The Math Behind the Market
Projection math: weighted averages, spread and distributions
9 min · How a projected number is built, and why the spread around it matters as much.
- Projection math
- Distributions
The stat
How a projected number is built, and why the spread around it matters as much.
Learn the number
A projection is usually a weighted average. Recent games, opponent strength and playing time are each given a weight, and the weights should sum to 1.
A projection is a centre. On its own it says nothing about how far results scatter around it.
Standard deviation is the typical distance from the average. Roughly two thirds of results land within one standard deviation of the mean, and about 95% within two.
A distribution is the whole shape: the centre, the spread, and how often each result appears. A 20-point projection with a spread of 3 is a completely different player from a 20-point projection with a spread of 12.
Read the stat
A player averaged 24 points in his last 5 games and 18 across the season. Recent form is weighted 0.4 and the season 0.6.
- Check the weights sum to 1: 0.4 + 0.6 = 1. Good.
- Weighted mean = (0.4 × 24) + (0.6 × 18).
- = 9.6 + 10.8 = 20.4 points.
- Now the spread: his game scores were 12, 16, 20, 24 and 28, whose mean is 20.
- Deviations are −8, −4, 0, +4, +8; squared they are 64, 16, 0, 16, 64, totalling 160.
- 160 ÷ 5 = 32, and the square root of 32 is about 5.7.
Projection 20.4 points with a standard deviation of about 5.7 — so roughly two thirds of games should land between about 15 and 26.
Your turn
Two players are both projected at 20 points. One has a standard deviation of 3, the other 11. What does that change?
Explain what it means
Quoting a projection without its spread hides most of the information. The centre tells you what to expect on average; the spread tells you how much to trust that expectation for any single game.
Make a prediction
Build a weighted projection for one player this week, then also write down the range you would expect two thirds of their games to fall inside.
Review what happened
Check whether the actual result landed inside your range. A result inside it is a success even if it missed the centre — that is what a spread is for.
Check your understanding
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Every question has to be right for this lesson to count as complete. Miss one and you can try it again.