Chapter 22: Player Performance Prediction - Exercises

Section A: Foundational Concepts (Questions 1-8)

Exercise 1: Understanding Projection Components

Explain the four sub-problems involved in player projection as outlined in the chapter. For each sub-problem, provide: a) A clear definition b) An example of how it applies to projecting a 27-year-old point guard c) One challenge specific to that sub-problem

Exercise 2: Historical Performance Weighting

A player has the following True Shooting percentages over the past three seasons: - Season 1 (oldest): 54.2% - Season 2: 56.8% - Season 3 (most recent): 59.1%

Using Marcel-style weighting (5/4/3 for most recent to oldest): a) Calculate the weighted average TS% b) Explain why more recent seasons receive higher weights c) Discuss a scenario where this weighting approach might be problematic

Exercise 3: Sample Size and Reliability

For a player who has taken 200 three-point attempts at a 38% rate: a) Calculate the standard error of the observed percentage b) Construct a 95% confidence interval for the player's true three-point percentage c) Explain what this confidence interval tells us about projection uncertainty

Exercise 4: Regression to the Mean

A rookie shoots 44% from three on 150 attempts in his first season. The league average is 36%. a) Using a prior weight equivalent to 300 league-average attempts, calculate the regressed estimate b) Explain why regression to the mean is particularly important for rookies c) How would your approach change for a 10-year veteran with the same statistics?

Exercise 5: Mean vs. Median Projections

Explain the difference between mean and median projections. Why might a team prefer one over the other when: a) Evaluating a potential max contract free agent b) Assessing late second-round draft picks c) Making in-season trade decisions

Exercise 6: Projection Horizon

Discuss how projection accuracy typically changes as the projection horizon increases. Specifically: a) Compare 1-year vs. 5-year projection accuracy b) Identify which player characteristics are easier vs. harder to project over longer horizons c) Explain how uncertainty should be represented in long-term projections

Exercise 7: Context Adjustment Basics

A player averaged 18.5 PPG on a team that played at the 5th-fastest pace in the league. The league average pace was 100 possessions per game, and his team averaged 105 possessions. a) Calculate his approximate points per 100 possessions b) Explain why pace adjustment is important for player comparison c) Identify two other contextual factors that should be considered in projections

Exercise 8: Projection System Comparison

Compare and contrast the CARMELO and RAPTOR projection systems: a) What are the key methodological differences? b) What are the strengths and weaknesses of each approach? c) Under what circumstances might one system outperform the other?

Section B: Aging Curves (Questions 9-16)

Exercise 9: Basic Aging Curve Interpretation

Using the following hypothetical aging curve data for points per 100 possessions:

a) At what age does the typical player peak in scoring? b) Project the scoring rate for a 24-year-old currently at 22.0 pts/100 through age 28 c) What limitations does this simple aging curve have?

Exercise 10: Delta Method Analysis

Design a study using the delta method to create an aging curve for assist rate: a) What data would you need to collect? b) How would you handle players who change teams? c) What are the selection bias concerns, and how would you address them?

Exercise 11: Survivorship Bias in Aging Curves

Explain why survivorship bias is a major concern in aging curve analysis: a) Provide a specific example of how survivorship bias could distort an aging curve b) Describe two methods for addressing survivorship bias c) How might survivorship bias differ between stars and role players?

Exercise 12: Skill-Specific Aging

Different basketball skills age differently. For each of the following skills, hypothesize the typical aging pattern and explain your reasoning: a) Three-point shooting percentage b) Defensive rating c) Assist-to-turnover ratio d) Rebounds per 100 possessions e) Free throw rate

Exercise 13: Position-Specific Aging

Compare aging curves for point guards vs. centers: a) Which position typically peaks earlier? Why? b) Which position typically has a longer career? Why? c) How should these differences inform projection systems?

Exercise 14: Injury Impact on Aging

A 28-year-old player misses an entire season due to ACL reconstruction: a) How should his projection differ from a similar player who didn't miss time? b) What historical data would you examine to inform this adjustment? c) How long might the injury impact persist in projections?

Exercise 15: Nonlinear Aging Effects

Explain why polynomial regression might be preferred over linear regression for modeling aging: a) What patterns can polynomial models capture that linear models cannot? b) What are the risks of using high-degree polynomials? c) Suggest an appropriate polynomial degree for aging curves and justify your choice

Exercise 16: Modern Era Aging Adjustments

Discuss how aging curves might differ in the modern NBA compared to historical data: a) What factors might cause players to peak later? b) What factors might accelerate decline? c) How should projection systems account for these changes?

Section C: Similarity Scores and Comparables (Questions 17-22)

Exercise 17: Euclidean Distance Calculation

Calculate the Euclidean distance between the following two players across five normalized statistics:

Player A: [0.8, -0.5, 1.2, 0.3, -0.2] Player B: [0.6, -0.3, 0.9, 0.5, 0.1]

a) Show your calculation b) What does this distance value tell us? c) How would you interpret a distance of 0.5 vs. 2.0?

Exercise 18: Feature Selection for Similarity

Design a similarity system for projecting young big men: a) Select 8-10 features you would include and justify each choice b) How would you weight these features? c) What features would you explicitly exclude and why?

Exercise 19: Comparable Selection

For a 22-year-old guard averaging 16 PPG, 4 RPG, 6 APG with a 54% TS%: a) List five criteria for selecting valid comparables b) How many comparables should be used and why? c) How would you weight comparables by similarity score?

Exercise 20: Similarity System Limitations

Discuss three major limitations of similarity-based projection systems: a) Describe each limitation b) Provide a specific example of how each could lead to projection errors c) Suggest a potential solution or mitigation for each

Exercise 21: Era Adjustment in Comparables

A current player's best comparable is a player from 1995: a) What statistical adjustments might be necessary? b) How would you account for changes in playing style? c) Should era-distant comparables be weighted differently?

