Quant Library · Match pricing · Football
Cards, Fouls and the Referee
A booking-market model built on what the data says about officials, which is not what the tipping industry says.
A shrunk multiplicative count model for cards and fouls -- league and season, both clubs, the official, and how competitive the match is priced -- with a negative binomial for the over/under lines. It prices the markets a goals model cannot reach, and it is the only model in the library whose headline finding is that a popular angle does not exist.
Inputs
5What it takes
| Name | Type | Units | Where it comes from |
|---|---|---|---|
| matches | list of (date, competition, season, home, away) | - | the platform's fixture ingest |
| match_stats | list of (fixture, home/away yellows, reds, fouls, corners) | counts | the football-data ingest |
| referee optional | string | - | the fixture record · absent for about seven matches in ten; an unknown official is priced as an average one |
| odds_1x2 optional | three decimal prices | decimal | any book, pre-match · used only to measure how competitive the match is, never as a target |
| lines optional | list of floats | goals/cards | the lines you want priced |
Outputs
4What it gives back
| Name | Type | Units | Notes |
|---|---|---|---|
| expected count | float | cards, fouls or corners | |
| over/under probabilities and fair prices | dict per line | probability and decimal | |
| referee factor | float | multiplier | with the number of matches it rests on, so a thin estimate is visible as one |
| contest factor | float | multiplier | which decile of competitiveness the match falls in |
Method
How it works
- Model the count as a product: a league-season base, a multiplier for each club home and away, one for the official, and one for how competitive the market priced the match.
- 4 further steps in the licensed specification
Assumptions
- A club's and an official's tendencies carry forward from the matches already seen. Measured by splitting each official's matches in half by date, they do: fouls correlate at 0.55 between halves and yellows at 0.43.
- 1 further assumptions in the licensed specification
Limits
- The referee is a much smaller term than the industry implies, and on the result it is nothing at all. On 14,002 refereed matches the split-half correlation of an official's effect is 0.05 on goals and 0.09 on home wins -- indistinguishable from noise. This model therefore makes no referee claim about the 1x2, and neither should anyone else.
- 5 further limits in the licensed specification
In the package
- The full specification: inputs, method, assumptions and limits
- The validation panel as measured on the day of purchase
- A reference implementation extracted from the running source
- Perpetual commercial use for one entity
Reference modules:
- 1 module(s), named in the licensed specification and shipped in the package
Read this before you buy. The platform's own walk-forward tests say the closing line forecasts football better than these models do. What they give you is a coherent price for every market and match, before the market opens, with the band and the working attached. Any model here that has been beaten by something simpler says so in its limits, and the validation panel above is generated from the platform's result files rather than typed in.