Chapter 7 Quiz: Rate Statistics and Pace Adjustment

Instructions

This quiz contains 25 questions covering rate statistics, pace adjustment, and per-possession analysis from Chapter 7. Questions include multiple choice, calculations, and short answer formats.

Scoring Guide: - Multiple Choice: 2 points each - True/False: 1 point each - Calculations: 4 points each - Short Answer: 3 points each

Section A: Per-Minute Statistics (Questions 1-6)

Question 1 (Multiple Choice)

The per-36 minutes convention is used because 36 minutes represents:

a) The maximum a player can play without overtime b) A typical starter's workload accounting for normal rest c) The league minimum for qualifying statistics d) An arbitrary number chosen for simplicity

Question 2 (Calculation)

A player scores 450 points in 900 minutes. Calculate: a) Points per 36 minutes b) Points per 48 minutes

Question 3 (True/False)

Per-minute statistics scale linearly, meaning a player who scores 10 points per 36 minutes in 18 minutes would likely score 20 points if given 36 minutes.

Question 4 (Short Answer)

Explain why per-36 minute statistics can be misleading for bench players who play limited minutes.

Question 5 (Multiple Choice)

Which of the following is NOT a limitation of per-minute statistics?

a) Small sample size inflation for low-minute players b) Non-linear scaling with increased playing time c) They cannot be calculated without team statistics d) Role context affecting production against different competition

Question 6 (Calculation)

A player has the following season totals: 1,640 points, 520 rebounds, 410 assists in 2,870 minutes. Calculate per-36 minute statistics for all three categories.

Section B: Possessions and Pace (Questions 7-13)

Question 7 (Multiple Choice)

The standard formula for estimating possessions is:

a) Possessions = FGA + FTA - OREB + TOV b) Possessions = FGA + 0.44 * FTA - OREB + TOV c) Possessions = FGA + 0.5 * FTA + TOV d) Possessions = FGA - OREB + TOV + FTA

Question 8 (Calculation)

Calculate the estimated possessions for a team with: - FGA: 88 - FTA: 24 - OREB: 12 - TOV: 14

Question 9 (Short Answer)

Explain why the free throw coefficient in the possessions formula is 0.44 rather than 0.5.

Question 10 (True/False)

The 1998-99 NBA season featured the slowest pace in league history at approximately 88.9 possessions per 48 minutes.

Question 11 (Multiple Choice)

Pace is defined as:

a) The number of shots a team takes per game b) The number of possessions per 48 minutes (or 40 for college) c) The average time per possession in seconds d) The ratio of fast break points to total points

Question 12 (Calculation)

A team has 95 possessions in a game where they played 48 minutes. Calculate their pace.

Question 13 (Short Answer)

Describe how the three-point revolution has affected NBA pace since 2015.

Section C: Per-Possession Statistics (Questions 14-18)

Question 14 (Multiple Choice)

Offensive Rating (ORtg) measures:

a) Points scored per game b) Points scored per 36 minutes c) Points scored per 100 possessions d) Points scored relative to league average

Question 15 (Calculation)

A team scores 108 points in 96 possessions. Calculate their Offensive Rating.

Question 16 (True/False)

A player's individual per-100-possession statistics require only their individual statistics to calculate.

Question 17 (Short Answer)

Explain the relationship between Usage Rate and Individual Offensive Rating.

Question 18 (Calculation)

Player X averages 28.5 PPG on a team with pace of 102.3. Player Y averages 27.2 PPG on a team with pace of 95.8. League average pace is 99.5.

Calculate pace-adjusted PPG for both players. Which player has the higher scoring rate after adjustment?

Section D: Era Adjustments (Questions 19-22)

Question 19 (Multiple Choice)

When comparing Wilt Chamberlain's 50.4 PPG (1961-62) to modern players, which adjustment is most important?

a) Three-point adjustment b) Pace adjustment c) Defensive rule adjustment d) Salary cap adjustment

Question 20 (Calculation)

Wilt Chamberlain's 1961-62 season: 50.4 PPG at pace of approximately 130. Calculate his points per 100 possessions.

Question 21 (Short Answer)

Explain the z-score approach to cross-era statistical comparison and its advantages over simple pace adjustment.

Question 22 (True/False)

Era-adjusted statistics can perfectly account for differences in competition level, training methods, and rule changes between different decades.

Section E: Rate vs. Counting Statistics (Questions 23-25)

Question 23 (Multiple Choice)

Which analytical goal is best served by counting statistics rather than rate statistics?

a) Comparing efficiency between players on different teams b) Projecting how a player might perform with more playing time c) Measuring total contribution over a season d) Historical comparisons across eras

Question 24 (Short Answer)

A player averages 22.4 PPG (26.8 per 36 minutes, 31.2 per 100 possessions) on a team with the league's slowest pace. Explain what this full context tells us that raw PPG alone does not.

Question 25 (Calculation)

Player A: 2,000 points in 2,800 minutes on a team with 102 pace Player B: 1,500 points in 2,100 minutes on a team with 96 pace League average pace: 99

Calculate: a) Points per 36 minutes for each player b) Pace-adjusted points per 36 for each player c) Which player is the more efficient scorer?

