Chapter 6 Exercises: Box Score Fundamentals

Instructions

Complete the following exercises to reinforce your understanding of box score statistics. Exercises are organized by difficulty level:

• ★ Basic understanding and calculation
• ★★ Application and interpretation
• ★★★ Analysis and synthesis
• ★★★★ Advanced problem-solving and research

Show all work for calculation problems. For analysis questions, support your conclusions with specific data points or logical reasoning.

Section A: Points and Scoring (Exercises 1-7)

Exercise 1 ★

Point Calculation

Calculate the total points for each player based on their shooting statistics:

Exercise 2 ★

Scoring Distribution

A player scores 32 points on the following: - 9-16 from two-point range - 3-8 from three-point range - 5-6 from the free throw line

a) Verify the point total is correct. b) What percentage of points came from each scoring type (2PT, 3PT, FT)? c) What is the player's overall field goal percentage?

Exercise 3 ★★

Era Comparison

Consider these two scoring performances:

1985 (no three-point emphasis): Player X: 28 PPG, 10.5 FGA, 4.2 FTA

2023 (three-point era): Player Y: 28 PPG, 18.3 FGA, 5.1 FTA

a) What does the difference in field goal attempts suggest about how each player scored? b) Calculate points per field goal attempt for each player. c) Discuss why comparing these raw PPG numbers may be misleading.

Exercise 4 ★★

Scoring Efficiency Trade-offs

A team's leading scorer averages 25 PPG on 20 FGA. The team is considering a trade for a player who averages 22 PPG on 15 FGA.

a) Calculate points per attempt for each player. b) If the new player takes the same 20 FGA as the current scorer, how many points would you project (assuming linear scaling)? c) Discuss at least two reasons why this linear projection might be inaccurate.

Exercise 5 ★★★

Historical Scoring Context

Research the following and answer:

a) Wilt Chamberlain averaged 50.4 PPG in 1961-62. The league average was 118.8 PPG per team. What percentage of his team's points did Wilt score (assuming 48 minutes of an approximately 48.5 minute average game)?

b) James Harden averaged 36.1 PPG in 2018-19. The league average was 111.2 PPG per team. Calculate the same percentage.

c) Discuss why comparing raw PPG across these eras is problematic.

Exercise 6 ★★★

Team Scoring Balance

Analyze the following championship team's scoring distribution:

a) Calculate points per minute for each player. b) Calculate points per attempt for each player. c) Which player appears most efficient? Why might this be misleading? d) Discuss how role affects these comparisons.

Exercise 7 ★★★★

Scoring Load Analysis

Design a metric that accounts for both scoring volume and efficiency, then apply it to these hypothetical players:

a) Create a formula that combines volume and efficiency. b) Apply your formula to rank these players. c) Justify your weighting choices. d) Discuss limitations of your metric.

Section B: Rebounds (Exercises 8-13)

Exercise 8 ★

Rebound Totals

Calculate total rebounds and offensive rebound percentage for each player:

Exercise 9 ★★

Rebounding Rate

A center plays 34 minutes in a game where his team played 240 total minutes. Team rebounds were 48 (12 OREB, 36 DREB). Opponent rebounds were 44 (10 OREB, 34 DREB). The center grabbed 3 OREB and 9 DREB.

a) Calculate the center's OREB%. b) Calculate the center's DREB%. c) Calculate the center's TRB%.

Exercise 10 ★★

Context-Dependent Rebounding

Two centers have identical rebounding numbers:

Center A: 11.2 RPG, 3.2 OREB, 8.0 DREB - Team pace: 104.2 possessions/game - Team 3PA: 38.4 per game

Center B: 11.2 RPG, 3.2 OREB, 8.0 DREB - Team pace: 96.8 possessions/game - Team 3PA: 24.1 per game

a) Which center likely has more rebounding opportunities? Why? b) How does three-point shooting affect rebounding patterns? c) Which center's rebounding numbers are more impressive in context?

Exercise 11 ★★★

Dennis Rodman Analysis

Dennis Rodman's 1995-96 season with the Bulls: - 14.9 RPG (5.4 OREB, 9.5 DREB) - 32.6 MPG - Team pace: 91.2 - Team total rebounds: 44.8 per game

a) Calculate Rodman's rebounding rate per minute. b) Calculate his per-36 minute rebounding. c) Estimate what percentage of his team's rebounds he secured. d) Research: What was his TRB% that season, and why is it historically significant?

