Chapter 20: Quiz - Game Strategy and Situational Analysis

Instructions

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

Section A: Multiple Choice (2 points each)

Question 1

The NBA's official definition of clutch time is: - A) Final 2 minutes, score within 3 points - B) Final 5 minutes, score within 5 points - C) Final 3 minutes, score within 5 points - D) Fourth quarter, score within 10 points

Question 2

What is Win Probability Added (WPA)? - A) A player's career winning percentage - B) The change in win probability resulting from a player's actions - C) The probability a team wins when a player scores - D) A measure of clutch shooting ability

Question 3

When intentionally fouling a trailing team, the primary goal is to: - A) Stop the clock and gain more possessions - B) Put the opponent's worst free throw shooter on the line - C) Create momentum through physical play - D) Force turnovers

Question 4

For a team with a 110 offensive rating, the break-even free throw percentage for "Hack-a-Shaq" is approximately: - A) 45% - B) 55% - C) 65% - D) 75%

Question 5

A "two-for-one" situation typically occurs when there are approximately how many seconds remaining in a period? - A) 20-25 seconds - B) 30-40 seconds - C) 45-55 seconds - D) 60-70 seconds

Question 6

Why do underdogs benefit from a faster pace? - A) They score more efficiently at higher pace - B) Faster pace increases variance, helping the worse team - C) The favored team gets tired faster - D) More possessions mean more highlight plays

Question 7

Research on clutch performance has found that year-to-year clutch statistics: - A) Highly correlate (r > 0.7) - B) Moderately correlate (r = 0.4-0.6) - C) Show weak correlation (r < 0.3) - D) Perfectly predict future clutch performance

Question 8

In the game theory "shoot or drive" example, what does Nash equilibrium imply? - A) One strategy always dominates - B) Both players should use pure strategies - C) Players randomize to make opponents indifferent - D) The offense always wins

Question 9

Studies on "icing the shooter" (calling timeout before free throws) have found: - A) Large negative effects on the shooter (5%+ decline) - B) Large positive effects on the shooter - C) Mixed or negligible effects - D) It depends entirely on the shooter's experience

Question 10

When protecting a 3-point lead in the final seconds, the analytical consensus on fouling is: - A) Never foul, always defend - B) Always foul to prevent the three-pointer - C) Fouling provides a small (~1-3%) win probability advantage - D) It depends entirely on opponent FT%

Section B: True/False (2 points each)

Question 11

Clutch performance is widely agreed to be a consistent, measurable skill that predicts future clutch success.

Question 12

Expected points from two free throws is calculated as: 2 x FT%.

Question 13

In game theory, a mixed strategy involves randomizing between options with specific probabilities.

Question 14

Favored teams should prefer higher-pace games to maximize their advantage.

Question 15

The value of a timeout is constant throughout the game.

Question 16

Three-point shooting becomes more valuable for trailing teams as time runs out.

Question 17

Free throw shooting in clutch situations tends to improve due to increased focus.

Question 18

Two-for-one strategies typically sacrifice shot quality for possession quantity.

Question 19

The "and-one" risk is a factor against intentional fouling when leading by 3.

Question 20

Win probability models assume all teams have equal talent if not otherwise specified.

Section C: Short Answer (4 points each)

Question 21

A team is down 7 points with 100 seconds remaining. Using the fouling thresholds from the chapter: a) Should they start intentionally fouling? b) What is the reasoning behind your answer?

Question 22

Explain why single-season clutch shooting percentage is unreliable. Include a numerical example showing the standard error for 100 clutch shot attempts.

Question 23

Define leverage index and explain why a tie game with 30 seconds left has higher leverage than the same tie game in the first quarter.

Question 24

A player shot 52% in clutch situations on 75 attempts and 44% in non-clutch on 800 attempts. Calculate the clutch differential and explain whether this difference is likely meaningful.

Question 25

Describe the key tradeoff in two-for-one situations: what do you sacrifice and what do you gain?

Section D: Problem Solving (6 points each)

Question 26

Foul or Defend Analysis

Your team leads by 3 points with 8 seconds remaining. The opponent has the ball at mid-court.

Given: - Opponent 3PT%: 34% - Opponent FT%: 78% - Probability of and-one foul: 4%

Calculate the expected outcomes for: a) Defending (allowing a 3-point attempt) b) Fouling (putting them on the line for 2 FTs)

Which strategy has higher win probability?

