Chapter 9: Exercises

Section A: Game Score Calculations (Exercises 1-6)

Exercise 1: Basic Game Score

Calculate the Game Score for a player with the following box score: - Points: 28 - Field Goals Made: 10 - Field Goals Attempted: 18 - Free Throws Made: 6 - Free Throws Attempted: 8 - Offensive Rebounds: 1 - Defensive Rebounds: 5 - Assists: 7 - Steals: 2 - Blocks: 0 - Personal Fouls: 3 - Turnovers: 4

Exercise 2: Historic Game Analysis

LeBron James recorded the following statistics in a playoff game: - Points: 45 - FGM: 16, FGA: 27 - FTM: 10, FTA: 12 - ORB: 3, DRB: 9 - Assists: 12 - Steals: 1 - Blocks: 2 - Fouls: 2 - Turnovers: 3

Calculate his Game Score and classify the performance according to the interpretation table in the chapter.

Exercise 3: Comparing Performances

Two players have the following Game Scores across five games:

Player A: 22.5, 18.2, 25.1, 19.8, 21.3 Player B: 31.2, 8.5, 28.6, 12.1, 25.4

a) Calculate the mean Game Score for each player. b) Calculate the standard deviation for each player. c) Which player would you prefer and why? Discuss the trade-off between consistency and peak performance.

Exercise 4: Negative Game Score

A player has the following line: - Points: 2 - FGM: 1, FGA: 9 - FTM: 0, FTA: 2 - ORB: 0, DRB: 1 - Assists: 1 - Steals: 0 - Blocks: 0 - Fouls: 5 - Turnovers: 4

Calculate the Game Score. What does a negative Game Score indicate about a player's contribution?

Exercise 5: Component Analysis

For the Game Score formula, calculate how each component contributes to the total for a player with: 20 points, 8-15 FG, 2-3 FT, 2 ORB, 4 DRB, 5 AST, 1 STL, 1 BLK, 3 PF, 2 TOV.

Break down the contribution from: a) Scoring efficiency (points, FG made, FG attempted, missed FT) b) Rebounding (ORB, DRB) c) Playmaking and defense (AST, STL, BLK) d) Negatives (PF, TOV)

Exercise 6: Game Score Threshold Analysis

A team plays 82 regular season games. If a player achieves: - Game Score > 30: 8 times - Game Score 20-30: 35 times - Game Score 10-20: 30 times - Game Score < 10: 9 times

What is the player's season average Game Score, assuming the specific averages are 34, 24, 14, and 6 for each category? How would you classify this player's season?

Section B: Usage Rate (Exercises 7-12)

Exercise 7: Basic Usage Rate Calculation

A player has the following statistics: - Minutes: 34.0 - FGA: 18 - FTA: 6 - Turnovers: 3

The team totals are: - Team Minutes: 240 (5 players x 48 min) - Team FGA: 88 - Team FTA: 24 - Team TOV: 14

Calculate the player's Usage Rate.

Exercise 8: Comparing Usage Rates

Three players on the same team have these statistics (team totals: 240 MIN, 90 FGA, 25 FTA, 15 TOV):

a) Calculate each player's Usage Rate. b) What do the combined Usage Rates tell you about the team's offensive distribution? c) If the remaining two players (not shown) combine for the rest of the minutes and attempts, what is their combined Usage Rate?

Exercise 9: Usage and Efficiency Trade-off

Consider two players over a season:

a) Which player is more valuable? Justify your answer. b) If Player Y increased his usage to 28%, estimate what his TS% might become based on the typical usage-efficiency trade-off. c) At what Usage Rate would Player Y likely match Player X's scoring output per 36 minutes?

Exercise 10: Historical Usage Analysis

Russell Westbrook's 2016-17 MVP season had a 41.7% Usage Rate. If in a game: - Westbrook played 38 minutes - Team total minutes: 240 - Team FGA: 92, Team FTA: 28, Team TOV: 16

How many possessions did Westbrook use, and how many FGA, FTA, and TOV would you expect him to have (assuming his usage was at his season average)?

Exercise 11: Usage Rate Components

A player has USG% = 28.5% with the breakdown: - FGA contribution: 65% of usage - FTA contribution: 20% of usage - TOV contribution: 15% of usage

If the player reduced turnovers by 25% while maintaining the same FGA and FTA, what would the new Usage Rate be?

Exercise 12: Team Construction Analysis

You are constructing a starting lineup. Research suggests optimal team usage distribution is: - Primary scorer: 28-32% - Secondary scorer: 22-26% - Third option: 18-22% - Fourth option: 14-18% - Fifth option: 12-16%

If you have players with the following Usage Rates and True Shooting percentages, construct the optimal starting five:

Justify your selections considering both usage and efficiency.

Section C: Assist Metrics (Exercises 13-16)

Exercise 13: Assist Percentage Calculation

A point guard has these statistics: - Minutes: 32 - Assists: 9 - Field Goals Made: 5 - Team Minutes: 240 - Team Field Goals Made: 42

Calculate the player's Assist Percentage.