Exercise 12 ★★★

Uncontested Rebound Problem

A point guard averages 8.1 RPG. Video analysis reveals: - 0.3 OREB per game (all contested) - 7.8 DREB per game (6.2 uncontested, 1.6 contested)

a) What does this distribution suggest about the point guard's rebounding value? b) How might team strategy inflate these numbers? c) Design a metric that accounts for contested vs. uncontested rebounds.

Exercise 13 ★★★★

Team Rebounding Optimization

A team's rebounding breakdown by position:

Team total: 6.1 OREB, 21.4 DREB

a) Analyze the contested percentage by position. What patterns emerge? b) The PG has unusually high DREB for the position. What strategy might explain this? c) If the team wanted to improve offensive rebounding, which position should they target in free agency? Justify your answer. d) Design a "Rebounding Value" metric that weights offensive rebounds, defensive rebounds, and contested percentage.

Section C: Assists and Playmaking (Exercises 14-19)

Exercise 14 ★

Assist-to-Turnover Ratio

Calculate the AST/TO ratio for each player:

Exercise 15 ★★

Assist Quality

Two point guards have similar assist numbers:

PG Alpha: 9.2 APG - Assists leading to 3-pointers: 3.8 - Assists leading to layups/dunks: 4.2 - Assists leading to mid-range shots: 1.2

PG Beta: 9.4 APG - Assists leading to 3-pointers: 2.1 - Assists leading to layups/dunks: 3.4 - Assists leading to mid-range shots: 3.9

a) Calculate expected points generated from assists for each PG (assume 35% on 3PT, 65% on layups/dunks, 42% on mid-range). b) Which PG creates more valuable scoring opportunities? c) What does this reveal about assist totals alone?

Exercise 16 ★★

Home Scorer Bias

A study found that a player averaged: - 8.4 APG at home - 7.1 APG on the road - Similar minutes and usage in both situations

a) What is the percentage difference in assists? b) What might explain this difference beyond actual performance? c) How should analysts account for this bias?

Exercise 17 ★★★

Potential Assists

A point guard's passing data:

a) What is the "conversion rate" (assists / potential assists)? b) How many expected points does this PG create through passing? (Estimate using typical shot values.) c) Compare to a PG with 10.1 APG but only 13.2 potential assists. Who creates more opportunities?

Exercise 18 ★★★

Assist Context

Analyze these two playmaking profiles:

Player X (Pick-and-Roll Heavy Team): - 11.2 APG, 3.4 TOV - 42% of assists to rolling bigs - 31% of assists to spot-up shooters - Average assist distance: 8.2 feet

Player Y (Motion Offense Team): - 7.8 APG, 1.9 TOV - 18% of assists to rolling bigs - 52% of assists to cutters - Average assist distance: 12.4 feet

a) Calculate AST/TO for each player. b) Discuss how system affects assist accumulation. c) Which player might be harder to replace? Why?

Exercise 19 ★★★★

Creating an Assist Value Metric

Design a comprehensive "Assist Value" metric that accounts for: - Raw assists - Assist-to-turnover ratio - Points generated from assists - Potential assists (opportunity creation) - Assist type (rim vs. 3PT vs. mid-range)

a) Write out your formula with clear variable definitions. b) Apply it to two historical point guards using available data. c) Discuss how your metric might change player rankings compared to raw assists. d) Identify at least three limitations of your metric.

Section D: Steals and Blocks (Exercises 20-25)

Exercise 20 ★

Defensive Counting Stats

Calculate stocks (steals + blocks) per game for each player:

Exercise 21 ★★

Steal Rate Analysis

A guard averages 2.3 SPG with the following context: - Team defensive rating: 114.2 (league average: 110.8) - Team steals per game: 7.2 (league average: 7.8) - Opponent turnover rate when guarded by this player: 18.2% - Opponent turnover rate overall against team: 13.1%

a) Is this player's team defense above or below average? b) What might explain the individual success despite team struggles? c) Discuss whether this player's steals help or hurt the team defense.

