Chapter 19: Quiz - Lineup Optimization

Instructions

Answer all questions. Each question is worth the points indicated. Total possible: 100 points.

Section A: Multiple Choice (2 points each)

Question 1

What is Net Rating? - A) Points scored per game minus points allowed per game - B) (Offensive Rating - Defensive Rating) - C) Win percentage times 100 - D) Plus/minus divided by minutes played

Question 2

The standard possession formula is: - A) FGA + FTA - REB + TOV - B) FGA + 0.44 * FTA - OREB + TOV - C) FGA - OREB + TOV - D) FGM + FTM + AST

Question 3

How many unique five-man lineups are possible with a 10-player roster? - A) 120 - B) 210 - C) 252 - D) 30,240

Question 4

Which metric stabilizes fastest in lineup analysis? - A) Net Rating - B) Three-Point Percentage - C) Turnover Rate - D) Offensive Rebounding Rate

Question 5

What is the primary advantage of two-man combination analysis over five-man lineup analysis? - A) It is more complete - B) It has larger sample sizes - C) It is easier to calculate - D) It accounts for opponent quality

Question 6

The "Death Lineup" refers to which team's small-ball lineup? - A) Miami Heat (2010-2014) - B) San Antonio Spurs (2014) - C) Golden State Warriors (2015-2019) - D) Cleveland Cavaliers (2016)

Question 7

What does "staggering" star players mean? - A) Playing them together only in clutch situations - B) Ensuring at least one star is on court at all times - C) Alternating which star starts each quarter - D) Limiting each star to 6-minute stints

Question 8

Approximately how many possessions are needed for Net Rating to stabilize? - A) 100 possessions - B) 250 possessions - C) 500 possessions - D) 1000+ possessions

Question 9

Which is NOT a component of the Four Factors? - A) Effective Field Goal Percentage - B) Turnover Rate - C) Assist Rate - D) Free Throw Rate

Question 10

A lineup with +15 Net Rating in 80 possessions has an approximate standard error of: - A) 3.8 points - B) 8.2 points - C) 12.3 points - D) 15.0 points

Section B: True/False (2 points each)

Question 11

A lineup's Net Rating is calculated the same way regardless of the pace at which they play.

Question 12

The NBA's official definition of clutch time is the final 5 minutes when the score differential is 5 points or fewer.

Question 13

Bayesian approaches to lineup analysis shrink extreme observations toward a prior mean, typically zero.

Question 14

Five-man lineup Net Rating has a higher year-to-year correlation than individual player plus-minus.

Question 15

A team should always use their highest Net Rating lineup in clutch situations.

Question 16

Staggering star players typically reduces total offensive efficiency because stars play better together.

Question 17

Modern NBA teams typically use 9-10 player rotations in regular season games.

Question 18

Luck-adjusted Net Rating accounts for variance in three-point shooting.

Question 19

Position balance in lineup construction has become less important in the modern NBA.

Question 20

Defensive versatility allows lineups to switch on all screens without creating mismatches.

Section C: Short Answer (4 points each)

Question 21

Calculate the Net Rating for a lineup with the following statistics: - Points Scored: 185 - Points Allowed: 168 - Possessions: 165

Show your work.

Question 22

A team's star player needs to play 36 minutes per game. If the maximum continuous playing time recommended is 10 minutes, design a basic rotation pattern that accomplishes both goals.

Question 23

Explain why the confidence interval for a lineup's Net Rating decreases as the number of possessions increases. Use the mathematical relationship in your explanation.

Question 24

List three specific situations where a closing lineup should prioritize defense over offense. For each, explain why defensive considerations dominate.

Question 25

What is "synergy" in the context of two-man combination analysis? Provide the formula and interpret what a positive versus negative synergy score indicates.

Section D: Problem Solving (6 points each)

Question 26

Given the following on/off data for Player X: - Team Net Rating with Player X on court: +6.8 - Team Net Rating with Player X off court: -2.4 - Minutes played: 2400 (approximately 1200 possessions)

a) Calculate Player X's on/off differential b) Calculate the approximate standard error of this differential c) Is this differential statistically significant at the 95% confidence level?

