title. Should one expect that BPM (or any measure of similar approach) will be popularized?
My conjecture is that unless the measure is seen both to generate "plausible" results in representing the absolute and relative ability of the best players in the league (especially of all time) it won't become "popular".
True (by definition) it will still have great value to those who want to more accurately predict team outcomes for fun and profit, but my guess is that it's not what the overwhelming majority of fans care about.
Here's the results of a small exercise detailing what I see as the problem. Looking at the top 35 results on the "Sortable Players List" at http://www.basketball-reference.com/about/bpm.html, I compare the possession-weighted xRAPM and BPM averages for the seasons of all players who completed their 28 to 35 year old seasons within the 14 year framework. There are 13 such players (The age range was selected so as to specifically include Shaq - the primary "player of concern" - and I stopped at 35 players because that was the 13th, Ray Allen, and I got lazy.)
What one finds is that six of these have a difference between these averages greater than one, and in each case, the possession-weighted xRAPM is larger (and then there is also Ray Allen with a difference of -1).
On a player by player basis, these six differences are: Shaq +4.6, Tim Duncan +3.3, Dirk Nowitzki +2.6, Ben Wallace +2.3, Kevin Garnett +1.8, and Marcus Camby +1.4. And these differences, of course, in addition to offering a different perspective on these players' absolute value are large enough to meaningfully shake up the corresponding ordinal rankings, and in a way that I expect would better accord with the perceptions of informed consumers (informed defined to exclude those who do not understand the co-equal value of defense in the abstract).
So, what's the point? Well, until the day comes that the hoi polloi is concerned about the accuracy of rankings of players 72 to 425, the greater effort should be to popularize xRAPM-type metrics, BPM-type metrics being much more of a niche interest. $0.02.
My conjecture is that unless the measure is seen both to generate "plausible" results in representing the absolute and relative ability of the best players in the league (especially of all time) it won't become "popular".
True (by definition) it will still have great value to those who want to more accurately predict team outcomes for fun and profit, but my guess is that it's not what the overwhelming majority of fans care about.
Here's the results of a small exercise detailing what I see as the problem. Looking at the top 35 results on the "Sortable Players List" at http://www.basketball-reference.com/about/bpm.html, I compare the possession-weighted xRAPM and BPM averages for the seasons of all players who completed their 28 to 35 year old seasons within the 14 year framework. There are 13 such players (The age range was selected so as to specifically include Shaq - the primary "player of concern" - and I stopped at 35 players because that was the 13th, Ray Allen, and I got lazy.)
What one finds is that six of these have a difference between these averages greater than one, and in each case, the possession-weighted xRAPM is larger (and then there is also Ray Allen with a difference of -1).
On a player by player basis, these six differences are: Shaq +4.6, Tim Duncan +3.3, Dirk Nowitzki +2.6, Ben Wallace +2.3, Kevin Garnett +1.8, and Marcus Camby +1.4. And these differences, of course, in addition to offering a different perspective on these players' absolute value are large enough to meaningfully shake up the corresponding ordinal rankings, and in a way that I expect would better accord with the perceptions of informed consumers (informed defined to exclude those who do not understand the co-equal value of defense in the abstract).
So, what's the point? Well, until the day comes that the hoi polloi is concerned about the accuracy of rankings of players 72 to 425, the greater effort should be to popularize xRAPM-type metrics, BPM-type metrics being much more of a niche interest. $0.02.
Re: The popularization of BPM
GMs actually should care quite alot about the true value of guys 70- 250 as much of their choice making involves them and the top 70 mostly either do what they want or are just not available.
Neil, your earlier study gave those with less than 250 minutes, mean performance rankings??? Not replacement level? Why? Given how many players score below to way way below replacement level on 14yr rapm, I wonder how replacement level isn't way lower and can't imagine the rationale / justification for giving low minute guys mean level performance rankings (essentially making them top 30% guys). How much could the correlations been in last test if the low minute guys were rated as replacement level or worse? Would the relative performance rankings have changed any? If the low minute guys were rated way worse wouldn't most or all of the very god players rate somewhat better? What are you going to do this time?
If you found the best performing metric mix by season, it might be possible to predict a different metric mix for future based on the trend in the metric mix ratios. If there is more signal to noise in that trend. Even if there isn't, the avg metric mix might be best.
Neil, your earlier study gave those with less than 250 minutes, mean performance rankings??? Not replacement level? Why? Given how many players score below to way way below replacement level on 14yr rapm, I wonder how replacement level isn't way lower and can't imagine the rationale / justification for giving low minute guys mean level performance rankings (essentially making them top 30% guys). How much could the correlations been in last test if the low minute guys were rated as replacement level or worse? Would the relative performance rankings have changed any? If the low minute guys were rated way worse wouldn't most or all of the very god players rate somewhat better? What are you going to do this time?
If you found the best performing metric mix by season, it might be possible to predict a different metric mix for future based on the trend in the metric mix ratios. If there is more signal to noise in that trend. Even if there isn't, the avg metric mix might be best.