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DEPARTMENT OF STATISTICS Division of Credit Modeling for Team Sports Zachary Hass 7/13/2017 2
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DEPARTMENT OF STATISTICS Outline 1. Overview of Division of Credit Modeling 2. Application to NCAA Women’s Volleyball 3
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DEPARTMENT OF STATISTICS Division of Credit Metric • Definition: A metric that apportions an outcome of team competition amongst the participating players based on their relative contribution • Elements 1. Outcome 2. Measuring Contribution 3. Valuing Contribution 4
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DEPARTMENT OF STATISTICS 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) 5
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DEPARTMENT OF STATISTICS 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 6
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DEPARTMENT OF STATISTICS 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 1.2 1 0.8 – Last second field goal can be worth most of a win 0.6 • May produce negative credit on a positive play 0.2 0.4 0 5:00 4:40 4:20 4:00 3:40 3:20 3:00 2:40 2:20 2:00 1:40 1:20 1:00 0:40 0:20 0:00 Team A Team B – Blocked shot in hockey in certain contexts (Routley, 2015) – High chance of a rebound goal 7
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DEPARTMENT OF STATISTICS Measuring Contribution 1. Player Presence – Assume player contribution is constant – Need data that tracks substitutions – Easier to get data, value actions / less informative about contribution 2. 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 8
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DEPARTMENT OF STATISTICS Valuing Contribution and Splitting Credit 1. Player Presence – – – • Plus/Minus APM, Network Modeling,… Multicollinearity 2. Player Actions – – – Markov model (Hockey, Volleyball) Finite State Machine (Engleman, 2011) Empirical Expectation (WAR, Baumer, 2011) 9
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DEPARTMENT OF STATISTICS 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,…) 10
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DEPARTMENT OF STATISTICS Credit Above Value Expected • An application to NCAA Volleyball • Demonstration Data: 2 Games, 331 plays, 12 players 11
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DEPARTMENT OF STATISTICS Outcome • Points – Rally Scoring • Assume points are equally valuable • Metric will be on the net points contributed scale – Similar to +/-, but unequal division 12
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DEPARTMENT OF STATISTICS Measuring Contribution • Action Grades – Serve, ‘Dig’, Set, Attack, Block – Advantageous, Average, Disadvantageous • Can grade using DataVolley • Outsource using Volleymetrics 13
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DEPARTMENT OF STATISTICS Value Actions: Markov Model Estimated Action Values Probability of a point for serving team 14
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DEPARTMENT OF STATISTICS • 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) 15
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DEPARTMENT OF STATISTICS 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 16
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DEPARTMENT OF STATISTICS 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 • 17
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DEPARTMENT OF STATISTICS Value Expected • Create a baseline to understand player efficiency Expected Point Won Player’s average proportion of opportunity for point won Expected Point Lost Player’s average proportion of opportunity for point lost 18
