Chapter 25: Game Outcome Prediction - Exercises

Section A: Fundamentals of Game Prediction (Questions 1-8)

Exercise 1: Baseline Models

Calculate baseline prediction accuracy for the following approaches: a) Predict home team wins every game (historical home win rate: 58%) b) Predict the team with better record wins c) Predict based on point differential in last 10 games

For each baseline, calculate expected accuracy and discuss limitations.

Exercise 2: Power Ratings

Given the following game results, calculate power ratings using the least-squares method:

Assume home court advantage of 3 points.

Exercise 3: Point Spread Interpretation

A game has the following betting line: Team A -6.5 vs Team B a) What is the implied expected margin? b) If the standard deviation of outcomes is 11 points, calculate Team A's win probability c) Calculate the probability Team A covers the spread

Exercise 4: Efficiency-Based Prediction

Team A: Offensive Rating 115, Defensive Rating 108 Team B: Offensive Rating 110, Defensive Rating 105 Expected Pace: 100 possessions

Calculate: a) Expected points for Team A b) Expected points for Team B c) Predicted margin

Exercise 5: Home Court Advantage Quantification

Using the following data, estimate home court advantage: - Home team average margin: +3.2 points - Home team win percentage: 57% - Average game total: 220 points

Exercise 6: Spread vs Moneyline Conversion

A team is favored by 7 points with an expected standard deviation of 12 points. a) Calculate implied win probability b) What moneyline odds correspond to this probability? c) At what spread would the team have 60% win probability?

Exercise 7: Model Accuracy Metrics

A prediction model produced the following results over 100 games: - Correctly predicted winner: 68 games - Average absolute margin error: 8.2 points - RMSE of margin: 10.5 points

Evaluate this model against typical benchmarks.

Exercise 8: Totals Prediction

Two high-paced teams play each other: - Team A: 112 PPG, 108 PA, Pace 102 - Team B: 115 PPG, 111 PA, Pace 104

Predict the game total and explain your methodology.

Section B: Advanced Model Building (Questions 9-16)

Exercise 9: Feature Engineering

Design 10 features for a game prediction model: a) List each feature b) Explain its predictive rationale c) Discuss how you would calculate it

Exercise 10: Elo Rating System

Implement an Elo rating update: - Team A rating: 1550 - Team B rating: 1480 - Team A wins by 8 points - K-factor: 20 - Home court adjustment: 50 points

Calculate new ratings for both teams.

Exercise 11: Regression Model Specification

Design a regression model for point spread prediction: a) Write the model equation b) Identify independent variables c) Discuss regularization approach d) Explain how to handle missing data

Exercise 12: Cross-Validation Design

Design a validation scheme for a game prediction model: a) Why is random splitting problematic? b) Propose a time-based validation approach c) How would you handle the NBA schedule structure? d) What metrics would you use to evaluate?

Exercise 13: Situational Adjustments

Quantify the following situational factors: a) Back-to-back game disadvantage b) Travel across 3 time zones c) Altitude advantage (Denver home games) d) Rivalry game intensity

Exercise 14: Pace-Neutral Predictions

Two teams with very different paces: - Team A: Pace 95, ORtg 108, DRtg 105 - Team B: Pace 105, ORtg 115, DRtg 112

a) Calculate expected game pace b) Predict each team's points c) Predict the margin and total

Exercise 15: Ensemble Methods

Design an ensemble combining: - Elo ratings - Efficiency-based model - Machine learning model

a) How would you weight the components? b) How would you optimize the ensemble? c) What are the benefits of ensembling?

Exercise 16: Real-Time Updates

Your pre-game prediction had Team A as a 5-point favorite. At halftime: - Team B leads by 3 - Team A's best player has 2 fouls - Both teams shooting above season average

Update your second-half prediction.

Section C: Market Efficiency and Betting (Questions 17-22)

Exercise 17: Closing Line Value

Your model predicted Team A -5. The line opened at Team A -3 and closed at Team A -5.5. a) Did your prediction have value at the open? b) How efficient was the closing line? c) Calculate expected value of betting at the open

Exercise 18: Vig Calculation

A sportsbook offers: - Team A -110 - Team B -110

Calculate: a) Implied probabilities for each side b) The overround (vig) c) Break-even win rate to profit

Exercise 19: Kelly Criterion Application

Your model gives Team A 55% win probability. The sportsbook offers -105. a) Calculate the edge b) Apply full Kelly criterion c) Apply half Kelly d) Discuss bankroll management

Exercise 20: Line Movement Analysis

The spread moved from Team A -3 to Team A -5 over 24 hours. a) What does this movement suggest? b) How might you incorporate line movement into your model? c) When does line movement have signal vs noise?

Exercise 21: Market Efficiency Testing

You have 1000 games with your predictions and closing lines: a) Design a test for systematic bias in your model b) Design a test for market efficiency c) What would prove your model adds value?

