Score your own predictions
You said 60% home win and it finished level. Were you right, wrong, or somewhere in between? Picking a winner can't tell you. These three scores can.
Your forecast
Draw, the rest:
Try an example
| Forecaster | Log loss | Brier | RPS |
|---|
"League averages" gives every match the same 43.7% home, 23.7% draw, 32.6% away: the baseline on the SPFL Prediction Board.
How the three scores work
Write your forecast as \(p_H, p_D, p_A\) and what happened as \(o_H, o_D, o_A\), with 1 for the actual result and 0 for the others.
$$\text{log loss} = -\ln(p_{\text{actual}})$$ $$\text{Brier} = \sum_{k} (p_k - o_k)^2$$ $$\begin{aligned} \text{RPS} = \tfrac{1}{2}\big[&(p_H - o_H)^2 \\ &+ (p_H + p_D - o_H - o_D)^2\big] \end{aligned}$$In plain football
- Log loss only looks at the chance you gave to what happened, and punishes a low one hard. Say 0% and be wrong, and it is infinite.
- Brier checks all three of your numbers against what happened and adds up the squared misses.
- RPS knows a draw sits between a home and an away win, so backing the draw when the away side wins costs less than backing the home side.
One match proves very little
A 60% favourite that loses hasn't shown the forecast was bad: it should lose four times in ten. Forecasters are judged on their average score over hundreds of matches. The research on evaluating prediction models does exactly that for eleven predictors over 5,258 matches.
Why never say 0%
Try "Never say never". Ninety per cent on the home side is a strong but reasonable view. Zero per cent on the away side is a claim that it cannot happen, and when it does, log loss has no finite answer. Even the most one-sided match deserves a few per cent for the upset.