Exercise 22 ★★

Block Percentage

Calculate BLK% for a center with these statistics: - Blocks: 2.4 per game - Minutes: 32.8 per game - Team minutes: 240 - Opponent 2-point attempts: 42.6 per game

Exercise 23 ★★★

Rim Protection Analysis

Compare these two rim protectors:

Center A: - 2.8 BPG - Opponents shoot 58% at rim when he contests - Contests 8.2 shots at rim per game - BLK%: 4.8%

Center B: - 1.4 BPG - Opponents shoot 52% at rim when he contests - Contests 11.4 shots at rim per game - BLK%: 2.4%

a) Calculate total expected points allowed at the rim per game for each (assuming 2 points per make). b) Who is the better rim protector? Justify your answer. c) Why might Box scores favor Center A?

Exercise 24 ★★★

Steals vs. Defensive Value

A player leads the league in steals (2.8 SPG) but his on/off defensive rating is: - On court: 112.4 defensive rating - Off court: 108.2 defensive rating

a) What does the on/off data suggest about overall defensive impact? b) How might high steal attempts hurt team defense? c) What additional information would help evaluate this player's defense?

Exercise 25 ★★★★

Creating a Defensive Box Score Metric

Traditional box scores poorly capture defense. Using only box score statistics (steals, blocks, defensive rebounds, personal fouls), create a "Box Score Defensive Impact" metric.

a) Write your formula with justified weights. b) Acknowledge what this metric cannot capture. c) Apply to three players with different defensive profiles. d) Compare your rankings to their actual defensive impact (using DRAPTOR, DLEBRON, or similar if available). e) Discuss why box score defense metrics will always be limited.

Section E: Turnovers and Efficiency (Exercises 26-30)

Exercise 26 ★

Turnover Rate

Calculate turnovers per 100 possessions for each player (use the formula: TOV% = 100 * TOV / (FGA + 0.44*FTA + TOV)):

Exercise 27 ★★

Turnover Context

A point guard has these turnover types: - Bad passes: 1.8 per game - Lost ball/stripped: 1.2 per game - Offensive fouls: 0.4 per game - Traveling/violations: 0.3 per game - Other: 0.2 per game

Total: 3.9 TOV per game with 10.2 APG

a) Calculate AST/TO ratio. b) Which turnover type is most problematic? Why? c) How might coaching address the "bad passes" category?

Exercise 28 ★★★

Risk-Reward Analysis

Compare these playmaking profiles:

Aggressive Passer: - 11.8 APG, 4.2 TOV - 3.2 potential assists that became turnovers per game - Average pass distance: 14.2 feet

Conservative Passer: - 8.4 APG, 2.1 TOV - 1.1 potential assists that became turnovers per game - Average pass distance: 9.8 feet

a) Calculate expected points created per game (assume 2.2 points per assist). b) Calculate expected points lost per game (assume 1.1 points per turnover). c) Calculate net point differential. d) Which player provides more value through passing? Discuss trade-offs.

Exercise 29 ★★★

Game Score Analysis

Calculate Game Score for this performance:

• 28 points, 10-18 FG, 3-6 3PT, 5-7 FT
• 3 OREB, 8 DREB
• 7 assists, 2 turnovers
• 1 steal, 2 blocks
• 3 personal fouls

Game Score = PTS + 0.4FGM - 0.7FGA - 0.4(FTA-FTM) + 0.7OREB + 0.3DREB + STL + 0.7AST + 0.7BLK - 0.4PF - TOV

Exercise 30 ★★★★

Creating a Possession-Based Efficiency Metric

Design a metric that evaluates a player's efficiency relative to their usage of team possessions.

a) Define "player possessions used" using box score data. b) Create a "Points Produced per Possession Used" metric. c) Account for assists (points created for others) in your formula. d) Apply to three players with different usage levels. e) Discuss how this compares to existing metrics like Offensive Rating.

Section F: Minutes and Usage (Exercises 31-35)

Exercise 31 ★

Per-36 Calculations

Calculate per-36 minute statistics:

Exercise 32 ★★

Minutes Distribution

A team's rotation has these average minutes:

Total: 240 minutes per game

a) Calculate total minutes for starters vs. bench. b) What percentage of minutes go to the top 5 players? c) This team is entering the playoffs. How might this distribution change?

