Overview of Division of Credit Modeling in NCAA Volleyball

2. Division of Credit Modeling for Team Sports Zachary Hass 7/13/2017

3. Outline • Overview of Division of Credit Modeling • Application to NCAA Women’s Volleyball

4. Division of Credit Metric • Definition: A metric that apportions an outcome of team competition amongst the participating players based on their relative contribution • Elements • Outcome • Measuring Contribution • Valuing Contribution

5. Potential Outcomes • Choice impacts scale of metric • Wins/Points • Plus/Minus – Hockey/Basketball • Win Share – Basketball (Berri, 1999) • Win Probability/Expected Points • NFL (Lock and Nettleton, 2014), NBA (Desphande and Jensen, 2016) • Point Probability in Hockey (Schuckers and Curro 2013)

6. Benefits of a Derivative Outcome • Address non-independence of consecutive plays on scoring • Football, baseball • Fill in scoring sparsity • Control for Context in Win Probability • Eg. Points scored during garbage minutes

7. Potential Issues with Derivative Outcome • Extra care to make sure model is capturing desired value • End of game change in win probability can be funny • Last second field goal can be worth most of a win • May produce negative credit on a positive play • Blocked shot in hockey in certain contexts (Routley, 2015) • High chance of a rebound goal

8. Measuring Contribution • Player Presence • Assume player contribution is constant • Need data that tracks substitutions • Easier to get data, value actions / less informative about contribution • Player Actions • Assume action value is constant • Need play-by-play data with relevant actions (grade quality) • Harder to get data, value actions / more informative about contribution

9. Valuing Contribution and Splitting Credit • Player Presence • Plus/Minus • APM, Network Modeling,… • Multicollinearity • Player Actions • Markov model (Hockey, Volleyball) • Finite State Machine (Engleman, 2011) • Empirical Expectation (WAR, Baumer, 2011)

10. Properties of Division of Credit Metrics • Place players on common scale • Crosses position or role • Can control for context of opportunity • Can use baseline for efficiency (eg. Runs above Replacement) • Outcome is conserved • Sums to 0 across all teams • Sums to team total • Additive • Can parse share based on desired strata (eg. Home/Away, by lineup,…)

11. Credit Above Value Expected • An application to NCAA Volleyball • Demonstration Data: 2 Games, 331 plays, 12 players

12. Outcome • Points • Rally Scoring • Assume points are equally valuable • Metric will be on the net points contributed scale • Similar to +/-, but unequal division

13. Measuring Contribution • Action Grades • Serve, ‘Dig’, Set, Attack, Block • Advantageous, Average, Disadvantageous • Can grade using DataVolley • Outsource using Volleymetrics

14. Value Actions: Markov Model Estimated Action Values Probability of a point for serving team

15. Observed Credit Proportion: Point Won • Divide point • for court presence • Intangibles / no-action plays • Action values accumulate • Player A average serve • Player B average dig, • Player C average set, • Player B advantageous Attack • Result = (0.31, 0.64, 0.01, 0.01, 0.01, 0.01)

16. Player Role: Dirichlet Model • Estimate across lineups – Remove action qualities: use action opportunity • Mixed Dirichlet likelihood with shared • Solution requires iterative update • bigger for greater opportunity • gives expected contribution given lineup

17. Play Context • All points are not created equal • Serving (46% vs. 61%) – built into action values • Home Field (54% vs. 51%) • Opponent Strength (49% vs. 55%) • Context helps evaluate player efficiency

18. Value Expected • Create a baseline to understand player efficiency Player’s average proportion of opportunity for point won Player’s average proportion of opportunity for point lost Expected Point Won Expected Point Lost

19. Credit above Value Expected • Avoids double use of the data in creating a baseline • Uses average opportunity (relative role) rather than game data • Adjusts baseline for game context • Useful for spotting unusual performances (good or bad)

20. CaVE Results

21. Observed Credit by Action

22. Observed Credit Opportunity

23. Observed Credit by Opportunity Opportunity < 1 point omitted

24. Summary • A Division of Credit Metric • Values play by an outcome • Measures and Values the contribution of the players • Divides the outcome based on the player contributions • CAVE • An application to NCAA Volleyball • Volleymetrics – Conference wide graded data

25. Estimated Action Values

26. Player Strength: Dirichlet Model • is the digamma function • average contribution parameter for player k. • Roster combination used in play p or the such combination • Player k’s number of plays • Player k’s observed credit on play p • Indicates if player k is in lineup j

27. Observed Credit: Point Lost • Result sums to negative 1 • Result = (-0.83, -0.03, -0.03, -0.03, -0.03, -0.03)

28. Impact of Player Presence Credit • Must choose credit value for court presence • Impacts player order • Actions vs. Intangibles • Stabilizes <