Chapter 22: Player Performance Prediction - Quiz

Instructions

This quiz contains 25 questions covering the key concepts from Chapter 22. Select the best answer for each multiple-choice question. Short answer questions should be answered in 2-4 sentences.

Multiple Choice Questions

Question 1

Which of the following is NOT one of the four sub-problems in player projection identified in the chapter? - A) Skill estimation - B) Aging adjustment - C) Salary cap impact - D) Uncertainty quantification

Question 2

In Marcel-style weighting systems, more recent seasons receive higher weights primarily because: - A) Older data is less accurate - B) Recent performance better reflects current ability - C) It's computationally simpler - D) It matches betting market preferences

Question 3

A player shoots 40% from three on 100 attempts. Using a prior of 35% with a weight of 200 attempts, what is the regressed estimate? - A) 35.0% - B) 36.7% - C) 37.5% - D) 38.3%

Question 4

The delta method for creating aging curves involves: - A) Comparing players of different ages in the same season - B) Tracking the same players across multiple seasons - C) Using polynomial regression on cross-sectional data - D) Weighting by career length

Question 5

Survivorship bias in aging curve analysis tends to: - A) Underestimate decline rates - B) Overestimate decline rates - C) Have no systematic effect - D) Only affect young players

Question 6

Which skill typically shows the earliest peak age in NBA players? - A) Three-point shooting - B) Free throw shooting - C) Athleticism-based defense - D) Playmaking

Question 7

In similarity-based projections, the appropriate number of comparables is typically: - A) 1-3 (very selective) - B) 5-15 (moderate) - C) 50-100 (broad) - D) All available players

Question 8

Which of the following would INCREASE the uncertainty in a player projection? - A) More seasons of data - B) Older player age - C) Consistent past performance - D) Strong comparable matches

Question 9

CARMELO projections primarily rely on: - A) Pure regression modeling - B) Player similarity scores - C) Expert consensus - D) Betting market odds

Question 10

When projecting a player changing teams, the most important adjustment is often: - A) Travel distance - B) Role and usage changes - C) Climate differences - D) Arena altitude

Question 11

The standard deviation of a proportion (like shooting percentage) is calculated as: - A) sqrt(p * (1-p) / n) - B) p / sqrt(n) - C) sqrt(p / n) - D) (1-p) / n

Question 12

Which statement about mean vs. median projections is correct? - A) Mean projections are always higher - B) Median projections are more appropriate when distributions are skewed - C) They are mathematically identical - D) Median projections account for aging

Question 13

A 95% prediction interval for a projection typically: - A) Is narrower than a 95% confidence interval - B) Includes only model uncertainty - C) Includes both model uncertainty and individual variation - D) Is inappropriate for player projections

Question 14

Regression to the mean is strongest for: - A) Statistics with large sample sizes - B) Statistics with small sample sizes - C) Veteran players - D) Commonly tracked metrics

Question 15

Walk-forward validation is preferred over standard k-fold cross-validation for projection models because: - A) It's computationally faster - B) It preserves temporal order of data - C) It uses more data for training - D) It produces narrower confidence intervals

Question 16

The RAPTOR projection system differs from CARMELO primarily in its use of: - A) Box score statistics only - B) Player tracking data - C) Similarity scores - D) Draft position

Question 17

When creating aging curves, controlling for playing time is important because: - A) Minutes are easier to project - B) Players with declining minutes may be declining for other reasons - C) Playing time is constant across ages - D) It improves statistical significance

Question 18

A player's projection should be adjusted downward if: - A) He is entering his prime years - B) His team's pace is increasing - C) He is recovering from a major injury - D) His usage rate is decreasing (in isolation)

Question 19

The coefficient of determination (R-squared) for year-over-year player projection models is typically: - A) Above 0.90 (very high) - B) Between 0.60 and 0.80 - C) Between 0.30 and 0.60 - D) Below 0.30 (low)

Question 20

Bayesian methods are particularly useful in player projection for: - A) Handling large datasets - B) Combining prior knowledge with observed data - C) Creating visualizations - D) Calculating traditional statistics

Short Answer Questions

Question 21

Explain why regression to the mean is necessary in player projections, and describe a situation where failing to regress would lead to a poor projection.