Exercise 14: Assist Ratio vs Assist Percentage

A player has: - AST: 6 - FGA: 12 - FTA: 4 - TOV: 2

a) Calculate the Assist Ratio. b) Why might Assist Ratio and Assist Percentage give different impressions of the same player?

Exercise 15: Point Guard Comparison

Compare these two point guards:

a) Calculate AST% for each player. b) Who is the better facilitator? Consider context in your answer.

Exercise 16: Historical Assist Leaders

John Stockton's 1990-91 season featured an AST% of approximately 50.7%. If he played 37 minutes per game and his team made 42 field goals per game (excluding his own 5.5 FGM), approximately how many assists per game did he average?

Section D: Rebounding Percentages (Exercises 17-21)

Exercise 17: Basic Rebounding Percentage

A center has: - Minutes: 30 - Offensive Rebounds: 4 - Defensive Rebounds: 8 - Team Minutes: 240 - Team ORB: 12, Team DRB: 35 - Opponent ORB: 10, Opponent DRB: 33

Calculate ORB%, DRB%, and TRB%.

Exercise 18: Positional Expectations

Three players have the following rebounding percentages:

Using the positional benchmarks discussed in the chapter, evaluate whether each player is above or below average for their position in rebounding.

Exercise 19: Dennis Rodman Analysis

Dennis Rodman's 1994-95 season featured approximately: - ORB%: 18.3% - DRB%: 28.4%

a) Calculate his TRB% assuming equal opportunities on both ends. b) How many standard deviations above average is his ORB%? (Assume league average ORB% is 5.5% with standard deviation 2.2%) c) What made Rodman exceptional according to these numbers?

Exercise 20: Rebound Rate Decomposition

A power forward has TRB% = 12.5%, with: - ORB% = 8.2% - DRB% = 18.1%

If the team gets 20% of available offensive rebounds and 75% of available defensive rebounds, what is this player's contribution to team rebounding on each end?

Exercise 21: Rebounding Impact Analysis

Two centers have the following season statistics:

a) Who is the better overall rebounder by percentage? b) If both played 36 minutes per game, estimate each player's rebounding output. c) Which player would be more valuable to a team that struggles with second-chance points against?

Section E: Defensive Percentages (Exercises 22-25)

Exercise 22: Steal Percentage

A guard has: - Minutes: 28 - Steals: 2 - Team Minutes: 240 - Opponent Possessions: 98

Calculate the player's Steal Percentage.

Exercise 23: Block Percentage

A center has: - Minutes: 26 - Blocks: 3 - Team Minutes: 240 - Opponent 2-Point FGA: 52

Calculate the player's Block Percentage.

Exercise 24: Defensive Specialist Analysis

An "elite defender" has these percentages: - STL%: 1.8% - BLK%: 0.5%

Using only these metrics, this player appears to be a below-average defender. Discuss at least three defensive contributions that would not be captured by these percentages and explain how this player might still be elite defensively.

Exercise 25: Rim Protection Analysis

Two centers have these statistics:

a) Based solely on BLK%, which is the better rim protector? b) Incorporating the additional data, reassess your answer. c) What does this exercise tell us about the limitations of box score metrics for defense?

Section F: Turnover Percentage (Exercises 26-28)

Exercise 26: Basic TOV% Calculation

A player has: - FGA: 15 - FTA: 6 - TOV: 3

Calculate the Turnover Percentage.

Exercise 27: Context Matters

Two players have identical TOV% of 14.5%:

Discuss why the same TOV% might be evaluated differently for these two players.

Exercise 28: Assist-to-Turnover Trade-off

A point guard is considering two playing styles: - Style 1: 8.5 AST, 3.2 TOV (conservative) - Style 2: 11.0 AST, 4.5 TOV (aggressive)

a) Calculate the assist-to-turnover ratio for each style. b) If each assist leads to approximately 2 points and each turnover costs approximately 1 point (in expected value), which style generates more value? c) What other factors might influence which style is preferable?

Section G: PER Calculations (Exercises 29-33)

Exercise 29: League Factors

Given the following league totals: - League FG: 98,500 - League FT: 52,300 - League AST: 56,800 - League PTS: 274,100 - League FGA: 210,500 - League FTA: 68,200 - League ORB: 25,600 - League TRB: 115,000 - League TOV: 36,200

Calculate: a) The factor b) VOP (Value of Possession) c) League DRB%

Exercise 30: Simplified PER Components

Without calculating full PER, rank these contributions from most positive to most negative: - 3 three-pointers made - 5 assists - 4 turnovers - 8 total rebounds (2 offensive, 6 defensive) - 4 personal fouls - 3 steals

Explain your reasoning using the PER formula components.

