Chapter 28 Quiz: Feature Engineering for Sports Betting

Instructions: Answer all 25 questions. This quiz is worth 100 points. You have 60 minutes. A calculator is permitted; no notes or internet access. For multiple choice, select the single best answer. For short answer, be precise and concise.

Section 1: Multiple Choice (10 questions, 3 points each = 30 points)

Question 1. Which of the following best describes "temporal leakage" in a sports prediction model?

(A) Using features that are highly correlated with each other

(B) Including information in training features that would not have been available at prediction time

(C) Training on too few games, causing the model to overfit to recent results

(D) Allowing the model to see the target variable during feature selection

Question 2. A feature has a variance inflation factor (VIF) of 12.4. What does this indicate?

(A) The feature has high predictive power for the target variable

(B) The feature is nearly constant across all observations

(C) The feature is highly correlated with other features in the model, causing multicollinearity

(D) The feature has a non-normal distribution requiring transformation

Question 3. When encoding the categorical variable "stadium" (32 NFL venues) for a gradient-boosted tree model, which approach is LEAST recommended?

(A) One-hot encoding all 32 stadiums

(B) Target encoding with leave-one-out smoothing

(C) Ordinal encoding (assigning integers 1-32 arbitrarily)

(D) Entity embeddings learned from a neural network

Question 4. An exponentially weighted moving average (EWMA) of EPA/play with alpha = 0.4 places what fraction of total weight on the most recent game?

(A) 0.40

(B) 0.24

(C) 0.60

(D) 0.16

Question 5. Which of the following is the primary advantage of using mutual information over Pearson correlation for feature selection in sports betting models?

(A) Mutual information is faster to compute

(B) Mutual information captures nonlinear and non-monotonic relationships

(C) Mutual information produces values between -1 and +1, making interpretation easier

(D) Mutual information is not affected by sample size

Question 6. A modeler creates a "rest advantage" feature defined as (home team days of rest) minus (away team days of rest). For a game where the home team had 8 days rest and the away team had 5 days rest, the feature value is +3. Why might this linear difference be suboptimal?

(A) The feature should use multiplication instead of subtraction

(B) The marginal benefit of additional rest is likely nonlinear (diminishing returns beyond 7 days)

(C) Days of rest should always be encoded as a categorical variable

(D) The feature should only be computed for outdoor games

Question 7. In a walk-forward validation setup for an NFL season model, which of the following correctly describes the expanding-window approach for Week 10 predictions?

(A) Train on Weeks 1-9 of the current season only, predict Week 10

(B) Train on all available historical data plus Weeks 1-9 of the current season, predict Week 10

(C) Train on Weeks 6-9 (a 4-week sliding window), predict Week 10

(D) Train on Weeks 1-17 of the previous season only, predict Week 10

Question 8. Which dimensionality reduction technique preserves the most interpretability when applied to a set of 50 team-level basketball statistics?

(A) Principal Component Analysis (PCA)

(B) t-SNE (t-distributed Stochastic Neighbor Embedding)

(C) Factor Analysis with varimax rotation

(D) Autoencoders

Question 9. A feature "turnover margin per game" has a Pearson correlation of 0.38 with the binary target "win." However, when the feature is added to an existing 12-feature model, the model's out-of-sample performance decreases. Which of the following is the most likely explanation?

(A) The correlation of 0.38 was a computational error

(B) Turnover margin is redundant with other features already in the model, adding noise without new signal

(C) Binary targets cannot be predicted using continuous features

(D) The sample size is too large for the correlation to be meaningful

Question 10. A modeler uses the closing line as a feature in their spread prediction model and reports 58% accuracy against the spread in backtesting. Why is this result misleading?

(A) 58% accuracy is below the breakeven threshold

(B) The closing line incorporates the very information the model is trying to predict, making the task trivially easy

(C) The closing line is only available for nationally televised games

(D) Spread prediction should use log-loss, not accuracy, as the evaluation metric

Section 2: Short Answer (8 questions, 5 points each = 40 points)

Question 11. Explain the difference between a "lagged feature" and a "rolling aggregate feature." Provide one example of each for an NBA betting model and state which is more resistant to single-game outliers.

Question 12. Define "target encoding" for a categorical feature. Write the formula for a smoothed target encoding that blends the category-specific mean with the global mean, and explain why smoothing is necessary.

