Design-weighted Regression Adjusted Plus-Minus

Transcription

1 Design-weighted Regression Adjusted Plus-Minus Schuckers, Im, Mcdonld, McNulty August 3, 208 Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, 208 / 26

2 A etter title Design-weighted Regression Adjusted Plus-Minus Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

3 A etter title Design-weighted Regression Adjusted Plus-Minus : A First Pss Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

4 A etter title Design-weighted Regression Adjusted Plus-Minus : A First Pss (nd n incompletion) Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

5 Regression Adjusted Plus-Minus (RAPM) [Rosenum, 2004] sketll... Sgrin nd Winston [Ilrdi, 2007] results for NBA seson [Ilrdi nd Brzili, 2007] - seprte Offensive nd Defensive Impct [Sill, 200] - regulriztion nd out of smple [Engelmn, 207] & [Engelmn, 205] - single event credit Applictions outside sketll: Hockey: [Mcdonld, 20] & [Schuckers nd Curro, 203] Soccer: [scryice, 2009], [Hmilton, 200, Hmilton, 200, Hmilton, 204] Footll:???? Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

6 RAPM Two-wy RAPM (Rosenum) + Sill if plyer j is on the field for the Awy tem for event i, x ij = 0 if plyer j is not on the field for event i, nd if plyer j is on the field for the Home tem for event i. () Augment design mtrix, X, with other predictors, nd choose pproprite response, Y. Y = Xβ (2) ˆβ = (X T X + λi) X T Y (3) Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

7 Gols Generlize RAPM Account for plyer impct Reduce multicollinerity Allow for wider ppliction Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

8 Generliztion of the design mtrix Two-wy RAPM d ij if plyer j is on the field for the Awy tem for event i, γ ij = 0 if plyer j is not on the field for event i, nd d ij if plyer j is on the field for the Home tem for event i. (4) Augment design mtrix, Γ, with other predictors, nd choose pproprite response, Y. Y = Γβ (5) ˆβ = (Γ T Γ + λi) Γ T Y (6) How to choose d ij s mesure of impct of the plyer j on event i? Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

9 Choosing d ij Schuckers Intuition: lrger d ij lrger impct on coefficient for plyer i B-Mc Intuition: smller d ij lrger impct on coefficient for plyer i Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

10 Choosing d ij Schuckers Intuition: lrger d ij lrger impct on coefficient for plyer i B-Mc Intuition: smller d ij lrger impct on coefficient for plyer i B-Mc wins Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

11 Choosing d ij Schuckers Intuition: lrger d ij lrger impct on coefficient for plyer i B-Mc Intuition: smller d ij lrger impct on coefficient for plyer i B-Mc wins nd we cn prove it Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

12 Choosing d ij Schuckers Intuition: lrger d ij lrger impct on coefficient for plyer i B-Mc Intuition: smller d ij lrger impct on coefficient for plyer i B-Mc wins nd we cn prove it ut not tody. Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

13 Choosing d ij Schuckers Intuition: lrger d ij lrger impct on coefficient for plyer i B-Mc Intuition: smller d ij lrger impct on coefficient for plyer i B-Mc wins nd we cn prove it ut not tody. ˆβ j is slope = Y i / d ij. Think of d ij s signed distnce metric from event i. Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

14 Choosing d ij Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

15 Choosing d ij Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

16 Choosing d ij Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

17 Choosing d ij Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, 208 / 26

18 Illustrtion: Footll Appliction to Footll dt (or not) Focus elow on OLine to strt, serious thoughts on formtion, QB s, lignment of WR s, etc. Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

19 Illustrtion: Footll d ij weights dependent on loction of the run from this formtion d LTE, d LT, d LG, d C, d RG, d RT, d RTE dropping i from nottion for now Source for imge: Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

20 Illustrtion: Footll d LG = 0.8, d C = 0.8 d RG =, d LT = d LTE =., d RT =. d RTE =.5 Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

21 Illustrtion: Footll d RG = 0.8, d RT = 0.8 d RTE =, d C = d LG =., d LT =.5 d LTE = Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