Answer Key

Section A: Per-Minute Statistics

Question 1: b) A typical starter's workload accounting for normal rest

Question 2: a) Per-36 = (450 / 900) * 36 = 18.0 points per 36 minutes b) Per-48 = (450 / 900) * 48 = 24.0 points per 48 minutes

Question 3: False. Player performance does not scale linearly with playing time. Fatigue, defensive attention, and role expansion typically reduce efficiency with increased minutes.

Question 4: Sample answer: Bench players often have inflated per-36 statistics because they (1) face weaker competition from opposing bench units, (2) play in specific favorable situations designed for their skills, (3) benefit from smaller sample sizes that don't regress to their true talent, and (4) may not maintain their production against starter-level competition or over extended minutes due to fatigue.

Question 5: c) They cannot be calculated without team statistics (Per-minute stats require only individual minutes and counting stats)

Question 6: - Points per 36 = (1,640 / 2,870) * 36 = 20.56 PPG - Rebounds per 36 = (520 / 2,870) * 36 = 6.52 RPG - Assists per 36 = (410 / 2,870) * 36 = 5.14 APG

Section B: Possessions and Pace

Question 7: b) Possessions = FGA + 0.44 * FTA - OREB + TOV

Question 8: Possessions = 88 + (0.44 * 24) - 12 + 14 = 88 + 10.56 - 12 + 14 = 100.56 possessions

Question 9: The 0.44 coefficient accounts for the various types of free throw situations: two-shot fouls count as approximately 1 possession for 2 FTA; three-shot fouls count as 1 possession for 3 FTA; and-one situations add 1 FTA without using an additional possession; technical free throws don't cost a possession. The weighted average of these scenarios yields approximately 0.44 FTA per possession.

Question 10: True

Question 11: b) The number of possessions per 48 minutes (or 40 for college)

Question 12: Pace = (95 / 48) * 48 = 95.0 (or if game minutes differed, use the formula)

Question 13: Sample answer: Since 2015, pace has increased from approximately 93-94 possessions per 48 minutes to 99-101. The three-point revolution contributed through: (1) faster shot clock usage as teams take early threes, (2) more rebounds leading to transition opportunities due to longer rebounds from three-point misses, (3) spacing opening up driving lanes for quicker offensive decisions, and (4) reduced post-up play which traditionally consumed more shot clock.

Section C: Per-Possession Statistics

Question 14: c) Points scored per 100 possessions

Question 15: Offensive Rating = (108 / 96) * 100 = 112.5

Question 16: False. Individual per-100-possession statistics require team possession data for the time the player is on court, which requires play-by-play data.

Question 17: Sample answer: Usage Rate measures the percentage of team possessions a player uses while on court. Individual Offensive Rating measures how efficiently they convert those possessions into points. High-usage players typically have lower Individual ORtg because they must take more difficult shots. The relationship demonstrates the efficiency-volume trade-off: players who use more possessions generally convert them less efficiently.

Question 18: - Player X: 28.5 * (99.5 / 102.3) = 27.72 pace-adjusted PPG - Player Y: 27.2 * (99.5 / 95.8) = 28.25 pace-adjusted PPG - Player Y has the higher scoring rate after adjustment, despite having lower raw PPG.

Section D: Era Adjustments

Question 19: b) Pace adjustment (The extreme pace difference of ~130 vs ~100 is the most significant factor)

Question 20: Points per 100 possessions = (50.4 / 130) * 100 = 38.77 points per 100 possessions

Question 21: Sample answer: The z-score approach calculates how many standard deviations above or below the mean a player's statistics fall within their own era: z = (Player Stat - Era Mean) / Era Standard Deviation. Advantages: (1) accounts for the spread of the distribution, not just the mean; (2) a z-score of +2.0 represents elite performance in any era; (3) allows fair comparison of dominance relative to contemporaries; (4) addresses both level differences (mean) and compression/expansion of performance (standard deviation).

Question 22: False. Era adjustments can account for pace and scoring environment but cannot fully capture differences in competition level (expansion, international talent), training methods, medical advances, rule changes affecting play style, and other factors that affect raw statistical output.

Section E: Rate vs. Counting Statistics

Question 23: c) Measuring total contribution over a season (Counting stats capture total impact; rate stats capture efficiency per opportunity)

Question 24: Sample answer: This context reveals that the player scores efficiently relative to their opportunities. The 26.8 per-36 shows their per-minute production is above their raw average, indicating they're productive in limited time. The 31.2 per-100 possessions is very high, showing elite efficiency per opportunity. The slow pace context explains why raw PPG is lower despite high efficiency - fewer possessions means fewer counting stat opportunities. Together, this suggests an efficient scorer whose raw numbers are suppressed by team pace.

Question 25: a) Points per 36: - Player A: (2,000 / 2,800) * 36 = 25.71 - Player B: (1,500 / 2,100) * 36 = 25.71

b) Pace-adjusted per 36: - Player A: 25.71 * (99 / 102) = 24.96 - Player B: 25.71 * (99 / 96) = 26.52

c) Player B is the more efficient scorer. Despite identical per-36 raw numbers, Player B produced those numbers on a slower-paced team with fewer opportunities.

Scoring

Grade Scale: - A: 68-76 points (90%+) - B: 61-67 points (80-89%) - C: 53-60 points (70-79%) - D: 46-52 points (60-69%) - F: Below 46 points