Chapter 10 Quiz: Plus-Minus and On/Off Analysis

Instructions

This quiz contains 25 questions covering plus-minus and on/off analysis from Chapter 10. Questions test your understanding of raw plus-minus, on/off splits, lineup analysis, and the foundation for adjusted metrics.

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

Section A: Raw Plus-Minus Fundamentals (Questions 1-5)

Question 1 (Multiple Choice)

Raw plus-minus measures:

a) A player's individual scoring b) The point differential while a player is on the court c) A player's efficiency rating d) The number of minutes played

Question 2 (Calculation)

A player plays three stints in a game: - First stint: Team scores 18, allows 14 (8 minutes) - Second stint: Team scores 22, allows 26 (12 minutes) - Third stint: Team scores 15, allows 12 (10 minutes)

Calculate the player's total plus-minus for the game.

Question 3 (True/False)

Raw plus-minus can be calculated from box score data alone without play-by-play information.

Question 4 (Short Answer)

Explain why raw plus-minus favors players who play alongside better teammates.

Question 5 (Multiple Choice)

Before approximately 2000-2001, systematic plus-minus calculation was difficult because:

a) The three-point line didn't exist b) Play-by-play data tracking substitutions wasn't widely available c) Players played fewer minutes d) The shot clock was different

Section B: On/Off Splits (Questions 6-10)

Question 6 (Calculation)

Given the following on/off data for a player: - On-Court: 850 points for, 790 points against, 750 possessions - Off-Court: 420 points for, 460 points against, 380 possessions

Calculate the player's On/Off Net Rating differential.

Question 7 (Multiple Choice)

An on/off differential of +12.0 means:

a) The player scored 12 more points than average b) The team's net rating is 12 points per 100 possessions better with the player on court vs. off c) The player assisted on 12 more baskets d) The team won by 12 points

Question 8 (True/False)

A player's on/off differential compares their impact to league-average replacement level.

Question 9 (Short Answer)

Explain how a star player with excellent backup (e.g., Kyrie Irving backing up LeBron James) might have a lower on/off differential than a star with a poor backup, even if both stars are equally talented.

Question 10 (Multiple Choice)

Defensive Rating in on/off analysis measures:

a) Blocks and steals per game b) Points allowed per 100 possessions c) Defensive efficiency rating d) Opponent field goal percentage

Section C: Lineup Analysis (Questions 11-15)

Question 11 (Multiple Choice)

With a 15-man roster, the theoretical number of possible five-player combinations is:

a) 15 b) 75 c) 3,003 d) 15,625

Question 12 (Calculation)

A five-man lineup plays 250 minutes together with the following results: - Points scored: 285 - Points allowed: 240 - Estimated possessions: 280

Calculate this lineup's Net Rating per 100 possessions.

Question 13 (True/False)

A lineup with 100 minutes and +20 Net Rating is more reliable than one with 500 minutes and +10 Net Rating.

Question 14 (Short Answer)

What made the Golden State Warriors' "Death Lineup" effective, and why couldn't the statistical impact be fully captured by individual player metrics?

Question 15 (Multiple Choice)

The primary challenge with five-man lineup analysis is:

a) Too many lineups to track b) Insufficient sample size for most combinations c) Lineups don't matter in basketball d) Coaches don't care about lineup data

Section D: Why Raw Plus-Minus Is Noisy (Questions 16-20)

Question 16 (Multiple Choice)

Research suggests single-season raw plus-minus correlates with next season's plus-minus at approximately:

a) 0.80-0.90 (very high) b) 0.60-0.70 (high) c) 0.30-0.40 (low) d) 0.05-0.10 (negligible)

Question 17 (True/False)

A starter's plus-minus may be inflated if they typically face opponent starters who are worse than the team's bench players.

Question 18 (Calculation)

A lineup has 200 minutes of data with a +15 Net Rating. Using the standard error estimate where SE = 37 / sqrt(possessions/100), and assuming 2 possessions per minute, calculate the approximate 95% confidence interval for this lineup's true Net Rating.

Question 19 (Short Answer)

Explain the concept of "garbage time" and how it can distort plus-minus statistics.

Question 20 (Multiple Choice)

Which factor does NOT contribute to noise in raw plus-minus?

a) Small sample sizes b) Teammate quality confounding c) Opponent quality variation d) Player height

Section E: Foundations for Adjustment (Questions 21-25)

Question 21 (Multiple Choice)

The fundamental goal of adjusted plus-minus methods is to:

a) Make all players look equal b) Isolate individual contribution from teammate and opponent effects c) Predict future performance perfectly d) Replace box score statistics entirely

Question 22 (Short Answer)

Explain why players who always play together create a "multicollinearity problem" for regression-based plus-minus methods.

Question 23 (True/False)

Regularized Adjusted Plus-Minus (RAPM) uses ridge regression to address collinearity and small sample issues.

Question 24 (Multiple Choice)

The "LeBron problem" in on/off analysis refers to:

a) LeBron plays too many minutes b) LeBron's presence elevates teammate performance, making it hard to isolate his individual contribution c) LeBron's statistics are too high d) LeBron's teams always win

Question 25 (Calculation)

A player has observed plus-minus of +10.0 per 100 possessions based on 800 possessions. Using Bayesian shrinkage with prior mean = 0 and prior strength = 400, calculate the shrunk estimate of their true plus-minus.

