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StatsAI Academy

Betting maths, system bets and model evaluation, explained with numbers you can check yourself. Every guide has a formula, a worked example and a section on limitations.

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Guides in order: each one builds on the one before.

  1. 1How to calculate implied probability from oddsp = 1 / oddsBasic2 min
  2. 2How to calculate the expected value of a betEV = p × odds − 1Basic3 min
  3. 3What is closing line value and how is it calculatedCLV = odds taken / closing odds − 1Intermediate3 min
  4. 4How system bets workcombinations = C(N, K)Basic3 min
  5. 5What is the Brier score and how is it calculatedBS = average of (p − outcome)²Intermediate2 min

Categories

Only categories with at least one published guide are shown.

Betting mathematics

What odds say about probability, how much the bookmaker keeps and how the value of a bet is measured.

5 guides
How to calculate implied probability from oddsOdds of 2.50 mean 1 / 2.50 = 40%. A market adds up to more than 100% because of the margin.Basic2 minHow to calculate the expected value of a betEV = p × odds − 1. Odds of 2.50 and p = 0.45 give +0.125 per unit.Basic3 minWhat is closing line value and how is it calculatedTaken at 2.20, closed at 2.00: CLV = 10.0%. Without the margin, 7.2%.Intermediate3 minWhat is the bookmaker margin and how is it calculatedSum of 1 / odds across all outcomes minus 100%. For 2.10 / 3.40 / 3.60 that is 4.81%.Basic3 minHow to remove the margin from odds (de-vig)Implied probabilities are scaled to 100%. The methods differ in how much margin they take off the longshot.Intermediate3 min

Systems and combinations

How a system bet is built and paid out, one combination at a time.

4 guides
How system bets work3/5 = 10 combinations of 3 selections. The stake is split across all; only complete ones pay.Basic3 minSystem bet 3/5: all 10 combinations and the payout10 trebles from 5 selections. With 3 winners it is in profit only if their odds multiply to more than 10.Basic3 minSystem bet 2/3: the simplest system bet3 doubles from 3 selections. With one loser it is in profit only if the remaining double is priced above 3.Basic2 minAccumulator or system bet: what you gain and what you give upAccumulator: biggest payout, everything must win. System: returns with a loser, less margin per combination.Intermediate3 min

Evaluation

How to check whether a model's probabilities are any good, and what “good” even means.

1 guide
What is the Brier score and how is it calculatedThe average of (p − outcome)². Lower is better; a constant 50% scores 0.25.Intermediate2 min

Tools

What the guides explain is calculated or measured here.

System bet calculatorK/N combinations, payout by number of winners and void selections.Open →AI model performanceBrier, log loss and calibration of probabilities against margin-free odds.Open →ResearchMonthly reports on how accurate the probabilities were.Open →

How we write

Every example is labelled with the kind of data it uses. Outside facts have a source, and every guide shows the date of its last real change. No ads and no promises of winnings.

  • Mathematical exampleMade-up numbers, calculated exactly, to show how a formula works.
  • Hypothetical simulationMany repeated random bets with a known probability.
  • Historical dataReal results and odds from past matches, with a source.
  • Actual StatsAI performanceNumbers from the AI model performance page, with the measured period.