Chapter 8 Quiz: Shooting Efficiency Metrics

Instructions

This quiz contains 25 questions covering shooting efficiency metrics from Chapter 8. Questions test your understanding of FG%, eFG%, TS%, shot selection, and the three-point revolution.

Scoring Guide: - Multiple Choice: 2 points each - True/False: 1 point each - Calculations: 4 points each - Short Answer: 3 points each

Section A: Field Goal Percentage (Questions 1-5)

Question 1 (Multiple Choice)

The fundamental limitation of Field Goal Percentage is that it:

a) Does not account for free throws b) Treats all made field goals as equal regardless of point value c) Cannot be calculated without play-by-play data d) Only applies to two-point shots

Question 2 (Calculation)

A player shoots 8-18 from two-point range and 4-12 from three-point range. Calculate: a) Overall FG% b) Total points scored (excluding free throws)

Question 3 (True/False)

League average FG% has remained relatively constant since the introduction of the three-point line.

Question 4 (Short Answer)

Explain when FG% remains a useful metric for player evaluation, despite its limitations.

Question 5 (Multiple Choice)

A player with 40% FG% who only shoots three-pointers produces more points per shot than a player with 50% FG% who only shoots two-pointers.

a) True, because 0.40 * 3 > 0.50 * 2 b) False, because 50% > 40% c) True, because three-pointers are always more efficient d) False, because the difference is negligible

Section B: Effective Field Goal Percentage (Questions 6-10)

Question 6 (Multiple Choice)

The eFG% formula gives made three-pointers a bonus of:

a) 0.25 additional makes b) 0.33 additional makes c) 0.50 additional makes d) 1.00 additional makes

Question 7 (Calculation)

Stephen Curry's 2015-16 season: 805 FGM, 402 3PM, 1598 FGA. Calculate his eFG%.

Question 8 (True/False)

For a player who never shoots three-pointers, eFG% equals FG%.

Question 9 (Short Answer)

Derive the eFG% formula starting from the goal of expressing points per shot in terms equivalent to two-point shooting.

Question 10 (Calculation)

Player A: 50% FG%, 0 three-pointers Player B: 35% FG%, all three-pointers

Who has the higher eFG%? Show your work.

Section C: True Shooting Percentage (Questions 11-16)

Question 11 (Multiple Choice)

The 0.44 coefficient in the TS% formula accounts for:

a) The probability of making a free throw b) The weighted average of different free throw situations c) The relationship between FGA and FTA d) Historical league averages

Question 12 (Calculation)

A player scores 25 points on 15 FGA and 8 FTA. Calculate their TS%.

Question 13 (True/False)

A player can have a TS% higher than 100%.

Question 14 (Short Answer)

Why is TS% considered the "gold standard" for measuring scoring efficiency? What does it capture that eFG% does not?

Question 15 (Calculation)

Player X: 20 PPG on 16 FGA, 4 FTA Player Y: 18 PPG on 12 FGA, 8 FTA

Calculate TS% for both players. Who is more efficient?

Question 16 (Multiple Choice)

True Shooting Attempts (TSA) is calculated as:

a) FGA + FTA b) FGA + 0.5 * FTA c) FGA + 0.44 * FTA d) FGA + 0.44 * FTM

Section D: Free Throw Rate and Shot Distribution (Questions 17-20)

Question 17 (Calculation)

A player attempts 800 FGA and 320 FTA in a season. Calculate their Free Throw Rate.

Question 18 (Multiple Choice)

Two free throws have an expected value of approximately:

a) 1.00 points b) 1.30 points c) 1.54 points d) 2.00 points

Question 19 (Short Answer)

Explain the concept of the "mid-range dead zone" and why analytics have led teams to reduce mid-range shooting.

Question 20 (True/False)

Corner three-pointers typically have higher expected value than above-the-break three-pointers.

Section E: The Three-Point Revolution (Questions 21-25)

Question 21 (Calculation)

If a player shoots 52% on two-pointers, what three-point percentage would produce equal expected value? (Use the break-even formula)

Question 22 (Multiple Choice)

NBA teams averaged approximately how many three-point attempts per game in 2023-24?

a) 15-20 b) 25-30 c) 34-38 d) 42-48

Question 23 (Short Answer)

Explain why the three-point revolution is described as "mathematically inevitable" once teams began using expected value analysis.

Question 24 (Calculation)

In 1994-95 (shortened three-point line), teams averaged 15.3 3PA at 35.9%. In 2023-24, teams averaged 35.1 3PA at 36.5%.

Calculate the expected points from three-point shooting per game for both seasons.

Question 25 (Short Answer)

Describe two counter-arguments or limitations to the heavy emphasis on three-point shooting in modern basketball.

Answer Key

Section A: Field Goal Percentage

Question 1: b) Treats all made field goals as equal regardless of point value

Question 2: a) FGM = 8 + 4 = 12; FGA = 18 + 12 = 30; FG% = 12/30 = 40.0% b) Points = (8 * 2) + (4 * 3) = 16 + 12 = 28 points

Question 3: False. League average FG% has fluctuated based on shot selection, defensive rules, and playing styles.

