Pricing a Football Match · From one distribution to every market
How sure is the number
lesson 5 of 620 minnot yet done
A probability of 55% from a model fitted on 4,000 matches and one from a model fitted on 40 are not the same 55%. The Laplace approximation puts a band around every number: the fitted parameters have a covariance (the inverse of the Hessian at the optimum), and drawing from it and re-pricing gives a distribution of prices.
θ ~ N(θ̂, H⁻¹)
On the Predict page the band is the How sure figure: a 90% interval on the favourite's probability. Tight bands come from sides with many recent matches; a promoted side in August has a wide one.
Why it matters
A price with a wide band is a price to leave alone. The uncertainty is also what a conformal set (in the Machine course) turns into a guarantee. For now, the rule is simple: read the band before the number.
Check yourself
explained after each answer