Quant Library · Match pricing · Football

Laplace Uncertainty

A band around every probability, from the curvature of the likelihood at its optimum.

The fitted parameters have a covariance: the inverse Hessian of the negative log likelihood. Draw from it, re-price, and you have a distribution over prices rather than a single number.

Read the specification (PDF) Run it on the API The match pricing family · £899

Inputs

What it takes

Name	Type	Units	Where it comes from
fit	fitted model	-	the Match Price Engine
matches	the weighted match list the fit used	-	the same source
draws optional	int	count	your choice; 400 is enough for a 90% interval

Outputs

What it gives back

Name	Type	Units	Notes
covariance	k x k array	-
interval	(low, high) per outcome	probability
width	float	probability points	what the Predict page calls How sure

Method

How it works

Compute the Hessian of the weighted negative log likelihood at the optimum by central differences.
2 further steps in the licensed specification

Assumptions

The likelihood is approximately quadratic near its optimum, which is the usual large-sample argument and is weakest for teams with few matches.

Limits

It is parameter uncertainty only. It says nothing about the model being the wrong shape, which is the larger error.
1 further limits in the licensed specification

Validation

What it was measured at

The band is reported on every price the Arena serves; these are its properties rather than a score.

Interval	90%	on the favourite's probability, from the parameter covariance
Draws	400	from the multivariate normal at the optimum
Typical width, established side	3 to 5 points	several seasons of matches behind the fit
Typical width, promoted side in August	10 to 15 points	which is the point of printing it
What it does not cover	model error	for coverage that survives the model being wrong, licence the conformal sets

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.