Devig calculator: remove the vig and get no-vig probabilities

A devig calculator takes the prices on every side of a market, strips out the sportsbook's margin, and hands back no-vig probabilities and odds. You can do it with a pencil, and it is worth knowing how, because the method you pick moves the answer.

This page is about the choice between methods. The basic walk-through of fair odds is on the fair odds calculator page, and converting a single price is covered on the implied probability calculator page. Here we compare three ways to devig and show where they disagree.

What "vig" is and why it has to come out

A two-way market priced at -110 / -110 looks even, but each side's implied probability is 52.38 percent. The two add to 104.76 percent. That extra 4.76 points is the vig (also called juice, hold or overround). Wikipedia's odds primer describes the same thing: the sum of the quoted probabilities for all outcomes exceeds 100 percent, and the excess is the bookmaker's profit on a balanced book.

To judge whether any price is good, you need a number with no margin in it to compare against. Devigging produces that number.

Three ways to remove it

All three start the same way: convert each price to an implied probability and add them up. They differ in how the excess is taken back out.

Multiplicative (normalization). Divide each probability by the total. Every side loses the same share. It is simple and it is what most free calculators do.

Additive. Subtract an equal number of points from each side (the excess divided by the number of outcomes). It works on near-even markets and can misbehave on lopsided ones, since a longshot can lose a large share of its probability.

Power. Find an exponent k so that each implied probability raised to k adds up to exactly 1. A 2017 comparison of margin-removal methods found that the power method universally outperforms the multiplicative method and outperforms or is comparable to the Shin method (American Journal of Sports Science). It takes more of the margin off longshots than favorites, which matches how books usually shade prices.

Same market, three answers

These are illustrations of the arithmetic, hypothetical prices rather than results.

A near-even game at -110 / -110. Every method gives 50 / 50. Nothing to choose.

A prop at -115 / -105. Implied probabilities are 53.49 and 51.22 percent, a total of 104.71. Multiplicative gives 51.08 / 48.92. Power (k about 1.071) gives 51.16 / 48.84. About a tenth of a point apart.

A heavy favorite at -200 / +170. Implied probabilities are 66.67 and 37.04 percent, a total of 103.70.

• Multiplicative: 64.29 / 35.71, fair odds -180 / +180
• Additive: 64.81 / 35.19, fair odds -184 / +184
• Power (k about 1.059): 65.08 / 34.92, fair odds -186 / +186

A big favorite at -1000 / +650. Implied probabilities are 90.91 and 13.33 percent, a total of 104.24.

• Multiplicative: 87.21 / 12.79, fair odds -682 / +682
• Additive: 88.79 / 11.21, fair odds -792 / +792
• Power (k about 1.132): 89.77 / 10.23, fair odds -878 / +878

On a coin flip the methods agree. On a -1000 favorite the fair price ranges from -682 to -878 depending on the method, and that gap decides whether a price on the underdog looks like value or not. Multiplicative tends to leave the longshot too high.

Three-way markets

Soccer-style markets with a draw work the same way. Take +150 / +230 / +190, which imply 40.00, 30.30 and 34.48 percent, a total of 104.79. Dividing each by the total gives 38.17 / 28.92 / 32.91 percent, or about +162 / +246 / +204. Futures with dozens of outcomes follow the same recipe, and the excess there can be far larger than 5 points.

Where to take the odds you devig

A devigged price is only as good as the market you start from. A single soft book's two-way line carries that book's shading and lag. Economist Steven Levitt found that bookmakers set a price and adjust it only occasionally, so two books can disagree for a while. A tighter reference comes from books that take sharp action, and published research agrees the market's own prices are informative: betting odds often beat mathematical models as forecasts (PLOS ONE).

One-sided markets

Many player props are posted with only an over, or with an over and under that aren't a true pair. If you only have one side, you can't measure the margin from the market itself. Anyone who devigs a one-sided prop is guessing at the margin, and the result is a rough estimate, not a fair price. When quant+ lacks enough prices it shows no fair value instead of inventing one.

How quant+ does it

On the odds comparison board each row shows the best price, the book, and the fair value underneath, already devigged. The default method is power, with multiplicative, additive and Shin available. The fair line is built from sharp books (Pinnacle and Circa) when they price the market and from a consensus of several books otherwise. The positive EV scanner then ranks prices that beat that line.

Limits

• Devigging estimates the market's view with the margin removed. It does not predict who wins.
• Stale prices give stale answers. A line that moved ten minutes ago can mislead.
• Method choice matters most on heavy favorites, longshots and futures.
• A tool can't tell you whether you are allowed to bet in your state or whether a book will take your action.

quant+ shows these numbers for information only. It doesn't place bets or connect to sportsbook accounts.

Quant+ is analytics for informational purposes. 21+. If you or someone you know has a gambling problem, call 1-800-GAMBLER.