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.
13 guides · about 56 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 min4 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
Expected Points (xPts): What a Season DeservedxPts turns each match's win, draw and loss probabilities into the points a team could expect. Summed over a season it tracks the real points table closely — which is exactly what makes the gap interesting.5 min6 sections
How to Read an xG TableThe two orders, the Δ column, and why our table refuses to show goals minus xG. A short guide to the numbers on Tofiko's xG view — and to the ones deliberately left out.4 min6 sections
How to Read a League TablePoints, goal difference, the colour bands and the maths that sometimes refuses to add up. What each column on a league table means, what it cannot tell you, and the competitions where checking the arithmetic makes it look broken.5 min5 sections
Football Form: What W-D-L Actually Tells YouFive letters, read left to right, carrying less than almost anyone assumes. What a form string measures, which direction it runs in, why the same five results mean different things in different leagues, and where it misleads.4 min5 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
Log Loss: Scoring Probabilities That Have to Be HonestLog loss grades probability forecasts and punishes confident mistakes hard. Learn how it is calculated, how it differs from the Brier score, and why a model can look fine on one and poor on the other.2 min3 sections