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← Why Judges Drop the Top Score

Why Judges Drop the Top Score

Three short lessons on judged sports: dropping the top and bottom card, difficulty as a multiplier, and one judge who leans.

Spark & Whetstone · sparkwhetstone.org/learn/why-judges-drop-the-top-score · CC BY-NC-SA 4.0. Answers are at the end, so you can try each question first.

Lesson 1. Drop the top and bottom

In diving, five judges each hold up a score. The highest and lowest are thrown away and the middle three are added. With seven judges, the top two and bottom two go.

Speedcubing does the same with times: the official average of five drops the best and the worst solve.

Question. Five judges give 6.0, 7.5, 7.0, 9.5 and 7.0. What is the sum of the middle three?

  1. 21.5
  2. 37.0
  3. 23.0

Say it back. In your own words: why do judged sports throw away the top and bottom scores?

Lesson 2. Difficulty as a multiplier

A diving score is the sum of the middle cards times the dive’s degree of difficulty. A harder dive done fairly well can beat an easy dive done perfectly.

That is a product with two factors: a smaller number times a bigger one can win.

Question. Dive P has middle cards adding to 21 and difficulty 3.0. Dive Q has middle cards adding to 27 and difficulty 2.2. Which scores more?

  1. Dive Q
  2. Dive P
  3. They tie

Say it back. In your own words: how can lower marks still win in diving?

Lesson 3. One judge who leans

If one judge gives a favoured diver a bonus, the plain average of all cards rises by the bonus divided by the number of judges, and keeps rising as the bonus grows.

Dropping the extremes caps that: once the leaning card is the one thrown away, a bigger bonus changes nothing. The price is that some honest information is thrown away too.

Question. Seven honest judges give 8.0 each. One judge adds a 3-point bonus. How much does the plain average rise?

  1. 3 points
  2. About 0.43 points
  3. Nothing, because the other six cancel it out

Say it back. In your own words: what does dropping the top score protect against, and what does it cost?

At the table: Judge the paper planes

Players: Four or more, ages 7 and up. You'll need: Paper for planes, cards numbered 1 to 10 for each judge.

  1. Everyone folds a paper plane and flies it once.
  2. Three or five judges hold up a card from 1 to 10 for each flight.
  3. Score each flight two ways: the plain average, and the middle cards only.
  4. Talk about any flight where the two ways disagreed, and why.

Answers

  1. 21.5 — 7.5 + 7.0 + 7.0 = 21.5. The 9.5 and the 6.0 are dropped.
  2. Dive P — 21 × 3.0 = 63.0 and 27 × 2.2 = 59.4, so the harder dive wins despite lower cards.
  3. About 0.43 points — 3 ÷ 7 ≈ 0.43. A trimmed average would ignore the bonus entirely, because the leaning card becomes the highest and is dropped.