Chapter 25: Game Outcome Prediction - Quiz

Instructions

This quiz contains 25 questions covering the key concepts from Chapter 25. Select the best answer for multiple-choice questions. Short answer questions should be answered in 2-4 sentences.

Multiple Choice Questions

Question 1

The historical home team win percentage in the NBA is approximately: - A) 50-52% - B) 55-58% - C) 62-65% - D) 70-75%

Question 2

In point spread betting, a spread of -6.5 for Team A means: - A) Team A is expected to lose by 6.5 points - B) Team A must win by more than 6.5 points to cover - C) Team A's win probability is 65% - D) The total points expected is 6.5 times some factor

Question 3

The Pythagorean expectation formula relates winning percentage to: - A) Points scored only - B) Points allowed only - C) The ratio of points scored to points allowed - D) The difference between points scored and allowed

Question 4

If the standard deviation of NBA game margins is approximately 12 points, a 6-point favorite has a win probability closest to: - A) 55% - B) 61% - C) 69% - D) 75%

Question 5

The Brier score measures: - A) Prediction accuracy (correct/incorrect) - B) Average margin error - C) Mean squared error of probability predictions - D) Correlation between predictions and outcomes

Question 6

For betting at -110 odds, the break-even win rate is approximately: - A) 50.0% - B) 52.4% - C) 54.5% - D) 55.0%

Question 7

Home court advantage in the NBA is worth approximately: - A) 1-2 points - B) 3-4 points - C) 5-6 points - D) 7-8 points

Question 8

The primary advantage of Elo ratings over simple win-loss records is: - A) They're easier to calculate - B) They account for margin of victory and opponent strength - C) They're more stable - D) They're used by all professional sports

Question 9

In game prediction, a "closing line" refers to: - A) The final score of the game - B) The betting line just before game time - C) The margin of victory - D) The predicted total points

Question 10

Log loss (cross-entropy) compared to Brier score: - A) Penalizes confident wrong predictions more heavily - B) Penalizes confident wrong predictions less heavily - C) Is mathematically equivalent - D) Only applies to binary outcomes

Question 11

The typical RMSE for point spread predictions in NBA games is approximately: - A) 5-6 points - B) 8-9 points - C) 11-12 points - D) 15-16 points

Question 12

"Closing line value" in betting refers to: - A) Getting a better line than the closing spread - B) Betting on underdogs - C) The total value of bets placed - D) The sportsbook's margin

Question 13

The Kelly criterion is used to: - A) Calculate game probabilities - B) Determine optimal bet sizing - C) Evaluate model accuracy - D) Adjust for home court advantage

Question 14

Back-to-back games typically affect team performance by: - A) +2-3 points for the rested team - B) +1-2 points for the rested team - C) No measurable effect - D) Depends on travel distance only

Question 15

A well-calibrated prediction model means: - A) It has high accuracy - B) Predicted probabilities match observed frequencies - C) It beats the market - D) It has low variance

Question 16

The "vig" or "juice" in betting represents: - A) The sportsbook's profit margin - B) The home team's advantage - C) The prediction model's edge - D) The closing line movement

Question 17

When evaluating game prediction models, time-based validation is preferred because: - A) It's computationally faster - B) It prevents look-ahead bias - C) It uses more data - D) It's the industry standard

Question 18

The Four Factors model for team strength includes all EXCEPT: - A) Effective field goal percentage - B) Turnover rate - C) Free throw rate - D) Three-point attempt rate

Question 19

Sharp bettors are characterized by: - A) Betting on favorites only - B) High volume, high accuracy - C) Random betting patterns - D) Always following line movements

Question 20

For NBA playoff games, home court advantage typically: - A) Increases significantly - B) Decreases significantly - C) Remains similar to regular season - D) Becomes irrelevant

Short Answer Questions

Question 21

Explain why predicting exact game scores is much harder than predicting point spreads or win probabilities. What additional uncertainty exists in score prediction?

Your Answer:

Question 22

A model shows 55% ATS (against the spread) accuracy over 200 games. Explain whether this is statistically significant and what additional information you would need to evaluate the model's value.

Your Answer:

Question 23

Describe how you would incorporate a star player injury into a game prediction model. What factors would you consider and what challenges exist?

Your Answer:

Question 24

Compare and contrast the Brier score and log loss as evaluation metrics for probabilistic predictions. When might you prefer one over the other?

Your Answer:

Question 25

Explain why betting markets (Vegas lines) are often used as benchmarks for game prediction models. What does it mean to "beat the market" and why is it difficult?

Your Answer:

Answer Key

Multiple Choice Answers

  1. B - NBA home teams historically win 55-58% of games, though this has varied over time.

  2. B - A spread of -6.5 means Team A is favored by 6.5 points and must win by 7+ to cover.

  3. C - Pythagorean expectation uses the ratio (or more precisely, points^n for both scored and allowed).

  4. C - Using z = 6/12 = 0.5, P(win) = norm.cdf(0.5) = 0.69 or approximately 69%.

  5. C - Brier score = (1/n) * sum((probability - outcome)^2).

  6. B - At -110, you risk 110 to win 100. Break-even = 110/210 = 52.4%.

  7. B - Home court advantage is typically worth 3-4 points in the NBA.

  8. B - Elo incorporates margin of victory and adjusts for opponent strength.

  9. B - The closing line is the final betting line before the game starts.

  10. A - Log loss uses -log(p), which goes to infinity as confident wrong predictions approach 0 probability.

  11. C - Typical RMSE for point spread predictions is around 11-12 points.

  12. A - CLV means getting a better number than where the line closes.

  13. B - Kelly criterion determines optimal bet sizing based on edge and odds.

  14. B - The second game of a back-to-back typically shows 1-2 point disadvantage.

  15. B - Calibration means 60% predictions win 60% of the time, etc.

  16. A - The vig is the sportsbook's built-in profit margin.

  17. B - Time-based validation ensures models don't use future information.

  18. D - The Four Factors are eFG%, TOV%, ORB%, and FT Rate.

  19. B - Sharp bettors are characterized by profitable, high-accuracy betting.

  20. C - Playoff home court advantage is similar to regular season (3-4 points).

Short Answer Rubric

Question 21 - Should discuss: (1) score prediction requires predicting both spread AND total, (2) within-game variance (garbage time, overtime), (3) multiple ways to arrive at same margin but different scores, (4) lower practical value of exact score prediction.

Question 22 - Should calculate: standard error ~ sqrt(0.55*0.45/200) = 3.5%, meaning 95% CI is roughly 48-62%. At 55%, result is within random chance. Would need: more games, comparison to benchmark, and consideration of betting costs.

Question 23 - Factors include: player's impact metrics (BPM, RAPM), expected replacement's production, team's depth, opponent matchups, rest of lineup adjustments. Challenges: limited injury data, varying recovery quality, psychological effects.

Question 24 - Brier: bounded 0-1, interpretable, less sensitive to extreme predictions. Log loss: more severely penalizes confident wrong predictions, undefined at 0/1. Prefer log loss when confident predictions matter most; Brier for general evaluation.

Question 25 - Markets aggregate information from many sophisticated participants, incorporate injury/situation news quickly, and have financial incentives for accuracy. "Beating the market" means systematic positive returns after accounting for vig. Difficult because markets are efficient - errors are random, not systematic.