- Forecast cumulative
- 0.540
- Observed cumulative
- 1.000
- Difference
- -0.460
- Squared term
- 0.2116
Free · Two-term proof · Browser-only
Football Ranked Probability Score calculator
Calculate RPS for one home–draw–away forecast, see every cumulative error and keep the normalization convention attached.
Canonical publication record
Abstract
A deterministic browser calculator for one complete home-draw-away forecast, exposing raw and normalized Ranked Probability Score, both cumulative boundary terms and every possible result without claiming RPS is football's uniquely correct scoring rule.
- Author and publisher
- Football Proof AI
- Technical report
football-ranked-probability-score/1.0.0- Published
- Last modified
- Release status
- Current release
- Review status
- Editorial technical note; not externally peer reviewed
- Version history
football-ranked-probability-score/1.0.0: Initial public release.
Interactive · Formula football-ranked-probability-score/1.0.0
See the two cumulative errors behind RPS
Set one complete home–draw–away forecast and the actual result. Linked controls keep the total at 100%; the calculation stays in this browser.
Input as
Linked probability total100.0%Changing one outcome redistributes the other two proportionally.
Actual match result
Selected result · Home win
Normalized RPS0.1258Range 0–1 · raw cumulative sum ÷ 2
Raw RPS0.2516Range 0–2 · sum of two squared errors
Lower is better under a fixed convention. This single score does not label a forecast—or a model—as good or bad.
Cumulative boundary decomposition
Raw RPS is the sum of exactly two visible terms
Each boundary compares a cumulative forecast with the cumulative observation.
- Forecast cumulative
- 0.800
- Observed cumulative
- 1.000
- Difference
- -0.200
- Squared term
- 0.0400
Selected calculation(0.2116 + 0.0400) ÷ 2 = 0.1258Always state whether the divisor is applied.
Same forecast · Three possible results
The outcome changes the cumulative target—not the forecast
Distance sensitivity made explicit
If a forecast says 100% home win…
RPS treats a draw as adjacent to a home win and an away win as the opposite end of the H→D→A ordering. Whether that is desirable for football evaluation is a published debate, not a settled fact.
- Home occurs0.0000Perfect
- Draw occurs0.5000Adjacent error
- Away occurs1.0000Opposite error
Exact three-outcome formula
How is football Ranked Probability Score calculated?
Fix the order as home → draw → away. Compare the forecast and observed cumulative probabilities after home, then after draw. Square both differences and add them. Divide by two only when reporting the normalized three-class convention.
Three-outcome normalized RPS[(FH − OH)² + (FH+D − OH+D)²] ÷ 2
Lower is better. Zero is perfect; one is the normalized maximum.
Convention before comparison
Raw and normalized RPS are not the same scale
Add the two squared cumulative errors without a divisor.
Divide the raw sum by K − 1, which is two for 1X2 football.
A published score without its category order, divisor and match sample is not safely comparable. This calculator always prints both conventions instead of silently choosing one.
Direct answer to the benchmark question
What is a good RPS for football predictions?
There is no universal single-match cutoff. A lower average is better only when models are scored on the same pre-declared fixtures, result coding, exclusions and normalization. Compare against honest baselines and retain uncertainty around the sample—not a label such as “excellent”.
Same fixtures?RequiredOtherwise difficulty can differ.
Same convention?RequiredRaw and normalized magnitudes differ.
Same cutoff?RequiredPost-match information invalidates the comparison.
Enough matches?RequiredOne result measures neither skill nor calibration.
Balanced research record
RPS is proper and distance-sensitive—the football interpretation is debated
RPS was developed for ordered categorical forecasts. In 1X2 football it treats draw as between home and away. Constantinou and Fenton argue that this repairs shortcomings in common football scoring practice; Wheatcroft disputes that distance sensitivity advances the usual evaluation goal and reports an advantage for the logarithmic score in simulations.
Use the metric that answers the question
RPS does not replace Brier score, log loss or calibration
Scores cumulative 1X2 boundaries and applies the H→D→A ordering.
Scores the three category probabilities directly without outcome distance.
Focuses on probability assigned to what occurred and strongly penalizes near-zero misses.
Asks whether repeated stated probabilities match observed frequencies.
Read the full accuracy-metrics convention, then use the 1X2 probability calculator or the complete-history audit for the distinct questions they answer.
From arithmetic to evidence
Calculate one row here. Validate a model across frozen history.
A transparent score is only the first layer. Honest evaluation also requires point-in-time features, identical match samples, public exclusions and uncertainty around aggregate differences.