Overround and Value: Removing Bookmaker Margin Carefully

Calculate the complete market

For illustrative 1X2 odds of 2.10, 3.50 and 3.80:

• Home raw implied probability = 1 / 2.10 = 0.47619.
• Draw raw implied probability = 1 / 3.50 = 0.28571.
• Away raw implied probability = 1 / 3.80 = 0.26316.
• Booksum = 0.47619 + 0.28571 + 0.26316 = 1.02506.
• Overround = 1.02506 - 1 = 0.02506, or 2.506%.

The calculation needs all mutually exclusive outcomes captured at the same timestamp. Mixing one bookmaker's home price with another's draw price produces a synthetic best-price book, which answers a different question.

Basic normalization

Basic normalization divides each reciprocal price by the booksum. The method is set out explicitly in Koning and Zijm's open study.

Home normalized share = 0.47619 / 1.02506 = 0.46455. Its reciprocal fair-price representation is 1 / 0.46455 = 2.15262.

Normalization is a method, not a fact

Basic normalization assumes the excess is allocated proportionally. Shin and other methods allocate it differently. A 37-competition comparison found Shin probabilities more accurate on average in its sample, while also finding that bookmaker and market size mattered (Štrumbelj, 2014). A later Premier League and La Liga comparison reached different method conclusions by league (Koning and Zijm, 2023).

Therefore, publish the raw prices, timestamp, booksum and method. Do not call one output “true odds” without qualification.

Overround does not identify value

A low-overround market can still offer an unattractive selection price under your model. A higher-overround market can contain one comparatively favourable price because margin need not be distributed equally. Evaluate the accepted selection price with a separately validated probability estimate. Koning and Zijm show why margin allocation and probability bias require empirical checking.

Comparison checklist

The source and method controls below follow the differences documented by Štrumbelj:

• Same operator, market, selection set and timestamp?
• All outcomes open and executable?
• Decimal conversion performed before summing?
• Method named: normalization, Shin, power or another model?
• Source-specific commission handled separately?
• Probability output checked against later outcomes?

Keep a method-sensitivity record

For each complete market, store the raw reciprocal probabilities and calculate at least the primary de-margin method. When the decision depends on a small difference, add an alternative such as Shin or a power method and report whether the sign changes. Do not choose the method after seeing which one creates value.

The studies by Štrumbelj and Koning and Zijm reached method- and market-dependent conclusions. A useful record therefore includes method name, implementation version, complete prices, rounding precision, and later calibration. If methods disagree materially, the honest output is uncertainty rather than a more confident fair price.

Continue learning

• Next guide: Regression to the Mean in Betting Analysis
• Related guide: Soft vs Sharp Bookmakers

Assumptions and limitations

The prices are illustrative and rounded, so displayed components may differ slightly from calculations using unrounded values. Overround is a snapshot property and does not equal realised operator margin, customer loss, or selection-level edge. The shorter vig definition explains terminology; the expected-value guide handles the actual decision price.