Proposal of offense/defense WPA metrics in B.LEAGUE Koji SUGIE*, Eiji KONAKA (Meijo Univ. Japan)

Outline Background STATS in basketball Impact metrics Proposed method Construction of consistent win probability model Main proposal: Offense/Defense Win Probability Added Numerical experiment Summary and future work

Background: stats in basketball  (Classical) stats: counts and ratios of events.  Attributed to the player who touched the ball last.

Background: stats in basketball  Detailed play-by-play records  Available in Japanese professional B.LEAGUE Stats and records can be used to evaluate each player’s contribution

Background: contribution evaluation from stats How to evaluate the contributions of the players who did not touch the ball? https://www.youtube.com/watch?v=qKde9M1gKvY&t=1311s 2022/07/18 accessed

Background: impact metrics “Impact metrics (IM)” tries to evaluate each player’s contribution in single value. Example: +/-, EFF, PIPM,LEBRON,RPM,RAPTOR, … Problem: Simple IM: do not include situation (time, score diff, …) Advanced IM: calculation methods are not fully disclosed in academic context (“magic recipe”)

Background: win probability model  How to include situation?  Time and score difference  Win probability model  Problem  Consistency Large score diff<->Large win prob.  Previous studies: Inconsistent win probability model (Deshpande[2016]) Deshpande[2016] Time[s] Score difference]

Research flow and main objective • Construct consistent win probability model • Contributions to win of all players is evaluated • Numerical evaluation • Japanese B.LEAGUE

Outline Background STATS in basketball Impact metrics Proposed method Construction of consistent win probability model Main proposal: Offense/Defense Win Probability Added Numerical experiment Summary and future work

Consistent win probability model with score difference  Win probability model ෝ 𝑤 𝑡, Δ𝑠  𝑡: time[s] from tipoff  Δ𝑠: score difference  Dataset  B1 League, 1736 matches  2016/9-2019/10 (3 regular seasons)

What is “consistency”  Consistent win probability model ෝ 𝑤 𝑡, Δ𝑠  ෝ 𝑤 𝑡, Δ𝑠 is consistent ⇔ ෝ 𝑤 is monotonic as Δ𝑠  Logistic regression is done for 𝑡 = 0, ⋯ , 2400

WPA originates in baseball (MLB) Offense WPA(WPA𝑂): sum of the change of ෝ 𝑤 in offense situation Offense situation=ball possession Defense WPA(WPA𝐷): sum of the change of ෝ 𝑤 in defense situation Defense situation=non-ball possession Total WPA：WPA = WPA𝑂 + WPA𝐷 for each player Definition of WPA (Win Probability Added) Can evaluate the contributions of the players who did not touch the ball

Example of WPA O/D ෝ 𝒘 𝒔𝒊 𝒕 𝒔𝒋 ෝ 𝒘 O/D O(Start) 0.65 18 702 9 0.35 D(Start) O(end) 0.72 21 722 9 0.28 D(end) D(start) 0.72 21 722 9 0.28 O(Start) ・ ・ ・ WPA𝐷 in Team 𝑗: 0.28 − 0.35 5 = −0.014 WPA𝑂 in Team 𝑖: 0.72 − 0.65 5 = 0.014 ・ ・ ・ Team 𝑖 Team 𝑗 ෝ 𝑤 722,12 = 0.72

Outline Background STATS in basketball Impact metrics Proposed method Construction of reasonable win probability model Main proposal: Offense/Defense Win Probability Added Numerical experiment Summary and future work

Numerical experiment 268 players in B1 League, 2018-19 regular season Following example Teams: Chiba (52 wins) and Tochigi (49 wins) Played more than 10000[s] (about 3[min/match])

Numerical experiment Team: Chiba Team: Tochigi

Discussion and analysis: pace  Team characteristics  WPA/s ~ Points/s  Tochigi has larger WPA𝑂/𝑠 and WPA𝐷/𝑠  Tochigi favored high-paced transition game WPA/s (Pink: Tochigi, Green: Chiba)

Discussion and analysis: PGs Team: Chiba Team: Tochigi Togashi Nishimura Watanabe Ikaruga

Discussion and analysis: PGs Team: Chiba Team: Tochigi high Low high high

Discussion and analysis: weakness of bench players ONO Ryumo Bench player Position: SF/PF Similar WPA𝐷 , but small 𝑊𝑃𝐴𝑂 compared with the regular SF and PF Team: Chiba Ono

Summary ☑ • Construct consistent win probability model ☑ • Contributions to win of all players is evaluated ☑ • Numerical evaluation in Japanese B.LEAGUE

Future work ☑ • Construct consistent win probability model New! • Contributions to win of all lineup will be evaluated • Pairwise comparison model New! • Numerical evaluation in Japanese B.LEAGUE

Many thanks! And welcome questions and comments! Sugie, Konaka. “Proposal of offense/defense WPA metrics in B.LEAGUE”