Research and analysis

Betting Maths Research

This is where Betting Maths tests questions rather than merely defining terms. We publish observed market studies when data is available, and clearly labelled mathematical models when the purpose is to isolate a mechanism.

Reproducible by design: observed-data studies identify their source, sample and calculation method. Modelled studies state their assumptions. Downloadable derived datasets are published where practical.

Real market data

Observed research

These studies use recorded market data rather than hypothetical prices. The current Premier League series deliberately examines the same dataset from different mathematical angles so the conclusions can be compared without changing the underlying sample.

Observed data

Premier League Opening-Weekend 1X2 Margins: 2025/26

We measured the book percentage on all 10 opening-round Premier League matches using real opening prices from Football-Data.co.uk.

Observed data

Do 1X2 Margins Tighten Before Kick-Off?

Opening and closing prices from the same 10 matches show a small average tightening, but not a consistent one.

Observed data

How Much Did Price Shopping Reduce 1X2 Overround?

Average opening prices produced a 105.56% book; combining the strongest listed prices reduced it to 101.74% in this 10-match sample.

Observed data

Did the Best-Available 1X2 Book Improve by Kick-Off?

A companion study comparing cross-bookmaker maximum opening and closing prices across the same Premier League round.

Research Data and Sources

Controlled examples

Mathematical models

Models let us hold assumptions constant and see what a particular mechanism does. They are not presented as observed bookmaker behaviour.

Model

How Bookmaker Margin Compounds in Accumulators

A reproducible model showing how a small pricing disadvantage on each leg can become much larger across a multi-leg accumulator.

Model

What Is a Cash-Out Offer Worth? A Fair-Value Model

A worked model for comparing a cash-out offer with the expected value of the bet at the current estimated probability.

Model

What Does an Extra Place Actually Change?

A transparent model showing how an additional place changes the expected return of the place half of an each-way bet.

How this differs from a guide

A guide explains a concept such as overround, lay liability or expected value. Research starts with a question, identifies the evidence needed, performs a calculation and publishes the result with its limitations.

For example, the bookmaker-margin guide explains how to calculate overround. The Premier League research series asks what happened in recorded markets: how large the books were, how they changed between snapshots, and how the arithmetic changed when different price sets were combined.

Research standards

  • Observed data and hypothetical models are labelled separately.
  • Sample sizes and time periods are stated.
  • Important formulas are shown or linked to methodology.
  • Derived datasets are published when licensing and practicality allow.
  • Limitations are part of the article, not hidden in a disclaimer.
  • Research conclusions do not become betting tips or predictions.
Data and SourcesCalculation MethodologyEditorial Standards
Responsible note: Research can explain prices and risk. It cannot make an uncertain event certain, and Betting Maths does not provide betting tips or guaranteed profit strategies.