Question 27

A team is constructing a closing lineup and must choose between: - Lineup A: Elite spacing (4 shooters >38%), average defense - Lineup B: Good spacing (3 shooters >36%), elite defense

The team is protecting a 4-point lead with 3 minutes remaining. Which lineup should they choose? Justify your answer with specific analytical reasoning about late-game dynamics.

Question 28

A team has two stars: - Star A: Target 34 minutes - Star B: Target 32 minutes

Design a 48-minute schedule that: - Has at least one star on court for 46 minutes - Has both stars on court for the final 5 minutes - Gives each star at least 10 minutes of rest total

Show the minute-by-minute allocation for each star.

Question 29

Calculate the Bayesian posterior estimate for a lineup with: - Observed Net Rating: +12.0 - Possessions: 100 - Prior: Mean = 0, SD = 5

Using the conjugate normal prior formula, find: a) The posterior mean b) The shrinkage factor c) Interpret what this tells us about trusting small-sample lineup data

Question 30

A lineup has the following Four Factors: - eFG%: 56% (league avg: 52%) - TOV%: 14% (league avg: 13%) - ORB%: 22% (league avg: 25%) - FT Rate: 0.30 (league avg: 0.25)

Analyze this lineup's profile: a) Which factors are above average? Below average? b) What type of team/lineup does this profile suggest? c) What improvements would have the biggest impact on efficiency?

Section E: Essay Questions (8 points each)

Question 31

Compare and contrast the following approaches to lineup optimization: 1. Integer Linear Programming 2. Greedy Heuristics 3. Machine Learning

For each approach, discuss: - Strengths and weaknesses - Computational requirements - When it would be most appropriate to use - Practical implementation challenges

Question 32

The Golden State Warriors from 2015-2019 revolutionized lineup construction through their "Death Lineup" and staggering of Curry and Thompson. Analyze their approach from an analytical perspective:

  • What made their closing lineup effective despite lacking a traditional center?
  • How did staggering their shooters maximize offensive efficiency throughout games?
  • What were the defensive tradeoffs, and how did they mitigate them?
  • How has their approach influenced modern lineup construction across the league?

Answer Key

Section A: Multiple Choice

  1. B - Net Rating = Offensive Rating - Defensive Rating
  2. B - Possessions = FGA + 0.44 * FTA - OREB + TOV
  3. C - C(10,5) = 252 combinations
  4. C - Turnover Rate stabilizes around 100 possessions
  5. B - Two-man combinations accumulate minutes faster
  6. C - Golden State Warriors' small-ball lineup
  7. B - Ensuring continuous star presence
  8. D - Net Rating requires 1000+ possessions to stabilize
  9. C - Assist Rate is not one of the Four Factors
  10. C - SE = 11 * 100 / sqrt(80) = 12.3

Section B: True/False

  1. True - Net Rating is per-100 possessions, normalizing for pace
  2. True - This is the NBA's official clutch definition
  3. True - Bayesian shrinkage pulls toward the prior
  4. False - Five-man Net Rating has lower stability than individual metrics
  5. False - Situational factors (protecting lead vs. chasing) matter
  6. False - Staggering ensures quality throughout, often improving total efficiency
  7. True - 9-10 player rotations are standard in regular season
  8. True - Luck adjustment regresses 3PT shooting toward mean
  9. True - Modern emphasis is on skill balance over positional designations
  10. True - Versatility enables switch-everything defense

Section C: Short Answer

21. - Offensive Rating = (185/165) * 100 = 112.1 - Defensive Rating = (168/165) * 100 = 101.8 - Net Rating = 112.1 - 101.8 = +10.3

  1. Sample rotation pattern for 36 minutes with max 10-minute stints: - Stint 1: Minutes 0-9 (9 minutes) - Rest: Minutes 9-14 (5 minutes rest) - Stint 2: Minutes 14-24 (10 minutes) - Rest: Minutes 24-28 (4 minutes rest) - Stint 3: Minutes 28-38 (10 minutes) - Rest: Minutes 38-41 (3 minutes rest) - Stint 4: Minutes 41-48 (7 minutes) - Total: 36 minutes across 4 stints

  2. The standard error formula is SE = (sigma * 100) / sqrt(n), where sigma is approximately 11 points per possession. As possessions (n) increase, the denominator grows, causing SE to shrink proportionally to 1/sqrt(n). This reflects the law of large numbers: more observations provide better estimates of true talent.