Exercise 22: Dynamic Similarity

Design a system that updates similarity scores as new data becomes available: a) How often should comparables be re-evaluated? b) What changes should trigger a re-calculation? c) How would you balance stability with responsiveness?

Section D: Projection Model Building (Questions 23-30)

Exercise 23: Feature Engineering

For a projection model predicting next-season Box Plus/Minus, create five engineered features from basic box score statistics: a) Define each feature mathematically b) Explain the basketball rationale for each c) Discuss potential multicollinearity concerns

Exercise 24: Model Selection

Compare the following approaches for player projection: a) Linear regression with regularization b) Random forest c) Gradient boosting d) Neural networks

For each, discuss: interpretability, handling of non-linear relationships, overfitting risk, and data requirements.

Exercise 25: Cross-Validation Design

Design a cross-validation scheme for a projection model: a) Why is standard k-fold cross-validation problematic for time-series data? b) Describe a walk-forward validation approach c) How would you handle players who span multiple validation folds?

Exercise 26: Incorporating Prior Information

Design a Bayesian projection model for three-point shooting: a) What prior distribution would you use for a rookie? Justify your choice. b) How would the prior differ for a veteran with 5000 career three-point attempts? c) Write the equation for the posterior mean estimate.

Exercise 27: Multi-Year Projections

Extend a single-year projection model to provide 3-year projections: a) How do aging curves integrate into multi-year projections? b) How should uncertainty compound over multiple years? c) Design an output format that communicates multi-year projections effectively

Exercise 28: Handling Missing Data

Your projection model requires tracking data, but a player has only played for teams without tracking systems for 2 of his 5 seasons: a) What are your options for handling the missing data? b) What are the tradeoffs of each approach? c) How would you validate your chosen approach?

Exercise 29: Model Calibration

Your projection model produces win probability estimates. Design a calibration analysis: a) What is calibration and why does it matter? b) Describe how you would create a calibration plot c) How would you quantify calibration error?

Exercise 30: Ensemble Projections

Design an ensemble that combines three different projection systems: a) What are the benefits of ensembling? b) How would you determine optimal weights for each component? c) When might an ensemble perform worse than individual models?

Section E: Uncertainty Quantification (Questions 31-35)

Exercise 31: Confidence vs. Prediction Intervals

Explain the difference between confidence intervals and prediction intervals in the context of player projections: a) Define each type of interval b) Which is more appropriate for projecting a specific player's next season? Why? c) Calculate both intervals (showing formulas) for a projection with mean 5.0 BPM, model standard error 0.5, and residual standard deviation 2.0

Exercise 32: Asymmetric Uncertainty

Player projections often have asymmetric uncertainty (more downside than upside, or vice versa): a) Why might a projection for a 35-year-old veteran have asymmetric uncertainty? b) How would you model and communicate asymmetric uncertainty? c) Design a visualization that effectively shows asymmetric projection ranges

Exercise 33: Scenario Analysis

For a young player with significant upside but injury concerns: a) Define three scenarios (pessimistic, baseline, optimistic) with specific criteria b) Assign probabilities to each scenario c) Calculate the expected value and explain how it differs from the baseline projection

Exercise 34: Monte Carlo Projection

Design a Monte Carlo simulation for projecting a player's 5-year career trajectory: a) What random variables would you simulate? b) How would you model correlations between variables? c) What outputs would you report from the simulation?

Exercise 35: Communicating Uncertainty

You need to present player projections to a non-technical audience (team owner): a) How would you visualize uncertainty in projections? b) What language would you use to describe uncertainty levels? c) What common misunderstandings about uncertainty should you address?

Section F: Applied Projection Problems (Questions 36-40)

Exercise 36: Free Agent Evaluation

A 28-year-old wing is available as a free agent. His last three seasons of VORP were: 2.8, 3.5, 4.1. a) Develop a 4-year projection for his value b) Incorporate aging curves and uncertainty c) Recommend a contract structure based on your projection

Exercise 37: Trade Analysis

Team A is considering trading a 24-year-old prospect (current VORP: 1.5) for a 30-year-old established player (current VORP: 4.0). a) Project the next 5 years of value for each player b) Account for uncertainty in your analysis c) Provide a recommendation with appropriate caveats

Exercise 38: Draft Projection

A college junior point guard has the following profile: - Age: 21 - PPG: 18.5 - APG: 6.2 - 3P%: 38.5% - FT%: 82.0% - Conference: Power 5

a) Identify appropriate NBA comparables b) Project his first three NBA seasons c) Quantify your uncertainty and explain the main sources

Exercise 39: Injury Recovery Projection

A player who averaged 25 PPG and 5.0 BPM before an Achilles injury is returning after missing a full season. He is 29 years old. a) Project his first season back b) Project his second season back c) Compare to his pre-injury baseline with uncertainty ranges

Exercise 40: System-Specific Projection

A player is being traded from a slow-paced, isolation-heavy team to a fast-paced, motion-offense team: a) What aspects of his statistical profile are most likely to change? b) How would you adjust his projection for the new context? c) What historical examples would inform your adjustments?

Answer Key Guidance

For exercises involving calculations, students should show all work. For conceptual questions, responses should demonstrate understanding of the underlying principles discussed in Chapter 22 and apply them appropriately to novel situations.

Instructors may wish to assign subsets of exercises based on course focus: - Foundational concepts: Exercises 1-8 - Aging curves: Exercises 9-16 - Similarity methods: Exercises 17-22 - Model building: Exercises 23-30 - Uncertainty: Exercises 31-35 - Applications: Exercises 36-40