Exercise 33 ★★★

Historical Minutes Comparison

Compare these historical seasons:

Wilt Chamberlain 1961-62: - 48.5 MPG, 50.4 PPG, 25.7 RPG

Joel Embiid 2022-23: - 34.6 MPG, 33.1 PPG, 10.2 RPG

a) Calculate per-36 minute statistics for both players. b) Calculate per-minute production. c) Discuss why per-minute rates may not scale to 48 minutes. d) What other factors complicate this comparison?

Exercise 34 ★★★

Usage Rate Analysis

Usage Rate = 100 * ((FGA + 0.44 * FTA + TOV) * (Tm MP / 5)) / (MP * (Tm FGA + 0.44 * Tm FTA + Tm TOV))

Calculate usage rate for a player with: - 22 FGA, 8 FTA, 4 TOV - 38 minutes played - Team totals: 88 FGA, 24 FTA, 14 TOV - Team minutes: 240

Exercise 35 ★★★★

Load Management Analysis

A star player's statistics with different rest patterns:

a) Analyze the relationship between rest and performance. b) Calculate weighted average statistics if the player played all 82 games. c) Calculate weighted average if the player sat all back-to-backs (12 games). d) Discuss the trade-off between games played and per-game performance. e) Design a "season value" metric that accounts for both availability and performance.

Section G: Synthesis and Application (Exercises 36-40)

Exercise 36 ★★

Complete Box Score Analysis

Analyze this complete box score:

a) Calculate FG%, 3P%, FT%, and TS% for each player. b) Calculate Game Score for each player. c) Identify each player's likely role based on their statistical profile. d) What story does this box score tell about how the game was played?

Exercise 37 ★★★

Triple-Double Evaluation

Two players achieve triple-doubles:

Player X: 24 points (8-18 FG, 2-6 3PT, 6-8 FT), 10 rebounds (1 OREB, 9 DREB), 11 assists, 5 turnovers

Player Y: 16 points (6-10 FG, 2-4 3PT, 2-2 FT), 12 rebounds (4 OREB, 8 DREB), 10 assists, 2 turnovers

a) Calculate efficiency metrics for both (TS%, AST/TO). b) Calculate Game Score for both. c) Which triple-double was more valuable? Justify your answer. d) Discuss what the triple-double label might obscure.

Exercise 38 ★★★

Empty Stats Identification

Identify potential "empty stats" concerns in this player profile:

Season Statistics: - 23.4 PPG, 7.8 RPG, 6.2 APG - 42.1% FG, 32.8% 3PT, 78.4% FT - 3.8 TOV per game - Team record: 28-54

a) Calculate TS%. b) Calculate AST/TO ratio. c) Identify at least three statistical red flags. d) What additional information would help evaluate this player? e) Is it possible these are not "empty stats"? Explain.

Exercise 39 ★★★★

Cross-Era Comparison Project

Select three players from different eras (pre-1980, 1980-2000, 2000-present) who played the same position. Using their best statistical season:

a) Compile their raw box score statistics. b) Calculate per-36 minute, per-100 possession, and relevant percentage-based metrics. c) Research and apply pace adjustments. d) Create visualization comparing their profiles. e) Write a 500-word analysis of how their statistical profiles reflect their eras. f) Discuss limitations of cross-era statistical comparisons.

Exercise 40 ★★★★

Box Score Metric Design Challenge

Create a comprehensive single-number metric using only traditional box score statistics that attempts to capture total player value.

Requirements: a) Use only statistics available in standard box scores (no tracking data). b) Justify all weights mathematically or logically. c) Account for position differences. d) Normalize for minutes played. e) Test on at least 10 players across multiple positions. f) Compare your rankings to established metrics (PER, WS, VORP). g) Write a critical analysis of your metric's strengths and limitations. h) Explain why this exercise demonstrates the inherent limitations of box score metrics.

Answer Key Reference

Selected answers are provided in the chapter's supplementary materials. For calculation problems, verify your work by checking that: - Point totals equal 22PM + 33PM + FTM - Per-36 calculations use (stat/minutes)*36 - Percentage calculations divide correctly and multiply by 100 - Game Score follows the exact formula provided

For analysis questions, strong answers will: - Reference specific numbers from the data - Acknowledge multiple interpretations - Discuss limitations of the analysis - Connect to broader chapter concepts