How to Devig Odds: Methods, Formulas, and Fair Value

Every sportsbook price has a markup baked into it. Strip that markup out and you are left with an estimate of the fair probability underneath, which is the number you need before you can say whether any other book's price is worth betting. That process is called devigging (sometimes written de-vigging, or removing the vig).

The mechanics take about a minute to learn. The part that actually decides your answer takes longer, and it is not the one most guides cover: which prices you feed the devig moves the fair number far more than which method you run it through. This guide covers both, starting with the calculator.

The Devig Calculator

Enter two prices from the same market and watch the fair probabilities and fair odds fall out. Switch the method dropdown to see how much (or how little) the choice moves the answer, and notice that the gap widens as one side gets more lopsided.

You can run the same calculation any time with the free devigging calculator, or convert between formats with the odds converter. The rest of this guide explains what the numbers mean and where they break down.

The Vig Inside Every Price

When a sportsbook sets a two-sided market, the implied probabilities of both outcomes add up to more than 100 percent. That excess is the vig (also called juice, margin, or overround), and it is how the book earns its cut.

Take a tennis match. The book offers Player A at 2.10 (+110) and Player B at 1.75 (−133). Convert each to an implied probability with 1 / odds:

• Player A: 1 / 2.10 = 47.6%
• Player B: 1 / 1.75 = 57.1%

Add them: 47.6% + 57.1% = 104.7%. Probabilities of a complete set of outcomes cannot really sum to more than 100 percent, so that extra 4.7 percent is the overround. Your job is to work out what the two prices would look like without it.

One clarification worth making early, because the two numbers get confused constantly. The overround is how much the market exceeds 100 percent. The hold is the book's share of the money paid out, which is the overround divided by the total. A 4.7 percent overround is a 4.5 percent hold. The low hold betting guide works through why that distinction changes what a bet costs you.

The Multiplicative Devig, Step by Step

The simplest method scales both probabilities down proportionally until they sum to 100 percent. It is called multiplicative (or proportional), and it is the one to learn first.

$q_i = \frac{p_i}{\sum_j p_j}$

Using the tennis prices above:

1. Total the implied probabilities: 104.7% (or 1.047)
2. Divide each side by that total:
   • Player A: 47.6% / 104.7% = 45.5%
   • Player B: 57.1% / 104.7% = 54.5%
3. Convert back to fair odds with 1 / probability:
   • Player A: 1 / 0.455 = 2.20
   • Player B: 1 / 0.545 = 1.83

So the fair price on Player A is 2.20, not the 2.10 the book is showing. If another book offers Player A at better than 2.20, that price is a candidate positive expected value bet. Candidate is the operative word: a fair price is an estimate, and any individual bet can still lose.

The Four Devig Methods

Multiplicative is a baseline, not the only option. The methods differ in how they hand back the overround, and SmartStake ships exactly four of them, matching the Devig Method dropdown in the Positive EV tool.

Multiplicative divides every probability by the total, so each side keeps its share. A side carrying twice the probability gives back twice the margin. Stable, fast, and the sensible default.

Additive subtracts the same number of probability points from each side, then renormalizes. Where multiplicative takes proportionally, additive takes equally, so it hands the longshot a relatively larger correction.

$q_i = p_i - \frac{\sum_j p_j - 1}{n}$

Power raises every probability to a common exponent chosen so they sum to 1. There is no closed form for that exponent, so the product solves for it by bisection. Because the exponent acts multiplicatively in log space, it corrects longshots harder than favorites.

$\sum_i p_i^{\alpha} = 1$

Probit converts each probability into a z-score on the normal distribution, shifts every one of them by the same constant, and converts back. It treats the market as a distribution being nudged rather than a set of numbers being scaled, which is why it behaves well around the 50 percent mark where spreads and totals live.

$\sum_i \Phi(\Phi^{-1}(p_i) + c) = 1$

You may see Shin listed as a fifth method elsewhere, including in older versions of this page. It models the margin as a book's defence against informed money and it is well established in the academic literature, but it is not one of the options SmartStake ships, so this guide no longer presents it as a choice you can make in the product.

