Chapter 23: Draft Modeling and Prospect Evaluation - Exercises

Section A: Statistical Translation Fundamentals (Questions 1-8)

Exercise 1: Per-Possession Translation

A college player averaged the following on a team that used 72 possessions per game: - 18.5 PPG - 7.2 RPG - 3.1 APG

a) Convert these statistics to per-100-possessions rates b) If the NBA averages 100 possessions per game, estimate his raw statistical output c) Apply the standard translation coefficients from Chapter 23 to project NBA statistics

Exercise 2: Usage-Efficiency Tradeoff

Two prospects have the following college statistics: - Player A: 22.5 PPG, 58.0% TS, 32% USG - Player B: 15.8 PPG, 62.5% TS, 22% USG

a) Using the usage-efficiency adjustment formula (beta = 0.012), adjust both players to a 25% usage rate b) Which player projects as more efficient at similar usage levels? c) What are the limitations of this adjustment?

Exercise 3: Conference Strength Adjustment

A forward from the Mountain West averaged 19.2 pts/100 possessions. A similar forward from the Big Ten averaged 16.8 pts/100 possessions.

a) Using conference adjustment factors (MW: 0.91, Big Ten: 1.08), calculate adjusted statistics b) Which player has the better conference-adjusted production? c) What factors might make individual conference adjustments imprecise?

Exercise 4: Free Throw Translation

Explain why free throw percentage is the most stable translation statistic from college to NBA. Calculate the 95% confidence interval for a prospect who shot: a) 82.5% on 200 attempts b) 75.0% on 80 attempts c) Which prospect's shooting translates with more certainty?

Exercise 5: Translation Coefficient Derivation

Describe the methodology for deriving translation coefficients: a) What data would you need to collect? b) What statistical method would you use? c) How would you account for playing time differences between college and NBA? d) What time period provides the best training data?

Exercise 6: Pace Normalization

Team A plays at 75 possessions per game. Team B plays at 65 possessions per game. A player on Team A averages 16 PPG. A player on Team B averages 14 PPG.

a) Calculate per-100-possession scoring rates b) Calculate per-40-minute scoring rates (assuming 35 MPG for each) c) Discuss when each normalization is most appropriate

Exercise 7: Competition Quality

A player scored 22.4 PPG overall but had split performance: - vs. Top 25 teams: 17.8 PPG (8 games) - vs. Unranked teams: 24.1 PPG (25 games)

a) Calculate a competition-quality-weighted average b) How does this affect his NBA projection? c) What is the minimum sample size against ranked teams to make this adjustment reliable?

Exercise 8: International Translation

A EuroLeague prospect (age 20, rotation player) averaged per 40 minutes: - 14.5 points, 6.2 rebounds, 2.8 assists, 56% TS

Using international translation factors, project his: a) First-year NBA per-40-minute production b) Adjusted for age (youth bonus) c) 90% confidence interval on points per 40

Section B: Physical Measurements and Combine Data (Questions 9-15)

Exercise 9: Wingspan Ratio Calculation

Calculate the wingspan-to-height ratio for the following prospects and classify their defensive projection:

Exercise 10: Athletic Composite Score

Design an athletic composite score for a point guard prospect with: - Max vertical: 38" - Lane agility: 10.8 seconds - Three-quarter sprint: 3.15 seconds

a) Normalize each measurement to a percentile (assume average PG values: vert 36", agility 11.2s, sprint 3.25s) b) Calculate a position-weighted composite using the weights in Chapter 23 c) Interpret the resulting score

Exercise 11: Reach Advantage

Two centers have identical height (6'11") but different measurements: - Center A: Wingspan 7'4", Standing reach 9'5" - Center B: Wingspan 7'0", Standing reach 9'1"

a) Calculate the reach advantage for Center A b) How does this translate to rim protection expectations? c) What other factors affect rim protection beyond reach?

Exercise 12: Frame Assessment

A 19-year-old prospect is 6'7", 195 lbs with a narrow frame. His comparables at similar age/frame were: - Player X: Added 25 lbs of muscle by age 23 - Player Y: Added 15 lbs by age 23 - Player Z: Added 30 lbs by age 23

a) What weight projection would you use? b) How does frame potential affect position projections? c) What risks come with projecting physical development?

Exercise 13: Combine Performance Analysis

Compare two shooting guards at the combine:

a) Calculate composite athletic scores for each b) Which prospect has the better physical profile overall? c) How might their different profiles affect NBA roles?