22 Illustrtion: Hockey Going to use THoR structure (Schuckers & Curro, 203) Rosenum pproch, single prmeter Off & Def per plyer Response =NP20, xg, home xg minus wy xg in next 20 seconds Events (HITs, SHOTs, BLOCKs,... ) Even Strength Covrites for tem/golie, rink, zone strts, Score effects, Score effects time remining in 3rd period Evlution on RMSE, Predicted OOS RMSE, Correltion plyer coeff. Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

23 Illustrtion: Hockey For given ply i, use d ij = for golies nd the following for F nd D: F D Off. Zone (5-3)/2 Neu. Zone Def. Zone (5-2)/3 Consider vlues for, = (,,, 7,, ) Evlution on RMSE, Predicted OOS RMSE, Correltion plyer coeff. Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

24 Illustrtion: Hockey For given ply i, use d ij = for golies nd the following for F nd D: F D Off. Zone.5 Neu. Zone Def. Zone Consider vlues for, = (,,, 7,, ) Evlution on RMSE, Predicted OOS RMSE, Correltion plyer coeff. Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

25 Illustrtion: THoR Seson, λ = 400, Rows =, Columns= Rtio of OOS RMSE (,)/ OOS RMSE (=,=) White is low (good), Red is high (low) Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

26 Illustrtion: THoR Columns=Sesons, Rows= λ, inside rows =, inside columns= Seson Seson Seson Seson Seson lmd = lmd = Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

27 Illustrtion: THoR Columns=Sesons, Rows= λ, inside rows =, inside columns= Seson Seson Seson Seson Seson lmd = lmd = White is low, Red is high Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

28 Illustrtion: THoR Columns=Sesons, Rows= λ, inside rows =, inside columns= Seson Seson Seson Seson Seson lmd = lmd = White is 99, Red is.00 Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

29 Illustrtion: THoR Summry of results: Some cses for some sesons do etter thn =, =. Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

30 Illustrtion: THoR Summry of results: Some cses for some sesons do etter thn =, =. Generlly very little improvement over RAPM Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

31 Illustrtion: THoR Summry of results: Some cses for some sesons do etter thn =, =. Generlly very little improvement over RAPM Sme results for Seson to Seson correltion Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

32 Illustrtion: THoR Summry of results: Some cses for some sesons do etter thn =, =. Generlly very little improvement over RAPM Sme results for Seson to Seson correltion Sme results for within smple correltion Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

33 Illustrtion: THoR Summry of results: Some cses for some sesons do etter thn =, =. Generlly very little improvement over RAPM Sme results for Seson to Seson correltion Sme results for within smple correltion Sme results for different set of events nd response (Fenwick) Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

34 Illustrtion: THoR Summry of results: Some cses for some sesons do etter thn =, =. Generlly very little improvement over RAPM Sme results for Seson to Seson correltion Sme results for within smple correltion Sme results for different set of events nd response (Fenwick) Two wy nture of hockey? Two wy nture of this model Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

35 Illustrtion: THoR Summry of results: Some cses for some sesons do etter thn =, =. Generlly very little improvement over RAPM Sme results for Seson to Seson correltion Sme results for within smple correltion Sme results for different set of events nd response (Fenwick) Two wy nture of hockey? Two wy nture of this model Wht I wouldn t give for trcking dt? Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

36 Next Steps Pick myself up Dig into coefficients (who chnges) Rosenum (2-wy) to Ilrdi & Brzli (Off & Def rtings) i d ij = k vs. i d ij 2 = k nd tr() Metrics of distnce Other sports? Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

37 208 Ottw Hockey Anlytics Conference Sept 4 (socil nd workshops) & 5, #OTTHAC8 Crleton University, Ottw, ON Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

38 Thnks Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26

39 Biliogrphy Engelmn, J. (205). Estimting plyer s influence on his temmtes oxscore sttistics using modified rpm frmework. Accessed April 8, 208. Engelmn, J. (207). Possession-sed plyer performnce nlysis in sketll (djusted +/- nd relted concepts). In Alert, J., Glickmn, M. E., Swrtz, T. B., nd Koning, R. H., editors, Hndook of Sttisticl Methods nd Anlyses in Sports. Chpmn nd Hll/CRC. Hmilton, H. (200). Some strting documents on the plus/minus prolem. some-strting-documents-on-the-plusminus-prolem-2. Schuckers, Im, Mcdonld, McNulty CASSIS-Schuckers August 3, / 26