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← The Points Curve

The Points Curve

Three short lessons on the World Aquatics points table: a cube of a ratio, the table read backwards, and why near the top one percent of time is worth about three percent of points.

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

Lesson 1. A cube of a ratio

World Aquatics scores a swim with one formula: points = 1000 × (base ÷ time)³. The base is a time set from world records at the start of each period; for 2026 long course, the men’s 50 freestyle base is 20.91 and the women’s is 23.61.

A swim equal to the base scores exactly 1,000. Bases are fixed for the period, so a new record can beat them: Cameron McEvoy’s 20.88 in March 2026 works out at about 1,004 points.

Question. A swim takes exactly twice the base time. How many points does it score?

  1. 250
  2. 500
  3. 125

Say it back. In your own words: why does a smaller time give more points?

Lesson 2. Reading it backwards

Turn the formula round to ask what time earns a given score: time = base × (1000 ÷ points) raised to one third.

Half the points is not twice the time. 1000 ÷ 500 = 2, and the cube root of 2 is about 1.26, so 500 points needs a time 1.26 × the base. Against the women’s 23.61, that is about 29.75 seconds.

Question. What time scores 800 points?

  1. About 1.25 times the base
  2. About 1.08 times the base
  3. About 1.2 times the base

Say it back. In your own words: why does half the points not mean double the time?

Lesson 3. One percent, three percent

Near the base, a swim 1% quicker earns about 3% more points — the cube turns a small change into three times as much. Worked exactly, it is 3.06%.

Children’s times sit far down the curve. A 10 & under girls’ AAAA in the long-course 50 free, 32.19, is about 395 points against the 23.61 base. That is a fact about the curve, not a grade on a child: compare a swimmer’s points only with their own.

Question. Near the base, a swim 2% quicker earns about how many more points?

  1. About 20% more
  2. About 6% more
  3. About 2% more

Say it back. In your own words: why is a hundredth worth more points at the top than near the bottom of the curve?

At the table: Score your own swims or walks

Players: Any number, 12 and up with a calculator. You'll need: A calculator, a published base time or world record for one event, your own times.

  1. Pick one event and write down its base time (World Aquatics publishes them; for a walk, use a record you look up).
  2. Each person times their own swim or walk of that distance, twice on different days.
  3. Work out 1000 × (base ÷ your time)³ for each try.
  4. Compare each person’s two tries — only your own, never each other’s — and say how big a change in time made the change in points.

Answers

  1. 125 — One half cubed is one eighth, and 1000 ÷ 8 = 125. Twice the time is far fewer than half the points.
  2. About 1.08 times the base — 1000 ÷ 800 = 1.25, and its cube root is about 1.077, so 800 points needs a time about 8% slower than the base.
  3. About 6% more — Near the base each 1% of time is worth about 3% of points, so 2% is about 6% (6.25% worked exactly).