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DEPARTMENT OF STATISTICS 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) 19
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DEPARTMENT OF STATISTICS CaVE Results Plyr A B C D E F G H J K L M Sum Credit G1 0.1 0.4 -3.8 -1.6 -1.3 0.0 -0.1 -0.7 1.1 -1.7 0.8 -0.2 -7.0 G2 1.0 7.7 -1.3 4.8 2.4 4.0 0.0 1.6 -0.9 -1.1 0.0 -0.2 18.0 Total 1.0 8.0 -5.1 3.2 1.1 4.0 -0.1 0.9 0.3 -2.8 0.8 -0.4 11.0 Value Expected G1 G2 Total G1 G2 Total -2.2 -0.2 -4.0 -1.4 -1.5 -1.0 -3.2 -1.0 -2.1 -1.0 0.4 -0.4 -17.8 1.4 7.0 0.4 2.6 2.0 2.6 0.0 0.9 0.5 -0.6 0.0 0.2 17.1 -0.8 6.8 -3.6 1.2 0.5 1.5 -3.2 -0.1 Credit above Value Expected -1.6 -1.6 0.4 -0.2 -0.7 2.3 0.6 0.2 -0.2 0.2 1.0 3.1 0.3 3.3 -0.7 0.4 0.2 10.8 -0.4 0.6 -1.7 2.2 0.4 1.5 0.0 0.7 -1.4 -0.5 0.0 -0.5 0.9 1.9 1.2 -1.5 2.0 0.6 2.5 3.1 1.0 1.9 -1.2 0.4 -0.2 11.7 20
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DEPARTMENT OF STATISTICS Observed Credit by Action Player A B C D E F G H J K L M Total Serve -1.0 0.0 -1.8 1.7 0.0 -2.6 0.0 0.0 0.0 -0.9 0.8 -1.3 -5.1 Dig 0.6 -2.0 -1.4 -0.6 1.0 0.6 -0.5 0.8 -1.0 -0.1 0.0 0.1 -2.5 Set 0.4 8.2 -0.3 -0.2 0.1 0.0 -0.5 -0.2 -0.1 -0.3 0.0 -0.1 6.9 Attack 0.1 2.5 0.6 -0.2 2.2 4.2 1.3 1.2 0.0 0.7 0.0 0.5 13.2 Block -0.2 -3.0 -3.1 0.0 -3.1 -0.1 -1.3 -2.2 0.0 -2.8 0.0 0.0 -15.8 Presence 1.1 2.4 1.0 2.5 0.9 2.0 0.9 1.3 1.5 0.5 0.0 0.4 14.3 Total 1.0 8.0 -5.1 3.2 1.1 4.0 -0.1 0.9 0.3 -2.8 0.8 -0.4 11.0 21
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DEPARTMENT OF STATISTICS Observed Credit Opportunity Player A B C D E F G H J K L M Total Serve 10.3 6.5 5.1 9.1 0.0 4.1 0.0 0.0 7.1 0.9 0.8 3.1 46.9 Dig 13.7 4.7 2.1 18.2 9.1 2.7 0.5 1.8 10.6 0.1 0.0 1.5 65.0 Set 1.6 40.0 0.7 3.3 0.1 0.1 0.5 0.2 0.3 0.3 0.0 0.1 47.2 Attack 2.6 5.5 5.3 0.6 12.7 13.5 5.6 5.8 0.0 4.1 0.0 0.5 56.2 Block 1.4 12.0 18.0 0.0 8.9 11.9 9.4 7.9 0.0 9.1 0.0 0.0 78.7 Presence 3.7 6.2 3.0 5.9 3.3 5.1 1.9 2.5 2.9 1.6 0.0 1.0 37.0 Total 33.3 74.8 34.2 37.1 34.2 37.3 17.9 18.2 20.9 16.1 0.8 6.2 331 22
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DEPARTMENT OF STATISTICS Observed Credit by Opportunity Player A B C D Serve -10% 0% -35% 19% Dig 4% -43% -67% -3% Set 25% 21% Attack 4% 45% 11% 17% 31% 23% 21% 17% 23% Block -14% -25% -17% -35% -1% -14% -28% -31% -20% Presence 30% 39% 33% 42% 27% 39% 47% 52% 52% 31% 40% 39% Total 3% 11% -15% 9% 3% 11% -1% 5% 1% -17% -6% 3% E F G H -63% 11% 22% 44% J K L M Total 0% -42% -11% -9% 7% -4% -6% 15% Opportunity < 1 point omitted 23
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DEPARTMENT OF STATISTICS 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 24
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DEPARTMENT OF STATISTICS Estimated Action Values Action Advantageous Average Disadvantageous Opportunity Serve 0.53 0.45 0.15 0.42 Dig 0.51 0.50 0.31 0.38 Set 0.55 0.50 0.37 0.44 Attack 0.59 0.51 0.39 0.46 Block 0.64 0.41 0.21 0.40 Opposite Dig 0.43 0.45 0.60 0.45 Opposite Set 0.41 0.44 0.56 0.41 Opposite Attack 0.35 0.45 0.56 0.40 Opposite Block 0.39 0.53 0.69 0.48 25
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DEPARTMENT OF STATISTICS 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 26
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DEPARTMENT OF STATISTICS Observed Credit: Point Lost • • Result sums to negative 1 • Result = (-0.83, -0.03, -0.03, -0.03, -0.03, -0.03) 27
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DEPARTMENT OF STATISTICS Impact of Player Presence Credit • Must choose credit value for court presence – Impacts player order – Actions vs. Intangibles – Stabilizes < 28
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