Chapter 24 · Worked solutions
Chapter 24 workings: Silicon Tipsters on Trial
Chapter twenty-four worked: a Brier score for five forecasts, judged against the 0.25 coin-flip baseline, and why one confident miss dominates.
The Brier score is the average squared gap between a forecast and what happened, coded 1 or 0. Lower is better. Saying 50 per cent every time scores exactly 0.25.
The exercises
Five forecasts, one score
Score five home-win forecasts against their results and compare with 0.25.
Square each gap
Forecast minus result, squared, in the table.
Average
Total 1.1250 ÷ 5 = 0.225.
Judge
Below 0.25, so better than a coin flip overall.
Look at match 3
The 0.75 that failed contributes 0.5625, exactly half the total. Confident misses cost most.
| Match | Forecast | Result | Gap | Squared |
|---|---|---|---|---|
| 1 | 0.60 | 1 | −0.40 | 0.1600 |
| 2 | 0.20 | 0 | +0.20 | 0.0400 |
| 3 | 0.75 | 0 | +0.75 | 0.5625 |
| 4 | 0.55 | 1 | −0.45 | 0.2025 |
| 5 | 0.40 | 0 | +0.40 | 0.1600 |
The answer
Brier 0.225, better than the 0.25 baseline; match 3 is half the error.
Related on this site
These are the workings. The argument for them, and the exercises themselves, are in chapter 24 of the book, Silicon Tipsters on Trial.
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