Chapter 20: Exercises - Game Strategy and Situational Analysis

Section 20.1: Clutch Performance Analysis

Exercise 20.1 (Basic)

Define "clutch time" according to the NBA's official definition. What are the specific criteria for time remaining and score differential?

Exercise 20.2 (Basic)

A player has the following performance splits: - Non-clutch: 22.5 PPG on 56% TS% - Clutch: 4.2 PPG on 51% TS% (in 8.5 clutch minutes per game)

Calculate the per-36-minute clutch scoring rate and compare to non-clutch. Is this player underperforming in clutch situations?

Exercise 20.3 (Intermediate)

Explain why single-season clutch statistics are unreliable indicators of a player's true clutch ability. Use sample size calculations to support your answer.

Exercise 20.4 (Intermediate)

A player has taken 120 clutch field goal attempts over a season with a true talent shooting percentage of 45%. Calculate: a) The standard error of their observed clutch shooting percentage b) The 95% confidence interval around their true ability c) Interpret what this means for evaluating "clutch" performance

Exercise 20.5 (Advanced)

Design a statistical test to determine whether a player's clutch performance differs significantly from their non-clutch performance. What p-value threshold would you use, and how would you adjust for multiple comparisons across many players?

Section 20.2: End-of-Game Decision Making

Exercise 20.6 (Basic)

List the six key categories of end-of-game decisions discussed in the chapter. Give one example situation for each.

Exercise 20.7 (Basic)

Your team is down 4 points with 45 seconds remaining and has possession. List the key factors you would consider in deciding your offensive approach.

Exercise 20.8 (Intermediate)

Create a decision tree for the following scenario: - Down 3 points, 18 seconds remaining - Opponent has possession - Your team has one foul to give before bonus

Map out the possible outcomes and decision points.

Exercise 20.9 (Intermediate)

A win probability model shows your team has a 35% chance of winning when down 5 points with 2 minutes left. After a made three-pointer (now down 2 with 1:48 left), the model shows 42%. Calculate the WPA (Win Probability Added) for that three-pointer.

Exercise 20.10 (Advanced)

Implement a function that takes current game state (score differential, time remaining, possession, timeouts, fouls) and returns win probability using a simplified model.

Section 20.3: Intentional Fouling Strategy

Exercise 20.11 (Basic)

When trailing, what is the primary reason for intentionally fouling? Explain the time-vs-points tradeoff.

Exercise 20.12 (Basic)

Your opponent shoots 78% from the free throw line. Calculate the expected points from two free throw attempts.

Exercise 20.13 (Intermediate)

Given the following scenario: - Down 6 points, 90 seconds remaining - Opponent FT%: 72% - Our 3PT%: 36% - Normal possession time: 16 seconds - Time to commit foul: 5 seconds

Calculate whether fouling increases expected possessions enough to improve comeback probability.

Exercise 20.14 (Intermediate)

The "Hack-a-Shaq" strategy targets poor free throw shooters. For a team with a 108 offensive rating, what is the break-even free throw percentage below which intentional fouling is beneficial?

Exercise 20.15 (Advanced)

Build a simulation that compares win probability when: a) Fouling immediately when down 8 points with 2 minutes left b) Playing defense normally for the first minute, then fouling c) Never intentionally fouling

Run 10,000 simulations and compare outcomes.

Section 20.4: Timeout Usage Optimization

Exercise 20.16 (Basic)

List five strategic purposes that timeouts serve beyond simply stopping the clock.

Exercise 20.17 (Basic)

Your team has 3 timeouts remaining with 4 minutes left in a close game. The opponent just scored their 8th straight point to take a 2-point lead. Should you call timeout? Justify your answer.

Exercise 20.18 (Intermediate)

Research suggests the "momentum" effect of timeouts stopping opponent runs may be overstated. Explain why regression to the mean might explain apparent timeout effectiveness.

Exercise 20.19 (Intermediate)

Design a decision rule for timeout usage that balances: - Immediate need (opponent run, fatigue) - Future option value (late-game situations) - Timeout inventory

Express your rule in terms of specific thresholds.

Exercise 20.20 (Advanced)

Create a simple expected value model for timeout decisions that compares V_now (value of calling timeout now) to E[V_later] * P(need later). What factors influence each component?

Section 20.5: Pace Manipulation

Exercise 20.21 (Basic)

Explain why a heavily favored team should prefer to slow the pace, while an underdog should prefer to increase it.

Exercise 20.22 (Basic)

Two teams play a game with an expected margin of 6 points for Team A. If the game has 95 possessions versus 105 possessions, how does this affect the variance of the final margin?

Exercise 20.23 (Intermediate)

Your team is protecting a 6-point lead with 3 minutes remaining. The opponent's offensive rating is 112. Calculate: a) How many possessions they need to catch up b) What pace (possessions per minute) would give them enough chances c) Your target possession length to limit their opportunities

Exercise 20.24 (Intermediate)

A team is a 7-point underdog. Using a variance of 3.0 points per possession, calculate their win probability at 90 possessions versus 110 possessions. Which pace should they prefer?

Exercise 20.25 (Advanced)

Implement a function that takes expected margin and pace, then calculates win probability using a normal distribution model. Create a visualization showing how win probability changes with pace for different expected margins.

Section 20.6: Two-for-One Situations

Exercise 20.26 (Basic)

Define a "two-for-one" situation and explain when it typically occurs (how many seconds remaining in a period).

Exercise 20.27 (Basic)

If a quick shot has an expected value of 0.92 points and a normal possession has 1.08 points, calculate the two-for-one advantage when successful (assuming you get both possessions while opponent gets one).