Exercise 14: Position Thresholds

A tweener prospect measures 6'6" with a 6'9" wingspan. He played small forward in college. a) Does he meet typical physical thresholds for NBA small forwards? b) What about shooting guard? c) How should position flexibility (or lack thereof) affect his draft value?

Exercise 15: Measurement Reliability

Discuss the reliability of different combine measurements: a) Rank the following by test-retest reliability: height, wingspan, vertical, agility, sprint b) How should measurement reliability affect weighting in prospect evaluation? c) What non-combine physical assessments might teams use?

Section C: Draft Value and Probability Modeling (Questions 16-22)

Exercise 16: Pick Value Calculation

Using the exponential decay model for pick value:

Expected WS = 45.2 × e^(-0.065 × Pick) + 12.8

a) Calculate expected career Win Shares for picks 1, 5, 10, 20, 30, and 45 b) Calculate the relative value of each pick compared to #1 c) Plot the pick value curve

Exercise 17: Bust Probability

Calculate bust probability for a prospect with: - Draft position: Pick 8 - Age: 22 - FT%: 68% - Wingspan ratio: 0.99 - Conference strength: 0.82

Using the factors from Chapter 23, calculate: a) Base bust rate for pick range b) Risk multiplier from each factor c) Final bust probability

Exercise 18: Value Over Replacement Pick

A team projects Prospect A to produce 35 career Win Shares (90% CI: 18-52) with pick #12. The expected value at pick #12 is 28 Win Shares.

a) Calculate the expected value over replacement pick (VORP) b) What is the probability Prospect A exceeds expectations? c) Should the team draft Prospect A or trade down?

Exercise 19: Variance by Draft Position

The variance of outcomes differs by draft position. Given: - Picks 1-5: SD = 18.5 WS - Picks 6-10: SD = 21.2 WS - Picks 11-20: SD = 19.8 WS

a) Why might picks 6-10 have higher variance than 1-5? b) How should variance affect draft strategy for teams at different positions? c) Calculate the probability of getting an All-Star (defined as 50+ career WS) at pick 3 vs. pick 8

Exercise 20: Position-Specific Draft Value

Apply position multipliers to expected value calculations:

A team has the 15th pick and is choosing between: - Point guard: Model projects 32 career WS - Center: Model projects 36 career WS

Using position multipliers (PG: 1.05, C: 0.90): a) Calculate position-adjusted projections b) Which prospect has higher expected value? c) How should position scarcity affect this decision?

Exercise 21: All-Star Probability Model

A prospect has the following characteristics: - Projected career WS: 55 - Age at draft: 19 - Conference: Big 12 - College production: 18 PPG, 7 RPG, 3 APG

Using the All-Star probability framework: a) Estimate base probability from Win Shares projection b) Apply age and production adjustments c) Final All-Star probability estimate

Exercise 22: Draft Trade Evaluation

Team A has pick #7 (relative value: 0.49) Team B offers picks #15 (0.28) and #22 (0.18)

a) Calculate total value offered by Team B b) What additional asset would make this trade fair? c) How does team situation affect this analysis?

Section D: Building Draft Models (Questions 23-30)

Exercise 23: Feature Selection

You are building a draft projection model. From the following features, select the 10 most predictive and justify: - Points per 100 possessions - Rebounds per 100 possessions - Assists per 100 possessions - True shooting percentage - Free throw percentage - Age at draft - Conference strength - Height (no shoes) - Wingspan - Max vertical - Lane agility - College wins - Tournament success - AAU ranking

Exercise 24: Target Variable Selection

Compare different target variables for draft modeling: a) Career Win Shares b) Peak season Win Shares c) Binary: Made All-Star (yes/no) d) Years as NBA starter

Discuss the advantages and disadvantages of each for model training.

Exercise 25: Model Architecture

Design a complete draft model architecture: a) Data preprocessing steps b) Feature engineering pipeline c) Model selection (justify your choice) d) Validation strategy e) Output format

Exercise 26: Class Imbalance

In draft modeling, most players "bust" relative to their pick. For picks 1-10: - ~25% become All-Stars - ~40% become quality starters - ~35% are "busts"

a) How does this imbalance affect model training? b) What techniques address class imbalance? c) Should different models predict different outcomes?

Exercise 27: Temporal Validation

Design a validation scheme for a draft model: a) Why can't we use standard cross-validation? b) Describe a walk-forward validation approach for draft classes c) How many years of test data do we need? d) How do we handle recent drafts with incomplete career data?