Exercise 22: Sharp Money Detection

Design a method to identify "sharp" betting action: a) What data would you need? b) What patterns indicate sharp action? c) How would you incorporate this information?

Section D: Model Evaluation (Questions 23-28)

Exercise 23: Brier Score Calculation

Calculate the Brier score for these predictions:

Exercise 24: Calibration Analysis

Your model's predictions vs actual outcomes: - Predicted 60%: Won 65% (150 games) - Predicted 70%: Won 68% (100 games) - Predicted 80%: Won 75% (50 games)

a) Is the model well-calibrated? b) Create a calibration curve c) Suggest improvements

Exercise 25: Log Loss Evaluation

For the same games in Exercise 23, calculate log loss and compare to Brier score.

Exercise 26: Margin Error Analysis

Your model's margin predictions vs actual margins: - Mean error: +0.8 (slight home bias) - MAE: 9.2 points - RMSE: 11.8 points

a) Interpret these errors b) How do they compare to Vegas lines? c) What does the difference between MAE and RMSE indicate?

Exercise 27: Against-the-Spread Performance

Your model went 270-230 against the spread (54% win rate) over 500 games betting at -110. a) Calculate profit/loss (assuming $100 per bet) b) Is this result statistically significant? c) Calculate confidence interval for true win rate

Exercise 28: Sample Size and Significance

How many games would you need to demonstrate your model adds value at: a) 53% ATS win rate (with 95% confidence) b) 55% ATS win rate (with 95% confidence) c) 57% ATS win rate (with 95% confidence)

Section E: Applied Prediction Problems (Questions 29-35)

Exercise 29: Pre-Game Prediction

Build a complete pre-game prediction for: - Home: Golden State Warriors (55-22, home 30-10) - Away: Los Angeles Lakers (47-30, away 20-18) - Context: Regular season, both teams rested

Include point spread, total, and win probability.

Exercise 30: Injury Impact

A team's starting point guard (24 PPG, +6 BPM) is ruled out. a) Estimate the impact on team efficiency b) Adjust your spread prediction c) Quantify uncertainty around this adjustment

Exercise 31: Playoff Adjustment

Regular season models need adjustment for playoffs: a) How does home court advantage change? b) How does pace typically change? c) How does scoring efficiency change? d) How would you adjust your model?

Exercise 32: Live Betting Prediction

At halftime of a game: - Pre-game prediction: Team A -4 - Current score: Team B leads by 6 - First half pace: 98 (season avg: 100) - Team A best player: 8 points on 3-12 shooting

Update prediction for second half and final margin.

Exercise 33: Season Win Total Prediction

For a team projected at 108 ORtg, 105 DRtg, with league averages at 110 ORtg and 110 DRtg: a) Estimate their net rating b) Convert to expected winning percentage (Pythagorean) c) Calculate expected wins over 82 games d) Provide a confidence interval

Exercise 34: Back-Testing Analysis

You want to backtest a model on 5 seasons of data: a) Design the backtesting procedure b) What pitfalls should you avoid? c) How would you report results? d) What would make results convincing?

Exercise 35: Model Comparison

Compare two models over 500 games: - Model A: 55% accuracy, 0.22 Brier score, 0.35 log loss - Model B: 53% accuracy, 0.21 Brier score, 0.33 log loss

Which model is better? Justify your answer.

Section F: Advanced Topics (Questions 36-40)

Exercise 36: Player-Based Predictions

Design a game prediction approach that: a) Starts with player projections b) Aggregates to lineup projections c) Combines lineups to game prediction d) Handles uncertainty properly

Exercise 37: Bayesian Game Prediction

Implement a Bayesian approach: a) Define prior distributions for team strengths b) Update with game results c) Generate predictive distributions d) Compare to frequentist approach

Exercise 38: Neural Network Predictor

Design a neural network for game prediction: a) What architecture would you use? b) What features would you input? c) What output would you predict? d) How would you train and validate?

Exercise 39: Simulation-Based Prediction

Design a Monte Carlo simulation for game prediction: a) What would you simulate? b) How many simulations needed? c) What outputs would you generate? d) What are the advantages over point estimates?

Exercise 40: Championship Probability

Using game prediction as a building block, estimate championship probabilities: a) How do single-game probabilities chain? b) How do you handle playoff seeding uncertainty? c) How would you simulate a playoff bracket? d) What drives championship probability most?

Answer Key Guidelines

Quantitative exercises should show complete calculations and explain methodology. Model design exercises should demonstrate understanding of statistical principles. Betting-related exercises should include appropriate caveats about risk.

Instructors may assign specific sections based on course focus: - Fundamentals: Exercises 1-8 - Model building: Exercises 9-16 - Markets: Exercises 17-22 - Evaluation: Exercises 23-28 - Applications: Exercises 29-35 - Advanced: Exercises 36-40