Exercise 20.28 (Intermediate)

Analyze this two-for-one scenario: - 38 seconds remaining in the quarter - Quick shot EV: 0.95 points (8 seconds used) - Normal shot EV: 1.10 points (18 seconds used) - Opponent EV: 1.08 points

Calculate expected point differential for two-for-one vs. one-for-one strategies.

Exercise 20.29 (Intermediate)

When does two-for-one backfire? List three specific situations where taking a quick shot to get two possessions is suboptimal.

Exercise 20.30 (Advanced)

Build a model that determines the optimal time threshold for attempting two-for-one based on: - Your team's quick shot efficiency - Your team's normal possession efficiency - Opponent's efficiency - Shot clock length

Section 20.7: Three-Point Shooting Strategy

Exercise 20.31 (Basic)

A team is down 8 points with 2 minutes remaining. Should they prioritize three-point shots? Why or why not?

Exercise 20.32 (Basic)

Compare the expected value and variance of: a) 10 two-point attempts at 50% b) 10 three-point attempts at 35%

Exercise 20.33 (Intermediate)

Your team is down 12 points with 3 minutes left (approximately 9 possessions). Calculate: a) Expected points from all 3-pointers (35%) b) Expected points from all 2-pointers (52%) c) Probability of scoring 12+ points with each strategy (use normal approximation)

Exercise 20.34 (Intermediate)

Research shows league-average 3PT% drops 1-2% in clutch situations. If a player normally shoots 38% from three, what is their expected clutch percentage? How should this affect shot selection?

Exercise 20.35 (Advanced)

Create a simulation comparing comeback probabilities for different shot selection strategies when trailing by various amounts (5, 10, 15 points) with 3 minutes remaining.

Section 20.8: Free Throw Shooting Under Pressure

Exercise 20.36 (Basic)

Why might free throw shooting decline in high-pressure situations despite being mechanically identical to practice conditions?

Exercise 20.37 (Basic)

A player shoots 82% from the line in non-clutch and 78% in clutch situations over their career. Calculate the differential and discuss whether this is meaningful.

Exercise 20.38 (Intermediate)

Analyze whether "icing the shooter" (calling timeout before free throws) is effective: - Control group: 78.2% FT% (no timeout) - Iced: 76.8% FT% (timeout called before) - Sample: 500 attempts each

Is this difference statistically significant?

Exercise 20.39 (Intermediate)

Design a study to test whether clutch free throw shooting is a persistent skill. What data would you need, and what statistical approach would you use?

Exercise 20.40 (Advanced)

Build a model that predicts clutch free throw performance based on: - Career FT% - Situation severity (score margin, time remaining) - Home/away - Previous shot result

Section 20.9: Game Theory Applications

Exercise 20.41 (Basic)

Explain the concept of a mixed strategy equilibrium using a basketball example.

Exercise 20.42 (Basic)

In a simple shot-or-drive decision, the payoff matrix is: | | Defend Shot | Defend Drive | |----------|-------------|--------------| | Shoot | 0.85 | 1.15 | | Drive | 1.25 | 0.70 |

Find the Nash equilibrium mixing probabilities.

Exercise 20.43 (Intermediate)

Your team leads by 3 with 10 seconds left. The opponent has the ball. Should you foul? Analyze using game theory, considering: - Their 3PT%: 36% - Their FT%: 76% - Probability of and-one foul: 3%

Exercise 20.44 (Intermediate)

Explain how a team should adjust their strategy when facing an opponent that deviates from equilibrium play. Provide a specific example.

Exercise 20.45 (Advanced)

Simulate the "foul up 3" decision 100,000 times with varying parameters (3PT%, FT%, and-one rate). Create a heat map showing when fouling is optimal.

Section 20.10: Comprehensive Simulation

Exercise 20.46 (Project)

Build an end-of-game simulator that models the final 3 minutes of a game, including: - Possession outcomes (scoring, turnovers) - Fouling decisions - Timeout usage - Shot selection (2s vs 3s)

Exercise 20.47 (Project)

Using historical play-by-play data, analyze which teams make optimal end-of-game decisions: - Two-for-one execution - Fouling when trailing - Timeout usage - Shot selection when trailing

Exercise 20.48 (Project)

Create a decision support tool that, given current game state, recommends: - Whether to foul - Whether to call timeout - Shot selection priority - Pace recommendation

Exercise 20.49 (Case Study)

Analyze a specific playoff game's final 5 minutes, evaluating each strategic decision against optimal play. Calculate estimated win probability cost of suboptimal decisions.

Exercise 20.50 (Research)

Investigate whether teams have improved their end-of-game decision-making over the analytics era (2010-present). Compare two-for-one execution, fouling decisions, and shot selection across eras.

Challenge Problems

Challenge 20.1

Derive the optimal fouling threshold as a function of: - Time remaining - Score differential - Opponent FT% - Your team's 3PT% - Possession time

Express as a closed-form solution or algorithm.

Challenge 20.2

Build a complete Markov chain model for end-of-game basketball that tracks all possible states and transition probabilities. Use it to calculate exact win probabilities.

Challenge 20.3

Develop a reinforcement learning agent that learns optimal end-of-game strategy through simulation. Compare its decisions to human coaching.

Challenge 20.4

Create a comprehensive game theory model for late-game basketball that accounts for: - Both teams' strategic choices - Information asymmetries - Dynamic updating based on outcomes - Multiple decision points

Challenge 20.5

Design a real-time decision support system that could be used during games to: - Display current win probability - Recommend optimal actions - Show WPA for recent plays - Alert for suboptimal opponent decisions to exploit