Transparency

What is a good Brier score in football predictions?

Published 2026-08-25

Ask what is a good Brier score for football predictions and the figures you find contradict each other: guides that treat 0.25 as the score of a pure guess, others where a guess scores 0.33, others still that quote model and bookmaker scores above 0.6 as respectable. Those numbers cannot all describe the same quantity, and they don’t. They come from three different definitions of the same metric applied to different numbers of outcomes, and comparing them across sources is meaningless.

That confusion is worth clearing up, because once it is gone the honest answer becomes surprisingly precise — and it is not a single threshold.

Why the published numbers disagree

The Brier score is the mean squared distance between the probabilities you published and the outcome that happened, coded as 1 for the winner and 0 for everything else. Three conventions are in circulation, and they differ by constant factors.

The binary form. With two outcomes you only need one probability, so the score is a single squared term: forecast 60% and the event happens, and you score (0.60 − 1)² = 0.16. The range is 0 to 1, and a 50/50 coin flip scores 0.25. This is where “0.25 is random” comes from.

The original multi-category form, which is what football’s home/draw/away actually needs. You square the error on all three outcomes and sum them:

• Forecast 55/25/20, home win happens: (0.55 − 1)² + (0.25 − 0)² + (0.20 − 0)² = 0.305
• Same forecast, away win happens: (0.55 − 0)² + (0.25 − 0)² + (0.20 − 1)² = 1.005

The range here is 0 to 2, and an even 33/33/33 forecast scores 0.667.

The averaged form, which divides that sum by the number of categories. The same 33/33/33 forecast now scores 0.222.

Three legitimate numbers — 0.25, 0.667, 0.222 — for forecasts that carry no information at all. A Brier score quoted without its convention and its number of outcomes is not a fact about a model. It is a fact about arithmetic nobody stated. Everything below uses the multi-category sum, the standard choice for 1X2 and the one used on our public track record.

What is a good Brier score for a three-outcome market

Now the number can be pinned down, because the useful reference points are calculable rather than surveyed.

When a forecast reports the true probabilities, its expected Brier score simplifies to 1 − Σp², where p runs over the outcome probabilities. That single identity generates the whole benchmark ladder.

Take a league where roughly 44% of matches end in home wins, 25% in draws and 31% in away wins. A forecaster who ignores the fixture entirely and publishes those base rates for every match expects:

1 − (0.44² + 0.25² + 0.31²) = 1 − 0.352 = 0.648

And the no-information forecast:

1 − 3 × (1/3)² = 1 − 0.333 = 0.667

Read the top two rows carefully, because they carry the most important fact about this metric: knowing nothing costs you about 0.019. The entire distance between a forecaster who has never watched football and one who at least knows which league they are in is under two hundredths of a point.

Everything a real model contributes — team strength, home advantage, squad availability, schedule — has to fit into the space below 0.648, and that space is small. Football’s outcomes are genuinely close to random at the margin, which is why a serious model beats the base rate by hundredths and not by tenths. It also means a Brier score quoted to two decimal places has thrown away most of its resolution. Three decimals is the minimum at which the metric says anything.

So the direct answer: for 1X2 under the multi-category convention, anything at or above 0.648 is worthless, and everything worth arguing about lives in a narrow band below it. There is no absolute figure that certifies a model as good, because the interesting variation is smaller than the differences between conventions.

The number that actually answers the question

Because the scale is compressed and convention-dependent, the useful quantity is not the Brier score but the Brier skill score, which expresses it as a percentage improvement over a benchmark you name:

BSS = 1 − (your Brier ÷ benchmark Brier)

Zero means you matched the benchmark. Positive means you beat it. Negative means you would have done better publishing the benchmark.

A worked example. Suppose a model averages 0.600 over a season of matches.

• Against the base-rate benchmark of 0.648: BSS = 1 − (0.600 ÷ 0.648) = +0.074. The model extracts about 7% of the available improvement.
• Against a market benchmark of 0.560: BSS = 1 − (0.600 ÷ 0.560) = −0.071. Against the closing price, the same model is behind.

One raw score, two opposite verdicts. This is why “is 0.600 good?” has no answer and “0.600 against which benchmark?” has two. Any published record that quotes a Brier score without naming the reference it was measured against has skipped the step that gives the number meaning.

How many matches before the score means anything

There is a third condition, and it disqualifies most published Brier scores outright.

Per-match Brier scores are spread out. For the base-rate forecast above, the three possible per-match values are 0.472 (home), 0.852 (draw) and 0.732 (away), giving a standard deviation of roughly 0.16. Real forecasts vary more than that, so treat 0.16 as a floor.

The standard error of a mean Brier over n matches is that spread divided by √n:

At 100 matches the error bar is ± 0.016 — wider than the entire 0.019 gap between a no-information forecaster and the base rate. A model measured over one hundred matches cannot be distinguished from a forecaster who knows nothing, no matter how good the headline figure looks. Separating a competent model from a strong one, a difference of perhaps 0.005, needs thousands of matches. This is the same sample-size arithmetic that governs strike rates and yields, applied to a metric that is often presented as if it were exempt.

The three-part answer

A Brier score is good when three things are true together, and the number alone establishes none of them:

1. The convention is stated — binary, multi-category or averaged, and over how many outcomes.
2. A benchmark is named and beaten, ideally expressed as a skill score against both a base rate and the closing market.
3. The sample is large enough that the improvement exceeds its own standard error.

A record that supplies all three is making a claim you can check. A record that supplies a decimal and a compliment is not, and the missing pieces are always the ones that would have made the figure look ordinary.

That is why our own scores sit on a track record with the sample size and the benchmarks beside them rather than in a headline. The number is only as good as the context it ships with — and if you want the underlying formula in more detail, our guide to the Brier score walks through the calculation match by match.