Question 4: Sample answer: FG% remains useful when (1) comparing players with similar shot profiles (e.g., two post players who rarely shoot threes), (2) analyzing zone-specific efficiency (FG% at the rim, mid-range, etc.), (3) comparing players within the same era and role, and (4) as a component of broader analysis when combined with shot distribution data.

Question 5: a) True, because 0.40 * 3 > 0.50 * 2 (1.20 > 1.00 expected points per shot)

Section B: Effective Field Goal Percentage

Question 6: c) 0.50 additional makes

Question 7: eFG% = (805 + 0.5 * 402) / 1598 * 100 = (805 + 201) / 1598 * 100 = 1006 / 1598 * 100 = 62.95%

Question 8: True

Question 9: Sample derivation: - Points from FG = 2 * FGM + 3PM (extra point for each three) - = 2 * FGM + 3PM - Points per FGA = (2 * FGM + 3PM) / FGA - To express as equivalent FG% (where 100% = 2 points): divide by 2 - eFG% = (FGM + 0.5 * 3PM) / FGA The 0.5 * 3PM term represents the half-credit for the extra point that three-pointers provide.

Question 10: - Player A: eFG% = FG% = 50% - Player B: eFG% = 35% * 1.5 = 52.5% (or: (0.35 + 0.5 * 0.35) / 1 = 52.5%) - Player B has the higher eFG%

Section C: True Shooting Percentage

Question 11: b) The weighted average of different free throw situations

Question 12: TSA = 15 + 0.44 * 8 = 15 + 3.52 = 18.52; TS% = 25 / (2 * 18.52) * 100 = 25 / 37.04 * 100 = 67.5%

Question 13: True. A player could theoretically have TS% > 100% if they scored primarily through and-one plays or technicals (getting points plus FTA without additional FGA cost).

Question 14: Sample answer: TS% is the gold standard because it accounts for all scoring methods: two-pointers, three-pointers, and free throws. eFG% only measures field goal efficiency and ignores free throws entirely. Since free throws are the most efficient shots in basketball (no defense, high conversion rate), TS% captures the value of players who draw fouls and score from the line. This provides a complete picture of a player's scoring efficiency per opportunity.

Question 15: - Player X: TSA = 16 + 0.44 * 4 = 17.76; TS% = 20 / (2 * 17.76) * 100 = 20 / 35.52 * 100 = 56.3% - Player Y: TSA = 12 + 0.44 * 8 = 15.52; TS% = 18 / (2 * 15.52) * 100 = 18 / 31.04 * 100 = 58.0% - Player Y is more efficient despite scoring fewer points

Question 16: c) FGA + 0.44 * FTA

Section D: Free Throw Rate and Shot Distribution

Question 17: FTr = 320 / 800 = 0.40 (or 40%)

Question 18: c) 1.54 points (assuming ~77% FT%)

Question 19: Sample answer: The "mid-range dead zone" refers to two-point shots outside the paint that yield the lowest expected value in basketball. These shots (typically 10-22 feet from the basket) convert at around 40-42%, yielding only ~0.80-0.84 expected points per attempt. By contrast, three-pointers yield ~1.08+ expected points and shots at the rim yield ~1.30 expected points. Analytics showed teams were leaving points on the table by taking mid-range shots when better alternatives existed. This led to the modern shot distribution where teams emphasize threes and rim attempts while minimizing mid-range shooting.

Question 20: True

Section E: The Three-Point Revolution

Question 21: Break-even 3P% = (2/3) * 52% = 34.67%

Question 22: c) 34-38 (approximately 35.1 per game)

Question 23: Sample answer: The three-point revolution was mathematically inevitable because expected value analysis revealed that even average three-point shooting (36%) produces more points per shot than average two-point shooting outside the restricted area. With 3P% * 3 > 2P% * 2 for typical conversion rates, maximizing three-point attempts became the optimal strategy. Once teams recognized this mathematical reality and front offices began prioritizing analytics, the shift became inevitable. The only shots that compete with threes in expected value are shots at the rim (~65% at 2 points = 1.30 EV), leading to the modern "rim or three" shot distribution.

Question 24: - 1994-95: 15.3 * 0.359 * 3 = 16.5 expected points from threes per game - 2023-24: 35.1 * 0.365 * 3 = 38.4 expected points from threes per game

Question 25: Sample answer: (1) Variance/Streakiness: Three-point shooting is inherently variable, leading to more unpredictable outcomes. Teams can go cold from three in crucial playoff moments, as happened to several heavily three-dependent teams. (2) Offensive rebounding: Long rebounds from three-point misses tend to favor the defense, reducing second-chance opportunities. Other valid answers include: playoff adjustments making threes harder, diminishing returns as defenses prioritize three-point defense, individual player limitations, and the value of shot diversity in late-game situations.

Scoring

Grade Scale: - A: 68-76 points (90%+) - B: 61-67 points (80-89%) - C: 53-60 points (70-79%) - D: 46-52 points (60-69%) - F: Below 46 points