Chapter 18: Exercises - Team Defensive Analytics

Section 18.1: Defensive Rating Fundamentals

Exercise 18.1

A team has the following statistics for a single game: - Points Allowed: 108 - Opponent FGA: 85 - Opponent FTA: 22 - Opponent OREB: 10 - Opponent TOV: 16

Calculate the team's Defensive Rating for this game.

Exercise 18.2

Two teams have the following season statistics: - Team A: 9,100 points allowed, 8,400 possessions, league average DRtg: 112.0 - Team B: 8,800 points allowed, 8,200 possessions, league average DRtg: 112.0

Calculate each team's Defensive Rating and relative Defensive Rating. Which team has better defense?

Exercise 18.3

The league average Defensive Rating has increased from 106.5 in 2014-15 to 114.2 in 2023-24. A team had a DRtg of 103.5 in 2014-15 and 111.8 in 2023-24. Analyze whether their defense actually declined or if they maintained their relative position.

Exercise 18.4

Using both teams' statistics for more accurate possession estimation, calculate possessions for a game where: - Home Team: FGA 88, FTA 24, OREB 12, TOV 14 - Away Team: FGA 91, FTA 20, OREB 9, TOV 15

Exercise 18.5

A team's Defensive Rating by quarter is: Q1: 105.2, Q2: 112.8, Q3: 108.5, Q4: 118.2. Possessions by quarter: Q1: 26, Q2: 24, Q3: 25, Q4: 28. Calculate the weighted game Defensive Rating and analyze the pattern.

Section 18.2: Rim Protection Analysis

Exercise 18.6

A rim protector has the following season statistics: - Shots contested at rim: 485 - Opponent makes when contested: 262 - Minutes played: 2,450 - League average FG% at rim: 65.2%

Calculate their DFG% at rim, contests per 36 minutes, and estimated points saved per game.

Exercise 18.7

Compare two rim protectors: - Player A: 54.2% DFG at rim, 9.2 contests per 36 minutes - Player B: 58.8% DFG at rim, 6.5 contests per 36 minutes

Calculate which player provides more value assuming league average rim FG% is 65%.

Exercise 18.8

A team's opponent rim shot frequency is 28.5% when their starting center is on court and 34.2% when he's off court. The rim FG% is 56.8% on vs. 63.2% off. Quantify the total defensive impact of this player's presence.

Exercise 18.9

Calculate the deterrence effect for a rim protector given: - Opponent drives per 100 possessions with player on: 42.5 - Opponent drives per 100 possessions with player off: 51.8 - Opponent PPP on drives with player on: 0.95 - Opponent PPP on drives with player off: 1.12

Exercise 18.10

A drop coverage scheme yields the following results: - Rim FG% allowed: 54.2% - Mid-range FG% allowed: 48.5% - Three-point FG% allowed: 38.2% - Shot distribution: 32% rim, 22% mid-range, 46% three

Calculate the weighted defensive efficiency and compare to a switch scheme with: 58.5% rim, 42.2% mid-range, 35.8% three, and distribution 38% rim, 15% mid-range, 47% three.

Section 18.3: Perimeter Defense

Exercise 18.11

A perimeter defender has the following statistics: - Three-point contests: 245 - Opponent makes on contests: 82 - Team opponent 3P% with player on: 34.8% - Team opponent 3P% with player off: 36.5%

Calculate their direct contest DFG% and on-off differential. Discuss the reliability of each metric.

Exercise 18.12

Analyze closeout quality data for a team: | Closeout Distance | Attempts | FG% | Frequency | |-------------------|----------|-----|-----------| | 0-3 feet (tight) | 320 | 31.2% | 22% | | 3-5 feet (good) | 480 | 34.8% | 33% | | 5-8 feet (late) | 420 | 38.5% | 29% | | 8+ feet (very late) | 230 | 41.2% | 16% |

Calculate the weighted three-point percentage allowed and the potential improvement if all late closeouts became good closeouts.

Exercise 18.13

A player's isolation defense statistics show: - Possessions defended: 185 - Points allowed: 158 - Turnovers forced: 22 - Fouls committed: 18

Calculate their PPP allowed in isolation. If the league average is 0.88 PPP, how does this player compare?

Exercise 18.14

Calculate the variance in three-point defense for a player with: - 150 three-point shots contested - 54 makes allowed (36.0%)

What is the 95% confidence interval? At what sample size would the confidence interval narrow to +/- 3 percentage points?

Exercise 18.15

A team's pick-and-roll ball handler defense shows: - Drop coverage: 0.82 PPP allowed, 55% of possessions - Switch: 0.95 PPP allowed, 30% of possessions - Blitz: 1.02 PPP allowed, 15% of possessions

Calculate the weighted PPP allowed. If blitzing could be reduced to 5% (redistributed to drop), what's the expected improvement?