Question 27

Two-for-One Expected Value

With 37 seconds remaining in the half: - Your quick shot EV: 0.90 points (uses 7 seconds) - Your normal shot EV: 1.12 points (uses 18 seconds) - Opponent shot EV: 1.08 points (uses 16 seconds)

Calculate: a) Expected point differential if you attempt two-for-one b) Expected point differential if you play one-for-one c) Which is optimal?

Question 28

Pace and Win Probability

Team A is favored by 8 points. Assume variance of 3.0 points per possession.

Calculate win probability for Team A at: a) 90 possessions b) 100 possessions c) 110 possessions

Use the formula: WP = Phi(margin / sqrt(variance * possessions))

Question 29

Comeback Probability

Your team is down 10 points with 4 minutes remaining. Estimate: a) Possessions remaining (assume 15 seconds per possession) b) Points needed to tie c) If you shoot all 3s at 35%, what is P(scoring 10+ points)?

Use binomial or normal approximation.

Question 30

Game Theory Equilibrium

In a pick-and-roll, the offense chooses: Pass to roller (P) or Shoot (S) The defense chooses: Drop coverage (D) or Switch (W)

Payoff matrix (offensive expected points): | | Drop | Switch | |------|------|--------| | Pass | 1.3 | 0.8 | | Shoot| 0.9 | 1.2 |

Find the mixed strategy Nash equilibrium: a) Probability offense should Pass b) Probability defense should Drop c) Expected value at equilibrium

Section E: Essay Questions (8 points each)

Question 31

End-of-Game Decision Framework

Describe a comprehensive framework for end-of-game decision-making that a coach could use. Include: - Key factors to consider at each decision point - How to integrate win probability thinking - When to deviate from "optimal" analytical recommendations - The role of personnel and matchups in adjustments

Question 32

The Clutch Performance Debate

Present both sides of the debate on whether "clutch" is a real, persistent skill:

For clutch as a skill: - What evidence supports this view? - What psychological factors might enable clutch performance?

Against clutch as a distinct skill: - What statistical evidence suggests clutch is mostly noise? - How do sample size issues affect conclusions?

Your assessment: - What is the most likely truth based on available evidence? - How should teams use clutch data in decision-making?

Answer Key

Section A: Multiple Choice

  1. B - Final 5 minutes, score within 5 points
  2. B - Change in win probability from player actions
  3. A - Stop clock and gain more possessions
  4. B - 55% (110 ORtg / 2 FTs = 55% break-even)
  5. B - 30-40 seconds
  6. B - Faster pace increases variance
  7. C - Show weak correlation
  8. C - Players randomize to make opponents indifferent
  9. C - Mixed or negligible effects
  10. C - Fouling provides small advantage (~1-3%)

Section B: True/False

  1. False - Clutch performance shows limited persistence
  2. True - Expected FT points = 2 x FT%
  3. True - Definition of mixed strategy
  4. False - Favorites prefer lower pace (less variance)
  5. False - Timeout value increases late in close games
  6. True - Higher variance helps trailing team catch up quickly
  7. False - FT% typically declines 2-3% in clutch
  8. True - Quick shots often sacrifice some quality
  9. True - And-one results in 3 FTs, potentially tying
  10. False - Models can incorporate team strength differential

Section C: Short Answer

21. a) Yes, begin fouling (7 points, <100 seconds fits the 7-9 point threshold) b) At 7 points down with 100 seconds, you need approximately 6-7 possessions. Normal play yields ~6 possessions; fouling can generate 8-10, improving comeback chances.

  1. Standard error = sqrt(p(1-p)/n) = sqrt(0.45*0.55/100) = 0.050 = 5 percentage points 95% CI spans +/- 10 percentage points, meaning apparent "clutch" or "choke" could be entirely random.

  2. Leverage Index = expected WP swing in situation / average WP swing Tie game with 30 seconds: each possession could swing WP by 30-40% First quarter tie: each possession swings WP by only 1-2% LI is 15-20x higher late in close games.

  3. Clutch differential = 52% - 44% = +8 percentage points Standard error for 75 attempts: sqrt(0.480.52/75) = 0.058 = 5.8% The +8% is within ~1.5 standard errors; could be random variation. Likely not meaningful* without more data.