Question 13. A modeler creates 200 candidate features and uses Lasso (L1 regularization) to select the most important ones. After tuning the regularization parameter lambda, the Lasso retains 18 features. Describe one advantage and one disadvantage of using Lasso for feature selection compared to using permutation importance with a Random Forest.

Question 14. Explain why a team's "season-to-date win percentage" is a poor feature for predicting outcomes in the first three weeks of an NFL season. Propose two alternative features that are more stable in small samples and explain why.

Question 15. Describe the "garbage time" filtering problem in NFL feature engineering. Define specific criteria you would use to identify garbage time plays, and explain the tradeoff between filtering too aggressively and not filtering at all.

Question 16. A feature "travel distance to game" is measured in miles and ranges from 0 (home game) to 2,800 (cross-country away game). Describe three different ways to transform this feature for use in a model, and explain the hypothesis behind each transformation.

Question 17. Explain the concept of "feature drift" in the context of a sports betting model that has been running for three seasons. Provide a concrete example of a feature whose distribution might change over time in the NFL, and describe how you would detect and respond to this drift.

Question 18. A dataset for NBA game prediction contains both team-level aggregate features (e.g., season offensive rating) and game-level contextual features (e.g., back-to-back indicator, travel distance). Explain why these two types of features require different update frequencies and describe a pipeline architecture that handles both.

Section 3: Applied Problems (4 questions, 7.5 points each = 30 points)

Question 19. You are building an NFL spread prediction model. You have the following candidate features for the home team:

• EPA/play (offense), EPA/play (defense)
• Success rate (offense), Success rate (defense)
• Turnover rate, Red zone efficiency
• Third-down conversion rate
• Yards per play (offense), Yards per play (defense)

Compute the correlation matrix conceptually (describe which pairs you expect to be highly correlated) and recommend a reduced set of 4-5 features that minimizes redundancy while maintaining coverage of distinct predictive dimensions. Justify each selection.

Question 20. A colleague presents an NBA model with the following feature engineering pipeline and asks for your review. Identify all issues:

1. Load all games from the 2019-2023 seasons.
2. Compute each team's season-average offensive and defensive rating.
3. Compute the difference (home team rating - away team rating) as the primary feature.
4. Standardize all features using the mean and standard deviation of the full dataset.
5. Train a logistic regression model using 80/20 random train/test split.
6. Report accuracy on the test set.

Question 21. Write Python code (or detailed pseudocode) for a function that creates an "opponent-adjusted EPA/play" feature for NFL teams. The function should: - Take a DataFrame of game results with columns [team, opponent, week, epa_per_play] - Iteratively compute opponent adjustments (at least 10 iterations) - Return each team's adjusted EPA/play for each week using only data from prior weeks

Describe the convergence behavior you expect.

import pandas as pd
import numpy as np

def compute_opponent_adjusted_epa(
    games: pd.DataFrame,
    n_iterations: int = 10
) -> pd.DataFrame:
    """Compute opponent-adjusted EPA/play using iterative adjustment.

    For each week w, uses only games from weeks 1 through w-1.
    Iterates to resolve the circularity of adjustments.
    """
    results = []
    all_weeks = sorted(games["week"].unique())

    for target_week in all_weeks[1:]:  # Can't compute for Week 1
        prior_games = games[games["week"] < target_week].copy()

        # Initialize: raw average EPA/play per team
        team_ratings = prior_games.groupby("team")["epa_per_play"].mean()

        for iteration in range(n_iterations):
            # Compute opponent strength for each game
            prior_games["opp_rating"] = prior_games["opponent"].map(team_ratings)

            # Adjusted EPA = raw EPA - opponent rating (facing a tough
            # defense yields higher adjusted EPA)
            prior_games["adj_epa"] = (
                prior_games["epa_per_play"] - prior_games["opp_rating"]
            )

            # Update team ratings to be the mean adjusted EPA
            team_ratings = prior_games.groupby("team")["adj_epa"].mean()

        for team, rating in team_ratings.items():
            results.append({
                "team": team, "week": target_week,
                "adj_epa_per_play": rating
            })

    return pd.DataFrame(results)

Question 22. Design a complete feature engineering experiment to determine whether adding player-level features improves an NBA spread prediction model beyond team-level features alone. Specify: - The control model (team-level features only) and treatment model (team + player features) - At least three specific player-level features you would construct - The evaluation methodology (validation scheme, metrics, statistical test) - The minimum sample size needed and how you would ensure the comparison is fair