Section 18.4: Defensive Versatility

Exercise 18.16

Calculate the versatility score for a player with the following matchup distribution: | Position | % of Time | PPP Allowed | League Avg PPP | |----------|-----------|-------------|----------------| | PG | 15% | 0.92 | 0.95 | | SG | 35% | 0.88 | 0.90 | | SF | 30% | 0.85 | 0.88 | | PF | 15% | 0.95 | 0.92 | | C | 5% | 1.15 | 1.02 |

Exercise 18.17

Analyze switching effectiveness for two players: - Player A: 85 switches received, 0.78 PPP allowed, 12% turnover rate - Player B: 142 switches received, 0.92 PPP allowed, 8% turnover rate

Which player is the more effective switch defender? Consider both quality and volume.

Exercise 18.18

A team wants to implement a switch-everything defense. Their roster's isolation defense PPP by player: - Player 1: 0.82 - Player 2: 0.88 - Player 3: 0.91 - Player 4: 0.95 - Player 5: 1.12

Calculate the expected isolation PPP allowed if opponents target each player proportionally to their weakness. What is the "weakest link" problem here?

Exercise 18.19

Calculate matchup entropy for two defenders: - Defender A: PG 45%, SG 30%, SF 20%, PF 5%, C 0% - Defender B: PG 15%, SG 25%, SF 30%, PF 20%, C 10%

Which defender has more versatility based on entropy? What are the limitations of this measure?

Exercise 18.20

A team's five-man lineup has the following switch success rates: | Matchup Type | Success Rate | Frequency | |--------------|--------------|-----------| | Guard-Guard | 78% | 35% | | Guard-Wing | 65% | 25% | | Wing-Wing | 72% | 20% | | Wing-Big | 58% | 12% | | Big-Guard | 42% | 8% |

Calculate the overall switch success rate and identify the most problematic matchup type.

Section 18.5: Shot Quality Defense

Exercise 18.21

Calculate expected FG% for the following shots using the base rates and adjustments provided: | Shot | Distance | Zone | Contest Level | |------|----------|------|---------------| | A | 4 ft | Rim | Tight | | B | 12 ft | Short Mid | Open | | C | 26 ft | Above Break 3 | Contested | | D | 24 ft | Corner 3 | Wide Open |

Base rates: Rim 65%, Short Mid 40%, Long Mid 38%, Corner 3 39%, Above Break 3 36% Adjustments: Wide Open +5%, Open +2%, Contested -3%, Tight -8%

Exercise 18.22

A team's shot quality defense metrics show: - Opponent expected FG%: 49.2% - Opponent actual FG%: 47.8% - Sample size: 4,200 shots

Calculate the xFG vs actual differential. Is this difference likely due to skill or luck? Use a significance test to support your answer.

Exercise 18.23

Compare shot quality defense for two teams: | Metric | Team A | Team B | |--------|--------|--------| | Opponent xFG% | 48.5% | 51.2% | | Opponent actual FG% | 49.2% | 48.8% | | Shots against | 5,200 | 5,100 |

Which team has better underlying defense? Which team has been "luckier"?

Exercise 18.24

A team allows the following shot distribution: | Zone | % of Shots | FG% Allowed | xFG% | |------|------------|-------------|------| | Rim | 28% | 62.5% | 64.0% | | Paint | 12% | 38.2% | 40.0% | | Mid-Range | 18% | 44.5% | 41.0% | | Corner 3 | 10% | 42.8% | 39.0% | | Above Break 3 | 32% | 35.2% | 36.0% |

Calculate the shot quality efficiency (xPTS per shot) and actual efficiency. Where is the team exceeding expectations, and where is it underperforming?

Exercise 18.25

Project shot quality regression for a team: - Current opponent 3P%: 33.5% (below league average of 36.5%) - Three-point attempts against: 2,800 - Regression factor: 300

What is the regressed opponent 3P%? How many additional points should they expect to allow over the remaining 1,200 attempts?

Section 18.6: Defensive Rebounding

Exercise 18.26

Calculate defensive rebounding metrics for a team: - Team DRB: 2,850 - Opponent ORB: 820 - Opponent FGA: 6,450 - Opponent FGM: 2,890 - Opponent second chance points: 985 - Total points allowed: 8,650

Exercise 18.27

Compare two rebounders' defensive rebounding: - Player A: 8.2 DRB/game, 75.5% DRB rate, plays 32 minutes - Player B: 6.8 DRB/game, 78.2% DRB rate, plays 28 minutes

Who is the better defensive rebounder? Consider per-minute production and rate metrics.

