Chapter 17: Exercises - Team Offensive Efficiency

Section 17.1: Offensive Rating Fundamentals

Exercise 17.1

A team has the following statistics for a single game: - Field Goal Attempts: 88 - Free Throw Attempts: 24 - Offensive Rebounds: 11 - Turnovers: 14 - Points Scored: 112

Calculate the team's offensive rating for this game using the standard possession formula.

Exercise 17.2

Two teams both scored 105 points in their respective games. Team A played at a pace of 95 possessions while Team B played at a pace of 110 possessions. Calculate each team's offensive rating and explain which team was more efficient.

Exercise 17.3

The standard possession formula uses a coefficient of 0.44 for free throw attempts. Explain why this coefficient is not 0.5 (which would represent two free throws per trip) and list three specific game situations that necessitate this adjustment.

Exercise 17.4

Using the advanced possession formula that incorporates offensive rebounding adjustment: $$\text{Possessions}_{adj} = \text{FGA} + 0.44 \times \text{FTA} - 1.07 \times \frac{\text{OREB} \times (\text{FGA} - \text{FGM})}{\text{FGA} - \text{FGM} + \text{OREB}} + \text{TOV}$$

Calculate possessions for a team with: - FGA: 85, FGM: 38, FTA: 22, OREB: 12, TOV: 13

Compare this to the standard formula result.

Exercise 17.5

A team's offensive rating improved from 108.5 to 112.3 between two consecutive seasons. The league average offensive rating also improved from 109.2 to 111.8. Calculate the team's relative offensive rating change and assess whether their improvement was truly meaningful.

Section 17.2: Individual vs. Team Offensive Rating

Exercise 17.6

Player A has the following per-game statistics: - Points: 22.5 - FGA: 18.2 - FTA: 5.8 - Assists: 4.2 - Turnovers: 2.8

Estimate this player's individual possessions used per game and calculate their approximate usage rate assuming the team averages 100 possessions per game and the player plays 34 minutes.

Exercise 17.7

A player has an individual offensive rating of 118 with a usage rate of 28%. Another player has an individual offensive rating of 122 with a usage rate of 15%. Using the expected relationship between usage and efficiency, determine which player is performing better relative to expectations.

Exercise 17.8

The team's offensive rating is 112.5 when Player X is on the court and 108.2 when Player X is off the court. Player X's individual offensive rating is 115.3. Reconcile these numbers and explain what each metric tells us about Player X's offensive contribution.

Exercise 17.9

Calculate the Points Produced for a player with: - FGM: 7 (including 2 three-pointers) - FTM: 4 (on 5 FTA) - Assists: 6 (assume teammates average 2.3 points per assisted shot) - Estimated 55% of made shots were unassisted

Exercise 17.10

A team's starting lineup has an offensive rating of 116.4 when all five starters play together. When the team's highest-usage player (32% usage) is replaced, the lineup's offensive rating drops to 108.7. Analyze this drop in terms of shot creation, spacing effects, and gravity.

Section 17.3: Play Type Analysis

Exercise 17.11

Given the following play type efficiency data for a team: | Play Type | Frequency | PPP | |-----------|-----------|-----| | Transition | 16% | 1.15 | | Pick & Roll (BH) | 22% | 0.94 | | Spot-Up | 20% | 1.02 | | Isolation | 10% | 0.85 | | Post-Up | 8% | 0.91 | | Cut | 7% | 1.25 | | Other | 17% | 0.92 |

Calculate the team's weighted offensive efficiency across all play types.

Exercise 17.12

A team wants to increase their offensive efficiency by shifting play type distribution. Currently they run 8% isolation plays at 0.85 PPP. If they reduce isolation to 4% and redistribute those possessions to spot-up (0.96 PPP league average), calculate the expected point differential over 100 possessions.

Exercise 17.13

Calculate the Play Type Versatility Index for a team with the following relative efficiencies (team PPP / league PPP): - Transition: 1.05 - Pick & Roll: 1.08 - Isolation: 0.92 - Spot-Up: 1.03 - Post-Up: 0.88

Each play type is weighted by its frequency (20% each for this simplified example).