There is also a fifth setting in the dropdown, Worst, which is not a method at all. It is covered further down, because it only makes sense once you have seen how far apart the four can get.

When the Method Changes the Answer

Here is the fact that should shape how much time you spend on this question: on a balanced market, all four methods return exactly the same answer.

Two matching prices of −110 devig to 50.0000 percent under multiplicative, additive, power and probit alike. So do two matching prices of −120, −130, −150 and −200. The vig is real and large in the last case, and it still changes nothing, because a symmetric market gives the methods nothing to disagree about.

They diverge when a market is lopsided, and they diverge more the further from even money it sits. A sharp +180 over against a −240 under devigs the under to a fair price of −198, −207, −208 or −213 depending on the method, a 15 point spread from one pair of prices. That is enough to flip a verdict on a bet.

Which markets are lopsided by construction? Player props and alternate lines, mostly. The player props guide works through exactly why the method question is a props question and close to a non-issue on a standard side, including the closed form behind it.

Here is the practical rule. Sides and totals sitting near even money: the method barely matters. Long props and alternate lines: the method matters, and no single answer is provably right.

The Prices You Feed the Devig

Now the part that matters more than everything above.

A devig does not check its inputs. Hand it two prices from a soft book and it hands back a fair number with the same confidence it gives you for Pinnacle, and that number inherits every bias the soft book baked in. Devigging a book you are about to bet at is close to meaningless, because you would be measuring that book against itself.

So the reference matters, and it has to be a book that prices the market seriously: high limits, fast reaction to news, and a willingness to take real money. The sharp money guide covers how to recognize one.

One refinement most explainers miss: sharpness belongs to a book in a market, not to a book. SmartStake's own sharp-book list is bet-type aware, so FanDuel counts as a reference on player props but not on main lines, while Bookmaker and BetOnline count on main lines but not props. Pinnacle and Circa carry the heaviest weight on both.

Devigging More Than One Book

Almost every explanation of devigging, including the earlier version of this page, describes it as an operation on two prices from one book. That is not what a tool actually does, and the difference is worth seeing.

SmartStake blends every qualifying sharp book into one synthetic pair before a single devig runs. Each book's decimal odds are averaged by weight (Pinnacle and Circa at 100, the rest at 50), and that blended pair is what gets devigged. Blend first, devig once. Not devig each book, then average.

Try it. Each book below holds a realistic margin, but they disagree about where the line sits.

The default state is the whole lesson on one screen. Pinnacle's pair devigs to 53.25 percent. Circa's devigs to 46.75 percent. Those two sharp books are 6.5 points apart on the same market, and the blend lands at exactly 50.00 percent on all four methods.

Compare the two levers. On this market, switching the devig method moves the fair price by zero, while dropping Pinnacle and reading Circa alone moves it from +100 to +114. Which prices you feed the devig is the bigger decision, and it is the one almost nobody writes about.

Toggle BetOnline off and the blend still reads 50.00 percent but the vig drops again, which is the effect the next section is about.

The Blend That Looks Too Tight

Watch the vig column in the widget. Every book is holding 4.34 percent or 4.76 percent. The blend holds 4.06 percent, tighter than any book in it.

That is not a bug and it is not free money. Averaging decimal odds across books that disagree pulls both sides of the blend toward the longer of the two prices, so the two implied probabilities sum to less than they do anywhere on the real market. The more the books disagree, the more the apparent margin collapses.

Hold each book at exactly 4.76 percent and move only where they think the line sits:

Two things fall out of that table, and they point in opposite directions.

The centre holds. Every row returns 50.00 percent, because the disagreement here is symmetric. Blending genuinely does cancel opposing errors, and that is the honest case for using more than one reference book.

The width collapses, and by the bottom row the blend implies a market summing to under 100 percent that no book is actually offering. So here is the takeaway worth carrying: a low vig on a blended line is not evidence that the market is tight. Past a point it is evidence that your reference books have diverged, which is exactly when the fair number underneath deserves the least trust.