  4. Sacrifice: Shot quality on first possession (quick shot = lower EV) Gain: Extra possession to score; opponent can't run clock out Net benefit when extra possession value > shot quality sacrifice

Section D: Problem Solving

26. a) Defending: - P(make 3) = 0.34 -> Overtime (50% win) -> 0.17 win - P(miss 3) = 0.66 -> Win = 0.66 - Total WP defending = 0.66 + 0.17 = 0.83

b) Fouling: - Normal foul: P(make both) = 0.78^2 = 0.608 -> down 1, ~40% win - P(make one) = 20.780.22 = 0.343 -> up 2, ~95% win - P(miss both) = 0.22^2 = 0.048 -> up 3, win - And-one (4%): 0.78^3 = 0.474 (tie), rest lead - Total WP fouling = 0.040.55 + 0.96(0.6080.40 + 0.3430.95 + 0.048*1.0) - = 0.022 + 0.96*(0.243 + 0.326 + 0.048) = 0.022 + 0.592 = 0.614

Wait, let me recalculate more carefully: - P(and-one) = 4%: If they make all 3 FTs (78%^3 = 47%), tie -> 50% win - P(regular foul) = 96%: 2 FTs - Both make (61%): Down 1, we have ball back with time - One make (34%): Up 2, high win probability - Both miss (5%): Win

Defending (0.83) > Fouling (~0.80) - but close. Depends on parameters.

27. a) Two-for-one: - Your quick shot: 0.90 - Opponent shot: -1.08 - Your second shot: 1.12 - Net: 0.90 - 1.08 + 1.12 = +0.94

b) One-for-one (shoot at 18 seconds): - Your shot: 1.12 - Time left: 37 - 18 = 19 seconds - Opponent might get shot (~80% chance) - Net: 1.12 - 0.8*1.08 = 1.12 - 0.86 = +0.26

c) Two-for-one is optimal (+0.94 vs +0.26)

  1. Using WP = Phi(8 / sqrt(3 * possessions)): a) 90 poss: Phi(8 / sqrt(270)) = Phi(8/16.4) = Phi(0.488) = 0.687 b) 100 poss: Phi(8 / sqrt(300)) = Phi(8/17.3) = Phi(0.462) = 0.678 c) 110 poss: Phi(8 / sqrt(330)) = Phi(8/18.2) = Phi(0.440) = 0.670

Higher pace (more possessions) lowers the favorite's win probability.

29. a) 4 minutes = 240 seconds / 15 = 16 possessions b) 10 points needed c) Expected 3-pointers made: 16 * 0.35 = 5.6 Expected points: 5.6 * 3 = 16.8 SD of points: 3 * sqrt(16 * 0.35 * 0.65) = 3 * 1.9 = 5.7 P(10+) = P(Z > (10-16.8)/5.7) = P(Z > -1.19) = 0.88

Wait - that assumes all 3s. Let me recalculate: Using binomial: need at least 4 made 3s (12 points) P(X >= 4) where X ~ Binomial(16, 0.35) = 1 - P(X <= 3) = ~0.78

30. Let p = P(offense passes), q = P(defense drops)

Offense indifferent when: 1.3q + 0.8(1-q) = 0.9q + 1.2(1-q) 1.3q + 0.8 - 0.8q = 0.9q + 1.2 - 1.2q 0.5q + 0.8 = -0.3q + 1.2 0.8q = 0.4 q = 0.5 (Defense drops 50%)

Defense indifferent when: 1.3p + 0.9(1-p) = 0.8p + 1.2(1-p) 1.3p + 0.9 - 0.9p = 0.8p + 1.2 - 1.2p 0.4p + 0.9 = -0.4p + 1.2 0.8p = 0.3 p = 0.375 (Offense passes 37.5%)

c) EV = 1.3(0.375)(0.5) + 0.8(0.375)(0.5) + 0.9(0.625)(0.5) + 1.2(0.625)(0.5) = 0.244 + 0.150 + 0.281 + 0.375 = 1.05 points

Section E: Essay Questions

  1. Key points for full credit: - State assessment: time, score, possessions, timeouts, fouls, personnel - Decision categories: shot selection, fouling, timeout, pace, substitutions - Win probability framework: calculate WP change for each option - When to deviate: matchup advantages, player confidence, momentum - Personnel factors: FT shooters, defenders, ball handlers

  2. Key points for full credit: - For: Psychological composure, experience under pressure, some statistical signal - Against: Sample size limitations, regression to mean, weak year-to-year correlation - Assessment: Small signal may exist (~2-3% variance explained), but mostly noise - Practical use: Don't overweight clutch stats; use for tiebreakers, not primary evaluation

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

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