Exercise 17.14

Compare two teams' offensive strategies:

Team A: 35% of possessions are transition/cuts (1.18 PPP), 65% are half-court sets (1.02 PPP)

Team B: 18% of possessions are transition/cuts (1.22 PPP), 82% are half-court sets (1.08 PPP)

Which team is more efficient overall? Which has the better half-court offense?

Exercise 17.15

A team's pick-and-roll ball handler efficiency dropped from 0.95 PPP to 0.88 PPP after opposing teams started blitzing the ball handler. Calculate how the team should adjust their pick-and-roll frequency if their roll man efficiency is 1.12 PPP and the blitz creates 2 additional roll man opportunities per 10 pick-and-roll possessions.

Section 17.4: Spacing and Floor Balance

Exercise 17.16

Calculate the average spacing for a lineup with players at the following positions (in feet from the baseline and sideline): - Player 1: (8, 25) - Player 2: (24, 5) - Player 3: (24, 45) - Player 4: (18, 15) - Player 5: (18, 35)

Exercise 17.17

A lineup has three players shooting above 38% from three and two players shooting below 30%. Using the spacing score formula: $$\text{Spacing Score} = (\text{Shooters}/5) \times 50 + (\text{Weighted 3PT\%}/0.40) \times 50$$

Calculate the lineup's spacing score if the weighted team three-point percentage is 35.5%.

Exercise 17.18

Compare the convex hull area for two lineups:

Lineup A (positions in feet): (5, 20), (5, 30), (22, 10), (22, 40), (15, 25)

Lineup B (positions in feet): (8, 15), (8, 35), (18, 20), (18, 30), (12, 25)

Which lineup has better spacing based on hull area?

Exercise 17.19

A team has a paint touch rate of 58% and generates 1.18 PPP on possessions with paint touches versus 0.94 PPP on possessions without. If they could increase paint touch rate to 65% without changing efficiency, calculate the expected change in overall offensive rating.

Exercise 17.20

Calculate the Floor Balance Index for a lineup where players are distributed across court quadrants as follows: - Far Right (Q1): 1 player - Near Right (Q2): 2 players - Near Left (Q3): 0 players - Far Left (Q4): 2 players

Section 17.5: Ball Movement and Passing

Exercise 17.21

A team averages 285 passes per game across 102 possessions. Calculate: a) Passes per possession b) If their potential assist rate is 28% and assist conversion rate is 54%, how many assists do they average?

Exercise 17.22

Calculate the Ball Movement Efficiency Score for a team with: - Passes per possession: 3.2 - Average touch time: 2.8 seconds - Potential assist rate: 26% - Assist conversion rate: 52%

Use weights of 0.25 for each component and the normalization standards from the chapter.

Exercise 17.23

Build a simple passing network for a five-player lineup given the following assist matrix (rows are passers, columns are scorers):

Calculate the out-degree centrality for each player.

Exercise 17.24

Calculate the ball distribution entropy for a team where touch percentages are: - Player 1: 32% - Player 2: 25% - Player 3: 20% - Player 4: 15% - Player 5: 8%

Compare this to the maximum possible entropy for five players.

Exercise 17.25

A team's assist network shows the following: - Network density: 0.62 - Max out-degree centrality: 0.45 - Mean out-degree centrality: 0.18

Classify this team's offensive topology and explain your reasoning.

Section 17.6: Half-Court vs. Transition

Exercise 17.26

A team has the following efficiency splits: - Transition (0-6 seconds): 1.18 PPP, 14% frequency - Early offense (7-14 seconds): 1.08 PPP, 28% frequency - Late shot clock (15-24 seconds): 1.02 PPP, 58% frequency

Calculate their overall offensive efficiency and the value of increasing transition frequency by 5 percentage points (taken from late shot clock possessions) without changing efficiencies.

Exercise 17.27

Compare optimal pace strategies for two teams: - Team A: Transition ORtg 118, Half-court ORtg 105 - Team B: Transition ORtg 112, Half-court ORtg 110

Which team benefits more from increasing pace? Calculate the break-even point where transition and half-court efficiency would be equal for each team.

