Free · Exact + clipped · Browser-only
Football log loss calculator for 1X2 predictions
Score one complete home–draw–away forecast with the logarithmic rule. Inspect the exact penalty, the declared clipping rule and what the same probabilities would score under every result.
Canonical publication record
Abstract
A deterministic browser calculator for exact and explicitly clipped logarithmic loss on one complete home-draw-away forecast, including natural-log nats, ignorance bits, the uniform 1X2 reference and every possible result.
- Author and publisher
- Football Proof AI
- Technical report
football-log-loss/1.0.0- Published
- Last modified
- Release status
- Current release
- Review status
- Editorial technical note; not externally peer reviewed
- Version history
football-log-loss/1.0.0: Initial public release.
Interactive · Formula football-log-loss/1.0.0
Expose the probability behind every log-loss score
Set one complete home–draw–away forecast and the result. Linked controls keep the total at 100%, and every calculation stays in this browser.
Input as
Linked probability total100.0%Changing one outcome redistributes the other two proportionally.
Actual match result
Observed result · Home win
Probability assigned to the result54.0%
Uniform 1X2 referenceln(3) = 1.0986121.584963 bits · exact row difference -0.482426
Lower loss rewards more probability on the observed result. ln(3) is only the same-row uniform reference—not a universal model-quality threshold.
Same forecast · Every possible result
One probability vector produces three counterfactual losses
The selected row uses only the probability assigned to what happened; the complete 1X2 vector is still required and must sum to one.
| Possible result | Assigned probability | Exact natural log | Exact bits | Clipped natural log |
|---|---|---|---|---|
| Home winSelected result | 54.0% | 0.616186 | 0.888969 | 0.616186 |
| Draw | 26.0% | 1.347074 | 1.943416 | 1.347074 |
| Away win | 20.0% | 1.609438 | 2.321928 | 1.609438 |
Exact scoring rule
How is football prediction log loss calculated?
Select the probability assigned to the result that actually occurred, write it as a decimal and take its negative natural logarithm. A complete 1X2 distribution must still sum to one, even though a single row's loss uses only the observed class.
One-match multiclass log loss−ln(pactual)
For a collection, average the row losses over the same pre-declared matches. Never compare averages built from different fixtures or exclusions.
Reference, not a quality label
The uniform 1X2 baseline is ln(3) = 1.0986
A 33.33% / 33.33% / 33.33% forecast scores approximately 1.0986 nats regardless of the result. That is a useful arithmetic check, not a universal “good score” threshold. League priors or time-matched market probabilities are usually stronger reference forecasts.
Overconfidence is expensive
Log loss penalty by observed-outcome probability
The penalty rises slowly near sensible probabilities and very sharply as the probability of what happened approaches zero.
| Probability given to result | Exact log loss (nats) | Interpretation |
|---|---|---|
| 100% | 0.0000 | A certain forecast that occurs |
| 80% | 0.2231 | A strong probability that occurs |
| 60% | 0.5108 | More likely than not |
| 50% | 0.6931 | Even chance in a binary framing |
| 33.33% | 1.0987 | Approximately uniform in 1X2 |
| 20% | 1.6094 | An unlikely outcome occurs |
| 10% | 2.3026 | A low-probability miss |
| 1% | 4.6052 | A severe overconfidence penalty |
| 0% | ∞ | Impossible under the forecast |
Exact result and implementation result
Zero probability means infinite exact loss; clipping must stay visible
Software often clips probabilities to a small interval before applying the logarithm. This prevents infinity in finite computation, but it changes the score. The calculator therefore preserves the exact result and displays a separate symmetric clipped result using your chosen ε: max(ε, min(1 − ε, p)).
The default ε of 10−15 is an explicit calculator convention, not a universal football standard. Publish the value whenever clipped scores are compared.
Same information, different units
Natural-log loss and ignorance bits
Uses ln and is the primary convention in this calculator.
Uses log₂ and is sometimes called ignorance score.
The rankings are identical because the scales differ by a constant factor. The numeric values are not directly comparable unless the logarithm base is the same.
One metric cannot answer every question
Log loss versus Brier score and calibration
Uses the observed outcome's probability and heavily penalizes near-zero misses.
Uses squared errors across all three outcome probabilities and has a bounded range.
Checks whether stated probabilities match frequencies over repeated forecasts.
Checks only whether the highest-probability label won and discards probability quality.
Use the metric convention guide, compare two models on matched rows, or audit a complete prediction history.
Primary method record
Sources and reproducibility boundary
The calculator performs deterministic arithmetic in your browser. It does not fetch forecasts, verify when they were published, certify a model or infer profitability.
From one row to honest evidence
Calculate here. Validate on frozen history.
An aggregate claim also needs pre-match timestamps, a complete denominator, fixed exclusions, an honest baseline and uncertainty.