Optimizing NHL Player Usage Through Advanced Statistical Analysis
Explore the challenges of using linear models in maximizing NHL player performance and discover the benefits of nonlinear models, time-on-ice cutoff analysis, polynomial regression, and player lineup strategies. Understand the complexities of player combinations and how statistical analysis can enhance team performance.
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Presentation Transcript
Maximizing NHL Player Usage Using a Linear Optimization Model Dawson Sprigings
Is a linear model the right choice? 1. Theoretical 2. Residual Analysis a. Residual = Observed - Predicted b. Example: i. Fake model to predict how many goals a player will score ii. Model Predicts -> 5 iii. Player Actually Scores -> 7 iv. Residual -> 2
2. Residual Analysis
2. Residual Analysis - Cumulative Residual Plot
Should you play your best players together? Short Answer: NO 7 Models All - Average Better Answer: It depends 3 Bad Players 2 Bad Players 1 Bad Player 3 Good Players 2 Good Players 1 Good Player Good = CF%RelTM > 1 SD
Diminishing Returns Model: Model Beta Coefficient 3 Good Players 0.51 Dependent Variable 2 Good Players 0.87 Actual Line CF% 1 Good Player 1.3 Independent Variable All Average 1.58 1 Bad Player 1.41 Estimated Line CF% 2 Bad Players 1 Est. Line CF% = (P1 CF%RelTM + P2 CF%RelTM P3 CF%RelTM)/3 3 Bad Players 1.02
Linear Optimization Maximize under a certain set of constraints Gives us the best possible lines Can use best lines as a baseline to see how much value is being lost Unfair to compare actual lines to best Compare to basic model instead
Basic Model vs. New Model Basic Model Uses straight line approach Output Sub-optimal lines Incorrect performance projections New Model Uses polynomial approach Uses 7 different models to account for line makeup Output
Basic Model vs. New Model - Effect Incorrect Projections Cost of Bad Lineups (Goals) Basic Model overestimated Minnesota - 7.88 Minnesota Los Angeles - 6.05 Los Angeles Carolina - 4.79 Arizona Boston - 3.25 Basic Model underestimated Florida Nashville
Summary & Future Work Polynomial regression is more appropriate than standard linear model Offense vs. Defense Improve the 7 models approach Apply different metrics Try to spread talent throughout lineup to maximize impact xG / WAR