Exercise 31: PER Interpretation

Five players have these PER values: - Player A: 28.5 - Player B: 18.2 - Player C: 15.0 - Player D: 11.8 - Player E: 8.5

a) Classify each player using the interpretation table from the chapter. b) If these five players are the starting lineup for a team, what does this distribution suggest about the team?

Exercise 32: PER Decomposition

A player has PER = 22.5. Through analysis, you determine: - Scoring contribution: +8.2 - Rebounding contribution: +3.5 - Assist contribution: +4.1 - Turnover penalty: -2.8 - Other factors: +9.5

a) What percentage of this player's positive PER comes from scoring? b) What percentage comes from turnovers (negative)? c) What might the "other factors" include?

Exercise 33: PER Limitations in Practice

Player X has PER = 19.5 with high usage (28%) Player Y has PER = 16.8 with low usage (15%)

Both play on the same team. If Player Y's role expanded to 25% usage, would you expect their PER to: a) Increase b) Stay the same c) Decrease

Explain your reasoning.

Section H: Player Impact Estimate (Exercises 34-36)

Exercise 34: PIE Calculation

A player has these statistics: - PTS: 22, FGM: 8, FGA: 16, FTM: 5, FTA: 6 - ORB: 1, DRB: 4, AST: 5, STL: 2, BLK: 0 - PF: 3, TOV: 2

The game totals (both teams combined) are: - PTS: 215, FGM: 82, FGA: 175, FTM: 42, FTA: 54 - ORB: 22, DRB: 88, AST: 52, STL: 16, BLK: 10 - PF: 44, TOV: 28

Calculate the player's PIE.

Exercise 35: PIE vs PER Comparison

Explain a scenario where a player might have: a) High PER but low PIE b) Low PER but high PIE

What does this discrepancy tell us about the metrics?

Exercise 36: Team PIE Distribution

In a game, the five starters on Team A had these PIE values: 18.5, 14.2, 11.8, 9.5, 7.2

a) What is the total PIE for the starting five? b) If the bench contributed a combined PIE of 8.8, what was Team A's total PIE? c) What does this suggest about how the game likely went for Team A?

Section I: Comprehensive Problems (Exercises 37-40)

Exercise 37: Complete Player Profile

Create a complete statistical profile for a player with these box score totals over 50 games: - Minutes: 1,650 - Points: 1,150 - FGM: 420, FGA: 890 - 3PM: 85, 3PA: 220 - FTM: 225, FTA: 280 - ORB: 45, DRB: 195 - AST: 185 - STL: 62 - BLK: 28 - PF: 115 - TOV: 135

Team totals for same 50 games: - Minutes: 12,000 - FGM: 2,050, FGA: 4,250 - FTM: 950, FTA: 1,180 - ORB: 550, DRB: 1,680 - AST: 1,250 - TOV: 720

Opponent totals: - ORB: 520, DRB: 1,580 - 2PA: 3,200 - Possessions: 5,100

Calculate: a) Game Score average (per game) b) Usage Rate c) Assist Percentage d) All three rebounding percentages e) Steal Percentage f) Block Percentage g) Turnover Percentage

Then provide a comprehensive evaluation of this player's strengths and weaknesses.

Exercise 38: Metric Disagreement

Two players have the following metrics:

a) Which metrics favor which player? b) Construct an argument for why Alpha is better. c) Construct an argument for why Beta is better. d) What additional information would you want to settle the debate?

Exercise 39: Building a Metric

Design a simplified composite metric for role players (low-usage players). Your metric should: - Not heavily penalize low scoring - Reward efficiency - Value defensive contributions appropriately - Be calculable from standard box scores

a) Write out your formula with coefficients. b) Justify each coefficient choice. c) Identify two limitations of your metric. d) Calculate your metric for a player with: 6 PPG on 4-8 FG, 1-2 FT, 1 ORB, 4 DRB, 2 AST, 1.5 STL, 0.5 BLK, 1 TOV, 2 PF in 22 MPG.

Exercise 40: Era Comparison

You want to compare players across eras using box score metrics. Consider: - Player from 1985: 25.0 PPG, 6.0 RPG, 5.0 APG, no three-pointers (league average pace: 102) - Player from 2020: 25.0 PPG, 6.0 RPG, 5.0 APG, 2.5 3PM/game (league average pace: 100)

a) How would pace differences affect raw PER comparisons? b) How does the three-point revolution affect PER comparisons? c) Design a methodology to make the comparison more fair. d) What limitations would remain even after your adjustments?

Answer Key Hints

Detailed solutions are available in the instructor's manual. Key calculation results:

• Exercise 1: Game Score = 21.7
• Exercise 7: Usage Rate = approximately 29.0%
• Exercise 13: Assist Percentage = approximately 30.5%
• Exercise 17: ORB% = approximately 15.6%, DRB% = approximately 21.2%
• Exercise 22: Steal Percentage = approximately 1.75%
• Exercise 26: Turnover Percentage = approximately 14.5%
• Exercise 34: PIE = approximately 12.3%