Formula: Posterior = (prior_strength * prior_mean + sample_size * observed) / (prior_strength + sample_size)

Answer Key

Section A: Raw Plus-Minus Fundamentals

Question 1: b) The point differential while a player is on the court

Question 2: - First stint: +4 (18-14) - Second stint: -4 (22-26) - Third stint: +3 (15-12) - Total: +4 + (-4) + 3 = +3

Question 3: False. Play-by-play data tracking substitutions and scoring by time segment is required.

Question 4: Sample answer: Raw plus-minus credits (or debits) a player for all points scored and allowed while they're on the court, regardless of who actually produced those points. If a player shares the court with elite scorers and defenders, the team will outscore opponents regardless of that specific player's individual contribution. Conversely, if a player only plays with weak teammates, their plus-minus will suffer even if they personally play well. The metric cannot distinguish between "Player X helped the team" and "Player X happened to be on court when good teammates helped the team."

Question 5: b) Play-by-play data tracking substitutions wasn't widely available

Section B: On/Off Splits

Question 6: On-Court: - ORtg = (850/750) * 100 = 113.3 - DRtg = (790/750) * 100 = 105.3 - Net Rating On = 113.3 - 105.3 = +8.0

Off-Court: - ORtg = (420/380) * 100 = 110.5 - DRtg = (460/380) * 100 = 121.1 - Net Rating Off = 110.5 - 121.1 = -10.6

On/Off Differential = +8.0 - (-10.6) = +18.6

Question 7: b) The team's net rating is 12 points per 100 possessions better with the player on court vs. off

Question 8: False. On/off differential compares to the player's backup/replacement within their own team, not league-average replacement level.

Question 9: Sample answer: On/off differential measures the swing in team performance between a player being on court versus their backup playing. If a star has an elite backup: - Star on court: +8.0 Net Rating - Elite backup on court: +4.0 Net Rating - On/Off: +4.0

If an equally talented star has a poor backup: - Star on court: +8.0 Net Rating - Poor backup on court: -6.0 Net Rating - On/Off: +14.0

The second star appears 3.5x more valuable by on/off, despite identical individual contribution. This is why on/off must be interpreted carefully and not confused with absolute player value.

Question 10: b) Points allowed per 100 possessions

Section C: Lineup Analysis

Question 11: c) 3,003 (calculated as 15 choose 5 = 15!/(5!*10!) = 3,003)

Question 12: - ORtg = (285/280) * 100 = 101.8 - DRtg = (240/280) * 100 = 85.7 - Net Rating = 101.8 - 85.7 = +16.1 per 100 possessions

Question 13: False. Sample size matters enormously. With 500 minutes, the +10 lineup has much more reliable data. The 100-minute +20 lineup has high variance; the true rating could easily be anywhere from +5 to +35.

Question 14: Sample answer: The "Death Lineup" (Curry-Thompson-Iguodala-Barnes/Durant-Green) was effective because: 1. Five shooters created unprecedented spacing 2. Switchable defense allowed aggressive help and recovery 3. Pace advantage exhausted opponents 4. Green at center enabled the configuration to exist

Individual metrics couldn't capture this because: - Spacing benefits are invisible in box scores - Switching success isn't recorded - The lineup's synergy exceeds sum of individual contributions - Green's enabling role creates no counting statistics

Question 15: b) Insufficient sample size for most combinations

Section D: Why Raw Plus-Minus Is Noisy

Question 16: c) 0.30-0.40 (low)

Question 17: False (this is tricky). A starter facing weaker opponent starters would likely have DEFLATED plus-minus because they're not getting inflated stats against weak bench units. Bench players facing weak opponent benches might have inflated plus-minus.

Question 18: - Possessions: 200 minutes * 2 = 400 possessions - SE = 37 / sqrt(400/100) = 37 / sqrt(4) = 37/2 = 18.5 - 95% CI uses z = 1.96 - Margin = 1.96 * 18.5 = 36.3

95% CI: +15 +/- 36.3 = (-21.3, +51.3)

This wide interval demonstrates why 200 minutes is insufficient for reliable conclusions.

Question 19: Sample answer: "Garbage time" refers to periods when the game outcome is effectively decided, typically when one team leads by 20+ points late in the game. During garbage time: - Teams play reserves who wouldn't normally get minutes - Effort and execution quality often decline - Statistics accumulated don't reflect competitive play

This distorts plus-minus because: - Players may have inflated plus-minus from blowout wins playing against demoralized opponents - Bench players may have good plus-minus against opposing benches in non-competitive situations - The data doesn't reflect how players would perform in meaningful minutes

Question 20: d) Player height (height has no direct effect on plus-minus calculation noise)

Section E: Foundations for Adjustment

Question 21: b) Isolate individual contribution from teammate and opponent effects

Question 22: Sample answer: When players always play together, their statistical indicators become perfectly correlated in regression analysis. For example, if Player A and Player B always share the court: - Every possession with A also has B - Every possession without A also lacks B - The regression cannot determine whether the +5 differential comes from A, B, or their combination

This is multicollinearity: the independent variables (player presence indicators) are too highly correlated to estimate individual coefficients. The regression has infinitely many solutions attributing credit between A and B. This is why lineup variation is necessary for adjustment methods to work.

Question 23: True

Question 24: b) LeBron's presence elevates teammate performance, making it hard to isolate his individual contribution

Question 25: Posterior = (400 * 0 + 800 * 10) / (400 + 800) = (0 + 8000) / 1200 = 8000 / 1200 = +6.67

The observed +10.0 is shrunk toward the prior mean of 0, reflecting uncertainty in the estimate.

Scoring

Grade Scale: - A: 61-68 points (90%+) - B: 54-60 points (80-89%) - C: 48-53 points (70-79%) - D: 41-47 points (60-69%) - F: Below 41 points