Exercise 28: Model Interpretation

Your draft model produces the following feature importances: 1. Age at draft: 0.18 2. Points per 100: 0.15 3. Conference strength: 0.12 4. Free throw %: 0.10 5. Wingspan ratio: 0.09

a) Interpret these importances in basketball terms b) What features are surprisingly important or unimportant? c) How would you explain these to a basketball operations executive?

Exercise 29: Ensemble Methods

Design an ensemble for draft projection combining: - Gradient boosting regressor (career WS) - Random forest classifier (bust probability) - Neural network (similarity-based)

a) How would you combine outputs from different model types? b) What weights would you assign to each model? c) How do you validate the ensemble vs. individual models?

Exercise 30: Model Updating

Your draft model was trained on data from 2005-2020. It's now 2025. a) What has changed in basketball that might affect model validity? b) How would you update the model? c) How do you balance recency with sample size?

Section E: International and One-and-Done Evaluation (Questions 31-36)

Exercise 31: International League Ranking

Rank the following leagues by NBA translation quality and justify: a) EuroLeague b) Spanish ACB c) Australian NBL d) Chinese CBA e) French Pro A

Exercise 32: International Statistical Translation

A 19-year-old EuroLeague prospect averages per 40 minutes: - Points: 18.2 - Rebounds: 7.5 - Assists: 2.8 - True Shooting: 58%

Project his: a) Year 1 NBA statistics (per 40 minutes) b) Year 3 NBA statistics c) Career Win Shares probability distribution

Exercise 33: One-and-Done Analysis

A one-and-done prospect played only 25 college games. His statistics: - 16.8 PPG, 4.2 RPG, 2.1 APG - 54% TS, 72% FT - Top-5 recruit out of high school

a) What additional information should heavily influence his projection? b) How should recruiting rankings be weighted? c) Compare projection confidence to a junior with similar statistics

Exercise 34: International Scouting Integration

For international prospects, scouts provide qualitative assessments. How would you integrate: a) "Elite basketball IQ, reads the game two passes ahead" b) "Questionable motor, effort inconsistent" c) "Thrives in structured offense, struggles in ISO situations"

Into a quantitative model?

Exercise 35: Age Adjustment for International Prospects

Two international prospects: - Player A: Age 19, averaging 10 PPG in EuroLeague - Player B: Age 23, averaging 16 PPG in EuroLeague

a) Apply age adjustments to compare their NBA projections b) Which has higher upside? Which has higher floor? c) How does age affect the projection confidence interval?

Exercise 36: Draft-and-Stash Evaluation

A team is considering drafting a 20-year-old international prospect with pick #28 and leaving him overseas for 2-3 years.

a) How should the stash timeline affect the player's draft value? b) What player characteristics make good stash candidates? c) Model the expected value vs. a player who contributes immediately

Section F: Applied Draft Analysis (Questions 37-40)

Exercise 37: Mock Draft Construction

Given projections for 8 prospects, construct a rational draft order:

a) Rank prospects by expected value b) Rank prospects by risk-adjusted value c) How might team-specific needs change this ranking?

Exercise 38: Trade-Up Analysis

Your team has pick #14. You identify a prospect you project at 45 WS who will be available at #14, but your preferred prospect (projected 65 WS) requires trading up to #6.

Team at #6 is asking for picks #14, #22, and a future first (estimated value: pick #20).

a) Calculate total value being traded away b) Calculate expected value gained c) What probability of success would justify this trade?

Exercise 39: Backtesting Exercise

Using historical data from a previous draft class: a) Build a simple draft model using available features b) Generate projections for that class c) Compare projections to actual outcomes d) Calculate model performance metrics (RMSE, correlation, bust prediction accuracy)

Exercise 40: Draft Report Writing

Select a prospect (real or hypothetical) and write a complete draft report including: a) Statistical analysis with translations b) Physical profile assessment c) Comparable players d) Projection with confidence intervals e) Recommended draft range f) Risk factors and upside scenarios

Answer Key Guidelines

For quantitative exercises, show all calculations and state assumptions. For qualitative exercises, demonstrate understanding of concepts and appropriate basketball context.

Instructors may assign specific sections based on course focus: - Statistical translation: Exercises 1-8 - Physical evaluation: Exercises 9-15 - Probability modeling: Exercises 16-22 - Model building: Exercises 23-30 - International: Exercises 31-36 - Applications: Exercises 37-40