Exercise 18.28

A team's box-out analysis shows: | Player | Box-outs per game | Success Rate | |--------|-------------------|--------------| | Center | 8.5 | 72% | | PF | 5.2 | 68% | | SF | 3.8 | 62% | | SG | 2.1 | 58% | | PG | 1.2 | 55% |

Calculate the team's total expected rebounds from box-outs per game.

Exercise 18.29

Analyze the rim protection vs. rebounding tradeoff: - Aggressive rim protection: 52% opponent rim FG%, 68% DRB rate - Conservative positioning: 58% opponent rim FG%, 76% DRB rate - Opponent rim attempts: 28 per game - Opponent total misses: 35 per game

Calculate which approach yields lower expected points (including second chances at 1.2 PPP).

Exercise 18.30

A center's contested rebound rate is 65% (vs. 45% team average). They grab 4.2 contested DRB per game. Calculate the additional value they provide assuming contested rebounds are worth 0.4 possessions more than uncontested rebounds (due to preventing opponent second chances).

Section 18.7: Transition Defense

Exercise 18.31

Calculate transition defense metrics: - Transition possessions against: 1,245 - Transition points allowed: 1,432 - Total possessions against: 8,150 - Total points allowed: 9,120 - Half-court points allowed: 7,688

Exercise 18.32

A team's transition opportunities against come from: | Source | Frequency | PPP Allowed | |--------|-----------|-------------| | Turnovers | 38% | 1.28 | | Missed shots | 45% | 1.15 | | After made baskets | 17% | 1.05 |

Calculate the weighted transition PPP allowed and identify the area most needing improvement.

Exercise 18.33

Analyze a player's transition defense impact: - Team transition frequency with player on: 14.2% - Team transition frequency with player off: 18.5% - Team transition PPP allowed with player on: 1.08 - Team transition PPP allowed with player off: 1.22

Quantify this player's total transition defense value per 100 possessions.

Exercise 18.34

A team averages 15 live-ball turnovers per game with 72% leading to transition opportunities. Their transition PPP allowed is 1.25. If they reduce turnovers to 12 per game (same transition rate), how many points per game would they save?

Exercise 18.35

Compare two teams' transition defense philosophies: - Team A: Contest every transition (1.18 PPP allowed, 16% frequency) - Team B: Get back and set defense (1.08 PPP allowed, 12% frequency)

Calculate the defensive impact of each approach over 100 total possessions.

Section 18.8: Individual vs. Team Defensive Metrics

Exercise 18.36

Calculate on-off defensive differential for a player: - Team DRtg with player on: 105.8 (1,850 possessions) - Team DRtg with player off: 112.4 (1,420 possessions)

What is the on-off differential? What sample size considerations should we keep in mind?

Exercise 18.37

Using simplified RAPM methodology, estimate defensive contribution for three players who always play together: - Combined on-court DRtg: 102.5 - League average DRtg: 112.0 - Individual box score indicators: Player A (2.1 STL, 1.8 BLK), Player B (1.5 STL, 0.3 BLK), Player C (0.8 STL, 0.2 BLK)

Propose a reasonable allocation of the 9.5-point defensive improvement among the three players.

Exercise 18.38

A player has the following multi-year defensive metrics: | Season | D-RAPM | On-Off | DRtg On | Minutes | |--------|--------|--------|---------|---------| | Year 1 | -1.8 | +4.2 | 106.5 | 2,100 | | Year 2 | -0.5 | +2.1 | 109.2 | 2,450 | | Year 3 | -2.2 | +5.8 | 104.8 | 2,280 |

Calculate the weighted average D-RAPM using minutes as weights. What does the year-to-year variation suggest about reliability?

Exercise 18.39

Build a composite defensive score for a player using these metrics and weights: - D-RAPM: -1.5 (weight: 25%) - On-Off Diff: +3.2 (weight: 20%) - DFG% at rim: 56.2% (weight: 15%) - Contests per 36: 14.5 (weight: 15%) - Versatility score: 72 (weight: 15%) - Steal rate: 2.1% (weight: 10%)

Normalize each to a 0-100 scale where 50 is league average.

Exercise 18.40

A team needs to evaluate which player to acquire for their switch-heavy defense: - Player A: Elite isolation defense (0.75 PPP), poor rim protection (62% DFG), high versatility (guards 1-4) - Player B: Good isolation defense (0.88 PPP), elite rim protection (54% DFG), limited versatility (guards 4-5)

Given the team's scheme, develop a framework to evaluate which player provides more value. Consider both direct defensive impact and scheme fit.