What are fair odds and no-vig lines?

The rest of this page walks through the maths behind it step by step, with a fully worked example, so the method is easy to check and repeat on any market.

What are fair odds?

A betting price has two things baked into it: the bookmaker’s honest estimate of how likely the outcome is, and a margin on top, so the book turns a profit regardless of the result. Fair odds are what is left once that margin is stripped back out. They are also called no-vig odds or true odds, and they represent the market’s best estimate of the real probability of an outcome, with no house edge attached.

Fair odds are not a price you can bet at. No bookmaker offers a book with zero margin, that is how the business survives. Fair odds are a benchmark, a way of asking whether the actual, bettable price on offer is generous, standard or short compared with what the market genuinely thinks is likely.

Implied probability

Every decimal odds price implies a probability. The formula is implied probability equals 1 divided by the decimal odds. Odds of 2.00 imply a 50% chance, since 1 divided by 2.00 is 0.50. Odds of 4.00 imply a 25% chance, since 1 divided by 4.00 is 0.25. Shorter odds mean a higher implied probability, longer odds mean a lower one. This conversion is standard across the industry, set out in detail in the maths of bookmaking.

Taken on its own, one outcome’s implied probability does not tell you much, because it still has the bookmaker’s margin sitting inside it. The margin only becomes visible once you look at every outcome in the market together.

The overround

Take every possible outcome in a market, convert each one to an implied probability, then add them all up. In a market with no bookmaker margin at all, those probabilities would sum to exactly 100%, because exactly one outcome has to happen. In practice, they always sum to a bit more than 100%. That excess is called the overround, the book percentage, or the vig, short for vigorish.

The overround is spread across every outcome, which is exactly why simply adding up the probabilities can’t be the final answer, and why devigging exists.

Devigging: removing the margin

There are a few recognised ways to strip the overround back out. Proportional, additive, power and the Shin method are the four commonly cited, and they can disagree slightly on how the margin should be shared out across outcomes. The simplest to explain correctly, and the one used here, is the proportional method. It works in three steps.

• Convert every outcome’s odds to an implied probability, 1 divided by the decimal odds.
• Add all of those implied probabilities together to get the total. The overround shows up here, as the amount over 100%.
• Divide each outcome’s implied probability by that total. This rescales all of them so they sum to exactly 100%, giving a fair, no-vig probability for each outcome.

From there, converting back to fair decimal odds is just the implied-probability formula run in reverse: fair decimal odds equals 1 divided by the fair probability.

The proportional method assumes the bookmaker has spread its margin evenly, in proportion, across every outcome. That is a simplification, since in practice a book can shade its margin unevenly toward the draw or toward the favourite, which is why the other methods exist. But proportional devigging is the standard starting point and is accurate enough for almost all everyday use.

A worked example

Take a three-way football match, home, draw, away. Say a bookmaker prices it Home 2.10, Draw 3.50, Away 3.60.

Adding up the raw implied probabilities gives 47.62% plus 28.57% plus 27.78%, which is 103.97%. That means the overround on this market is 103.97% minus 100%, so 3.97%, the bookmaker’s margin.

Devigging with the proportional method means dividing each implied probability by that 103.97% total. Home becomes 47.62 divided by 103.97, which is 45.80%. Draw becomes 28.57 divided by 103.97, which is 27.48%. Away becomes 27.78 divided by 103.97, which is 26.72%. Add those three back up and they come to exactly 100.00%, which is the check that the devig has worked.

Converting each fair probability back into odds, 1 divided by 0.4580 is 2.18, 1 divided by 0.2748 is 3.64, and 1 divided by 0.2672 is 3.74. Every fair price is a little longer than the original bookmaker price, which is exactly what removing a margin should do. The book was always going to pay a bit less than the true probability justified, on every outcome at once.

Why fair odds matter

Fair odds are the benchmark, not the bet. A value bettor’s basic method is to compare the fair, no-vig price for an outcome against the actual, bettable price on offer somewhere. If a bookmaker is offering longer odds than the fair price, for example 2.30 on Home when the fair price worked out at 2.18, that gap is where a possible edge lives. The bookmaker is paying out more than the market’s own devigged estimate says the outcome is worth.

That is a signal, not a guarantee. A single bet at a price longer than fair can still lose, because the underlying event is still genuinely uncertain. The case for value betting is a long-run one. If the fair-price estimate is sound and you consistently take prices longer than fair, the expected return across many bets is positive, even though any individual result is unaffected by the maths that produced the price.

It is also only as good as the inputs. A no-vig line calculated from a soft, low-liquidity bookmaker’s odds is not automatically a solid estimate of the true probability, since if the bookmaker’s own pricing is off, the devigged number inherits that error. Sharper markets, generally the ones with the most volume and tightest margins, tend to produce more reliable fair prices to devig in the first place.

The same principle, turning a record into a fair price, is what FootyMetrics’ player matchups tool does for player prop markets. Instead of starting from a bookmaker’s odds, it starts from a player’s actual historical record for a stat, works out how often they have hit a given line, and expresses that as a fair price, so it can be compared against whatever a bookmaker is actually offering on the same market.