Exercise 17.28

A team generates transition opportunities from: - Defensive rebounds: 22% lead to transition (8 DREBs per game average) - Steals: 65% lead to transition (7 steals per game) - After made baskets: 8% lead to transition (38 opponent makes per game)

Calculate total transition possessions per game and compare to league average of 15 per game.

Exercise 17.29

Analyze shot clock efficiency decay using the following data: | Shot Clock | eFG% | Sample Size | |------------|------|-------------| | 22-24 sec | 58% | 450 | | 18-22 sec | 54% | 680 | | 14-18 sec | 51% | 890 | | 8-14 sec | 49% | 1250 | | 0-8 sec | 44% | 730 |

Calculate the weighted average eFG% and determine the efficiency cost of each second off the shot clock.

Exercise 17.30

A coach wants to push pace. Current stats: 95 possessions/game, 108 ORtg, 106 DRtg. Projections with faster pace: 102 possessions/game, 106 ORtg, 108 DRtg. Calculate expected point differential per game for both scenarios.

Section 17.7-17.8: Shot Creation and Conversion

Exercise 17.31

Calculate expected points for each shot zone using the following data: | Zone | Attempts | League FG% | Value | |------|----------|------------|-------| | Restricted Area | 28 | 63% | 2 | | Paint (non-RA) | 12 | 40% | 2 | | Mid-Range | 15 | 42% | 2 | | Corner 3 | 8 | 39% | 3 | | Above Break 3 | 25 | 36% | 3 |

Exercise 17.32

A team shot 42% from three on 850 attempts last season. Calculate their regressed three-point percentage using a regression factor of 250 and a league average prior of 36%.

Exercise 17.33

Player A's shot creation value (xPTS generated) is +45 over the season while their shot conversion value (actual minus expected) is -38. Player B has shot creation of +12 and conversion of +25. Which player contributed more total value? Which would you prioritize in roster construction?

Exercise 17.34

Calculate the team's shot quality defense versus shot conversion luck using: - Opponent xFG%: 48.5% - Opponent actual FG%: 46.2% - Sample size: 3,200 shots

Determine if the difference is statistically significant at the 95% confidence level.

Exercise 17.35

A team's shot profile shows: - 35% at rim (1.26 expected value per shot) - 8% paint non-RA (0.80 EV) - 22% mid-range (0.84 EV) - 35% three-pointers (1.08 EV)

Calculate the optimization potential if they shifted 10% of mid-range shots to three-pointers, assuming their three-point EV drops to 1.02 due to more contested attempts.

Section 17.9: Four Factors and Integration

Exercise 17.36

Calculate Dean Oliver's Four Factors for a team with: - FGM: 42, FGA: 88, 3PM: 12 - TOV: 14, Possessions: 98 - OREB: 11, Opponent DREB: 32 - FTM: 18, FTA: 22

Exercise 17.37

Using the Four Factors weights (eFG%: 40%, TOV%: 25%, OREB%: 20%, FTr: 15%), calculate the composite offensive score for two teams:

Team A: eFG% 54%, TOV% 13%, OREB% 28%, FTr 0.25 Team B: eFG% 51%, TOV% 10%, OREB% 32%, FTr 0.32

Exercise 17.38

A team ranks 5th in eFG%, 22nd in turnover rate, 18th in offensive rebounding rate, and 8th in free throw rate. Using percentile rankings, calculate their expected offensive rating percentile.

Exercise 17.39

Classify a team's offensive archetype given: - Transition frequency: 19% - Three-point rate: 42% - Isolation frequency: 7% - Post-up frequency: 4% - Assist rate: 62%

Exercise 17.40

Build a comprehensive offensive profile for a team with: - Offensive Rating: 114.5 - Four Factors: eFG% 55.2%, TOV% 12.8%, OREB% 26.5%, FTr 0.28 - Play Type Versatility Index: 103.5 - Shot Creation Value: +2.5 per 100 possessions - Top Play Type: Transition (1.18 PPP, 16% frequency) - Weakest Play Type: Post-up (0.82 PPP, 5% frequency)

Summarize their offensive identity and suggest one area for improvement.