Understanding Bookmaker Overround (Vig)
In sports betting, bookmakers do not offer fair odds. Instead, they incorporate a profit margin known as the overround, vigorish, or "juice". This ensures that over a large sample of bets, the bookmaker retains a mathematical edge regardless of the outcome.
Why does the overround exist? It serves as the bookmaker's built-in commission. If a bookmaker takes equal action on both sides of our coin flip example, they collect $105.26 for every $100 they pay out, guaranteeing a $5.26 profit.
Methods for Calculating Fair Odds
To find expected value (+EV), a bettor must strip the overround from the bookmaker's odds to estimate the "true" probability of an event. There are several mathematical models to achieve this, each with different assumptions about how the bookmaker distributes their margin.
1. The Multiplicative Method (Margin Proportional to Odds)
The multiplicative model assumes that the bookmaker applies the margin proportionally across all outcomes. This is the simplest method but often flawed, especially for long-shot odds.
Worked Example: Match Odds: Home 2.10, Draw 3.40, Away 3.50.
Implied probabilities: Home = 1/2.10 = 47.62%, Draw = 1/3.40 = 29.41%, Away = 1/3.50 = 28.57%.
Total Margin = 47.62% + 29.41% + 28.57% = 105.60% (5.60% overround).
Fair Probabilities: Home = 47.62 / 1.056 = 45.10% (Fair Odds = 2.22).
2. The Additive Method (Equal Margin per Outcome)
The additive model posits that the bookmaker adds a fixed percentage to the implied probability of every outcome, regardless of the price.
Using the same odds (2.10 / 3.40 / 3.50) with an overround of 5.60% across 3 outcomes, we subtract 1.867% (5.60% / 3) from each implied probability. Home Fair Prob = 47.62% - 1.87% = 45.75% (Fair Odds = 2.19).
3. The Power Method
The power method operates on the assumption that bookmakers scale odds using an exponent, which better models the favorite-longshot bias (where bookmakers hide more margin in longshots).
The exponent k is found iteratively such that the sum of all true probabilities equals exactly 1.0 (100%).
4. Shin's Method (The Insider Trading Model)
Developed by H.S. Shin (1991), this mathematically rigorous model assumes a proportion of bettors possess insider information, and the bookmaker adjusts odds to compensate for this adverse selection. It requires a Newton-Raphson numerical solver to find the optimal proportion of insider trading (z).
Shin's method is widely considered the most accurate model for football match odds, as it inherently accounts for the favorite-longshot bias seen in real markets.
Finding +EV Bets with Fair Odds
Once you calculate the true probability of an outcome using a sharp bookmaker's closing line, you can compare it to the odds offered by a softer bookmaker. If the soft bookmaker's odds are higher than the fair odds derived from the sharp bookmaker, you have identified a +EV bet.
Use our No-Vig Fair Odds Calculator to automate these derivations across all four mathematical models.