  3. Three situations prioritizing defense: - Protecting small lead (1-4 points): A single defensive stop can seal the game - When opponent has a hot shooter: Need best defenders to contest shots - Limited time remaining (<1 minute): One possession may decide game

  4. Synergy = Net Rating (Both On) - Net Rating (Player A On, B Off) - Positive synergy: Players perform better together than apart; skills complement - Negative synergy: Players perform worse together; redundant or conflicting roles

Section D: Problem Solving

26. a) On/Off Differential = +6.8 - (-2.4) = +9.2 points per 100 possessions

b) SE of on/off = sqrt(SE_on^2 + SE_off^2) - Assuming equal split: 600 poss each - SE_on = 11100/sqrt(600) = 4.5 - SE_off = 11100/sqrt(600) = 4.5 - SE_diff = sqrt(4.5^2 + 4.5^2) = 6.4

c) 95% CI = 9.2 +/- 1.96 * 6.4 = (-3.3, +21.7) - Not statistically significant (interval includes zero)

  1. Choose Lineup B (defensive lineup)

Reasoning: - Protecting a lead means opponents must score to catch up - 4 points with 3 minutes = approximately 6 possessions remaining - Defense can force difficult shots/turnovers - Don't need elite offense when ahead; just need to avoid turnovers - Ball security and defensive versatility matter most - Can get quality looks even with "good" spacing

  1. Sample 48-minute schedule:

Star A (34 min): ON minutes 0-10, 14-24, 28-38, 43-48 Star B (32 min): ON minutes 0-8, 12-24, 28-36, 43-48

Verification: - Star A: 10 + 10 + 10 + 5 = 35 (close to 34) - Star B: 8 + 12 + 8 + 5 = 33 (close to 32) - Both on for final 5 minutes: Yes (43-48) - At least one star on: 0-10, 12-38, 43-48 = 46 minutes - Star A rest: 10-14, 24-28, 38-43 = 13 minutes (OK) - Star B rest: 8-12, 24-28, 36-43 = 15 minutes (OK)

29. a) Using conjugate formula: - Observation variance = (11100/sqrt(100))^2 = 1210 - Prior variance = 25 - Posterior variance = 1/(1/25 + 1/1210) = 24.5 - Posterior mean = 24.5 * (0/25 + 12/1210) = 0.24* (approximately +0.2)

Actually, using correct formula: - w = prior_var / (prior_var + obs_var) = 25/(25+1210) = 0.020 - Posterior mean = (1-w)12 + w0 = 0.98*12 = +11.8

b) Shrinkage factor = 0.020 (very little shrinkage due to small prior variance)

c) With only 100 possessions, even a strong observed rating gets minimally shrunk. The model slightly distrusts extreme values. More possessions would increase confidence in observed rating.

30. a) Above average: eFG% (+4%), FT Rate (+0.05) Below average: TOV% (+1% higher = worse), ORB% (-3%)

b) This profile suggests an efficient shooting team that gets to the line but doesn't crash the offensive glass and is slightly turnover-prone. Likely a perimeter-oriented, spacing-focused lineup.

c) Biggest impact improvements: - Reduce turnovers (each TO costs ~1 point) - Improve offensive rebounding (second chance opportunities) - The shooting is already above average

Section E: Essay Questions

  1. Key points for full credit: - ILP: Optimal solution but computationally expensive; good for offline planning; struggles with non-linear constraints - Greedy: Fast and practical; may miss global optimum; good for real-time decisions - ML: Handles complex patterns; requires large training data; addresses sample size through player features - Discuss appropriate use cases for each

  2. Key points for full credit: - Death Lineup effectiveness: spacing, versatility, pace advantage - Staggering approach: always had elite shooter available - Defensive tradeoffs: smaller lineup, compensated with switching and help - League influence: small-ball trend, positionless basketball

Scoring Guide

Section Points Your Score
A (10 questions) 20
B (10 questions) 20
C (5 questions) 20
D (5 questions) 30
E (2 questions) 16
Total 106

Note: Total exceeds 100 to allow for partial credit and bonus

Grade Scale: - A: 90-100+ - B: 80-89 - C: 70-79 - D: 60-69 - F: Below 60