The numbers under the prices

Math & Models

The maths of betting is smaller than it looks: a handful of ideas about probability, margin and measurement do almost all the work. These guides explain the ones that matter, and how we grade our own forecasts with them.

8 guides · about 36 min to read all

What you'll take away

  • How to strip the bookmaker's margin out of a price
  • How expected goals become a full grid of scorelines
  • What separates a good probability from a lucky one
  • How to read a track record without fooling yourself

Math & Models

How Our Models Work: Poisson, Dixon-Coles and EloTofiko runs two families of football models — goal-based (Poisson and Dixon-Coles) and strength-based (Elo) — and blends them into one ensemble probability. Here's what each one actually does, in plain words.
3 min3 sections
The Poisson Distribution: Turning Expected Goals Into ScorelinesOne number in, every scoreline out. How the Poisson distribution turns expected goals into a grid of results, why 1X2, Over/Under and BTTS are just sums of that grid, and where the maths breaks.
7 min6 sections
The Brier Score: How We Grade Our Own PredictionsThe Brier score is the standard way to measure how good a set of probabilities is. Learn how it works in two minutes, what counts as a good score in football, and how to read Tofiko's model-vs-market Performance page.
3 min4 sections
Fair Odds: What the Bookmaker's Margin HidesBookmaker odds always overstate every outcome's probability — that's the margin, their built-in fee. Learn how to strip it out, why the naive method gets favourites and longshots wrong, and why every market % on Tofiko is margin-free.
3 min3 sections
Calibration: The Only Promise a Prediction Can KeepA 65% prediction isn't 'right' or 'wrong' on one match — it's a promise about the long run. Calibration checks whether those promises are kept: do 65% calls win 65% of the time? Here's how it works and how we test ourselves weekly.
2 min4 sections
Expected Goals (xG), Explained Without the HypexG scores every shot by how often chances like it go in. It describes a performance better than the scoreline does — but it discards finishing, ignores game state, and providers disagree.
6 min6 sections
Elo Ratings in Football: One Number Per TeamElo gives every team one strength rating and updates it after each result. How the expected score is calculated, what the K-factor does, and what football forces you to add that chess never needed.
6 min6 sections
Home Advantage: How Much It's Worth and How Models Price ItHome teams win more, and the effect is big enough to dominate a 1X2 book. How large it is, what causes it, what the empty stadiums of 2020 revealed, and how a goals model encodes it.
6 min5 sections

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