Chapter 21: Exercises - Win Probability Models

Overview

These exercises progress from basic win probability concepts to building complete WP systems with calibration and decision analysis.

Level 1: Fundamentals

Exercise 1.1: Game State Encoding

Create a function to encode game states into feature vectors.

Task: 1. Define the key features that affect win probability 2. Implement normalization for each feature 3. Handle edge cases (overtime, end of game)

Starter Code:

def encode_game_state(score_diff: int,
                     seconds_remaining: int,
                     yard_line: int,
                     down: int,
                     distance: int,
                     has_ball: bool) -> np.ndarray:
    """
    Encode game state as feature vector.

    Returns normalized features suitable for ML model.
    """
    # Your code here
    pass

Exercise 1.2: Simple Win Probability

Build a simple win probability model using score differential and time.

Task: 1. Use only score_diff and time_remaining as features 2. Fit logistic regression to historical data 3. Evaluate on held-out test set

Exercise 1.3: Win Probability at Game Start

Calculate the baseline win probability at game start based on team strength.

Task: 1. Use pregame point spreads to estimate win probability 2. Implement the conversion formula: WP = 1 / (1 + 10^(-spread/10)) 3. Validate against historical results

Level 2: Intermediate

Exercise 2.1: Feature Engineering

Create comprehensive features for win probability.

Task: 1. Implement interaction terms (score × time) 2. Create categorical indicators (red zone, trailing late) 3. Add timeout differential features

Exercise 2.2: Calibration Analysis

Evaluate and improve model calibration.

Task: 1. Calculate calibration curve (predicted vs. actual by bin) 2. Compute Expected Calibration Error (ECE) 3. Apply isotonic regression to improve calibration

Starter Code:

def calculate_calibration(predictions: np.ndarray,
                         outcomes: np.ndarray,
                         n_bins: int = 10) -> pd.DataFrame:
    """
    Calculate calibration statistics.
    """
    # Your code here
    pass

Exercise 2.3: Win Probability Added

Calculate WPA for each play in a game.

Task: 1. Calculate WP before and after each play 2. Compute WPA = WP_after - WP_before 3. Identify the highest-WPA plays in the game

Level 3: Advanced

Exercise 3.1: Gradient Boosting WP Model

Build a gradient boosting win probability model.

Task: 1. Implement feature engineering pipeline 2. Train XGBoost or GradientBoosting classifier 3. Compare to logistic regression baseline 4. Analyze feature importance

Exercise 3.2: Fourth Down Decision Analyzer

Build a fourth-down decision analysis system using WP.

Task: 1. Calculate WP for each decision option (go, punt, FG) 2. Incorporate conversion and field goal probabilities 3. Recommend optimal decision 4. Calculate "break-even" conversion rate

Exercise 3.3: Live Win Probability Tracker

Build a system to track WP throughout a game.

Task: 1. Process play-by-play data in order 2. Calculate WP after each play 3. Identify key momentum swings 4. Generate game WP chart

Level 4: Expert

Exercise 4.1: Complete WP System

Build an end-to-end win probability system.

Requirements: - Data preprocessing pipeline - Multiple model options (logistic, GBM, neural network) - Calibration module - WPA calculation - Visualization dashboard

Exercise 4.2: Contextual WP Adjustments

Implement adjustments for specific game contexts.

Task: 1. Home field advantage adjustment 2. Weather impact modeling 3. Altitude/environment factors 4. Team-specific strength adjustments

Project: Real-Time Win Probability System

Build a complete real-time WP tracking and analysis system.

Requirements

  1. Data Ingestion: Process live play-by-play data
  2. Model Inference: Real-time WP predictions
  3. WPA Tracking: Cumulative WPA for players/teams
  4. Decision Analysis: Fourth-down recommendations
  5. Visualization: Live WP chart and key play highlights

Deliverables

  1. Working prediction system
  2. Calibration analysis
  3. Historical validation
  4. Documentation