This is why the guardrails around the blend exist rather than being incidental. SmartStake enforces a minimum number of contributing books, drops books whose two sides are too thin or too lopsided to be real, and collapses an operator's multiple skins into a single vote so one book cannot enter the average three times. On the fallback path used when no configured sharp book prices a leg, it goes further and trims any book more than 2.5 standard deviations from the group before averaging.

In normal conditions none of this bites. Two sharp books sitting 2 to 3 points apart shrink the blended vig by around a tenth of a point, and you can ignore it. Treat a collapsing blended vig as a signal to look at the individual books, not as a discount.

Worst Case Pricing

Which brings us back to the fifth item in that dropdown. Since no method is provably right on a lopsided market, SmartStake's answer is to refuse to count edge that depends on the choice.

Worst-case pricing runs all four methods and takes the least favorable result for the side you are betting. A bet only makes the board if it survives every reasonable reading of the market. That filters out some genuinely good bets, and in exchange a bet that clears is not an artifact of a setting.

Which method turns out to be the worst depends on the side, so the two sides of one market often get their conservative price from different methods. The player props guide shows what that conservatism costs on a real example.

Frequently Asked Questions

What does devigging mean in betting?

Devigging means removing a sportsbook's built-in margin from a price to estimate the fair probability underneath. The two sides of a market at one book add up to more than 100 percent, and devigging scales them back to 100 percent so you can compare the result against the price another book is offering.

How do you devig odds by hand?

Convert both sides to implied probabilities with 1 divided by the decimal odds, add them together to get the overround, then divide each side by that total. Two prices of 2.10 and 1.75 imply 47.6 percent and 57.1 percent, summing to 104.7 percent, so the fair probabilities are 45.5 percent and 54.5 percent. That is the multiplicative method.

Which devig method is the most accurate?

No method is provably the most accurate, because checking would require knowing the true probability you were trying to estimate. On a balanced market all four methods return the same answer, so the choice does not matter. On a lopsided market they diverge, and SmartStake handles that by pricing a bet at the least favorable of the four rather than picking a favorite.

Does SmartStake support the Shin method?

No. SmartStake ships four devig methods, which are multiplicative, additive, power and probit, plus a worst-case setting that takes the least favorable of the four for the side you are betting. Shin is a well-known approach in the academic literature but it is not one of the options in the product.

Which book should you devig to find fair odds?

Devig a sharp, high-limit book rather than the one you intend to bet at, because a soft book's price carries its own bias and devigging it only produces a confident-looking number built on a guess. SmartStake blends every qualifying sharp reference book by weight before running a single devig.

Why does a blended line show less vig than any single book?

Averaging decimal odds across books that disagree about where the line sits pulls both sides of the blend toward longer prices, so the two implied probabilities sum to less than they do at any individual book. A falling blended vig is a sign your reference books have diverged, not a sign the market is tight.

From Fair Odds to a Real Edge

A fair price on its own is not a bet. It is break-even by definition, so the edge only appears when you find a different book offering better than fair, and the size of that gap is what the expected value calculator turns into a number. Over enough bets, closing line value is the evidence that your fair prices were any good.

Three things decide whether a devig is worth trusting, in descending order of importance: the books you feed it, how much those books disagree, and the method. Most guides only cover the third.

Doing that by hand across every market is the part that does not scale, which is what the Positive EV tool automates: it blends the sharp books, devigs the result, compares it to every other book, and surfaces the gaps. Devigging is not risk free and no fair price guarantees a winner.

Further Reading

• Joseph Buchdahl (Football-Data). Accessible explanations of overround allocation and devigging in fixed-odds markets. football-data.co.uk
• Hyun Song Shin (1992 and related). Insider trading and price formation, the foundation behind the Shin adjustment.
• Practitioner notes on probit and logit link-based margin removal used in sports trading.

Related Guides and Tools

• Guide: No Vig Fair Odds, and what fair value means
• Guide: The No Vig Calculator walkthrough
• Guide: Player Props Explained, where the method choice bites
• Guide: Positive EV betting
• Guide: What sharp money is
• Guide: Line shopping
• Tool: Devigging Calculator
• Tool: Odds Converter
• Tool: Expected Value Calculator