Your Answer:

Question 22

A projection system shows that Player A will average 22.5 PPG next season with a 90% prediction interval of [17.2, 27.8]. Explain what this interval means and how a team should use this information in decision-making.

Your Answer:

Question 23

Describe two advantages and two disadvantages of using similarity scores (comparables) for player projection compared to pure regression approaches.

Your Answer:

Question 24

A 32-year-old player has shown no decline in his statistics over the past two seasons. Explain why a projection system should still project some decline and what factors might explain his maintained performance.

Your Answer:

Question 25

You are tasked with projecting a player who has played internationally for three years before entering the NBA draft. Describe three challenges specific to this projection and how you would address each.

Your Answer:

Answer Key

Multiple Choice Answers

  1. C - Salary cap impact is not one of the four sub-problems; skill estimation, aging adjustment, context adjustment, and uncertainty quantification are the four components.

  2. B - Recent performance is more indicative of current skill levels due to potential improvement, decline, or changes in playing style.

  3. B - Regressed estimate = (0.40 * 100 + 0.35 * 200) / (100 + 200) = (40 + 70) / 300 = 110/300 = 36.7%

  4. B - The delta method tracks the same players across multiple seasons to measure within-player changes, avoiding cross-sectional confounds.

  5. A - Because poorly aging players exit the league, the remaining sample over-represents good agers, understating typical decline.

  6. C - Athletic attributes like speed, quickness, and leaping ability typically peak in the early-to-mid 20s.

  7. B - Using 5-15 comparables balances having enough data with maintaining similarity quality.

  8. B - Older players have more uncertain futures due to increased injury risk and potential for rapid decline.

  9. B - CARMELO is fundamentally built on finding similar historical players and using their career paths.

  10. B - Role and usage changes have the largest impact on statistical production when changing teams.

  11. A - This is the standard formula for the standard error of a proportion.

  12. B - When outcome distributions are asymmetric, the median is a more robust measure of central tendency.

  13. C - Prediction intervals include both model/parameter uncertainty and the inherent variability in individual outcomes.

  14. B - Statistics with fewer observations have more noise and thus require stronger regression to the mean.

  15. B - Walk-forward validation ensures that models are only trained on past data, mimicking real-world projection scenarios.

  16. B - RAPTOR incorporates player tracking data while CARMELO relies on traditional statistics.

  17. B - Declining playing time often signals underlying decline, creating a selection effect in the data.

  18. C - Injury recovery creates uncertainty and typically involves a ramp-up period with reduced performance.

  19. C - Year-over-year prediction is moderately reliable but far from perfect due to inherent variability.

  20. B - Bayesian approaches excel at systematically combining prior information with new observations.

Short Answer Rubric

Question 21 - Strong answers should explain that observed statistics include both true skill and random noise, that extreme observations tend to have more noise, and provide a concrete example (e.g., a player shooting 50% from three on 50 attempts would be poorly projected without regression).

Question 22 - Should explain that there's a 90% probability the actual value falls in this range, that the wide interval reflects substantial uncertainty, and teams should consider this range when making decisions rather than focusing solely on the point estimate.

Question 23 - Advantages might include: captures non-linear patterns, provides interpretable results, naturally incorporates multiple factors. Disadvantages might include: limited by historical data availability, may miss unique players, sensitive to feature selection.

Question 24 - Should note that aging is inevitable, maintained performance may reflect survivor bias in the question, random variation may mask gradual decline, and projection systems use population-level data that strongly indicates decline at this age.

Question 25 - Challenges include: different competition level, different statistical contexts, different playing styles. Solutions include: using translation coefficients for leagues, adjusting for pace/role differences, finding historical international-to-NBA comparables.