How to de-vig a betting market, and why the offered price is not a probability

The overround is the entire business

Take the standard American two-way price: minus 110 on both sides. Minus 110 implies 110 divided by 210, or 52.38%. Both sides together imply 104.76%. That extra 4.76 points is the overround, and expressed as a share of the money at risk it is a 4.55% hold. Nothing about either individual price is dishonest. The margin lives in the sum, which is why looking at one side of a market tells you nothing about how expensive it is.

This is also why the phrase "the market has it at 52%" is usually wrong. Nobody at that book believes the outcome is 52.38% likely. They believe it is roughly a coin flip and they are charging you for the privilege of taking a side. Until you remove the margin you are reading a price tag, not an estimate.

Three methods, three different answers

The multiplicative method divides every implied probability by the total. On minus 200 and plus 170, the raw implieds are 66.67% and 37.04%, summing to 103.70%. Divide both by 1.0370 and you get 64.29% and 35.71%. The additive method instead subtracts the margin in equal parts, taking 1.85 points off each side for 64.81% and 35.19%. Half a point apart on a near coin flip, which is inside the noise of anything you are doing with the number.

Now price a real favourite: minus 1000 against plus 700. Multiplicative gives the longshot 12.09%. Additive gives it 10.80%. Same market, same two defensible methods, and the number your entire bet depends on moved by roughly a tenth of its own value. The Shin method exists because of this: it models the margin as the book protecting itself against better-informed traders, which loads more of the margin onto the longshot, and it lands closer to observed settlement rates on markets with a long tail.

Our position: multiplicative on liquid two-way markets, Shin on anything with a long tail or more than three outcomes, and never mix. A de-vigged price from one method compared against a raw price from another is not a comparison, it is a rounding error wearing a conclusion.

• Convert every outcome to implied probability.
• Sum them. The excess over 1 is the overround.
• Divide each by the sum, or run Shin if the market has a long tail.
• Check the de-vigged set sums to exactly 1 before using it.

The mistake that costs money: using the fair price as the payout

De-vigging answers one question, which is what the market thinks. It does not change what you get paid. When you size a stake with Kelly or compute expected value, the payout term is the raw offered price, because that is the money that actually arrives. The de-vigged number belongs only where you need the market as an estimate: as the reference probability in a forecast, as the benchmark in closing line value, or as a sanity check on your own estimate.

Putting the fair price in the payout slot inflates every edge you compute by roughly the size of the margin, which for a three-way market can be most of the edge you thought you had.

What de-vigging cannot fix

A de-vigged price from a soft book is still a soft estimate. Removing margin does not add information, and a market that nobody with size can bet into is not aggregating anything. Two conditions decide whether a fair price is worth using: the book takes real money without instantly restricting the winners, and the price has moved recently enough to reflect current information.

Margins are also not constant across a book. Main lines carry the thinnest margin, and props and same-game markets carry several times it. If you de-vig a prop with a 12% overround and treat the result as a market consensus, you have carefully removed a large margin from a price that was never a consensus to begin with.