How to Remove the Vig from Betting Odds

A bookmaker's posted odds bake in a margin, so the implied probabilities across a market sum above 100%. Every decimal odds price is a probability in disguise: 2.10 implies 47.6%, 1.50 implies 66.7%. Removing that margin (devigging) strips it out so the adjusted probabilities sum to exactly 100%, turning a price into a clean estimate of the true outcome probability.

What the vig is and why it needs removing

The vig (also called vigorish, juice, margin, or overround) is the bookmaker's built-in edge on every market. It ensures the book profits regardless of outcome. Because of it, the implied probabilities across all outcomes sum to more than 100%. Using those raw numbers to estimate value means working with inflated figures that favor the book.

Devigging removes that inflation. The result is a no-vig probability, sometimes called a fair or true-odds estimate, with the margin stripped out so the probabilities sum back to exactly 100%.

A no-vig line isn't a guaranteed truth. It's the market's estimate of the real outcome probability.

From a sharp book running 2-3% margins, it's a strong estimate. From a soft book with higher margins, it's noisier. The quality of the no-vig line depends on the quality of the book pricing it.

Converting odds to implied probability

Before you can remove anything, you need to convert odds to implied probabilities.

Three odds formats appear in practice: decimal, fractional, and American. Each converts to a probability with its own formula.

Decimal:
P = 1 / decimal_odds
2.10 → 1 / 2.10 = 47.6%

Fractional (a/b):
P = b / (a + b)
4/6 → 6 / (4 + 6) = 60%

American (moneyline):
Negative:  P = |odds| / (|odds| + 100)
Positive:  P = 100 / (odds + 100)

-150 → 150 / 250 = 60%
+150 → 100 / 250 = 40%

Why the market sums above 100%

Add the implied probabilities for every outcome in a market and the total will exceed 100%. The excess is the margin.

Overround = (sum of implied probabilities) − 100%

Three-way football market example:

Home  2.10 → 47.6%
Draw  3.60 → 27.8%
Away  3.40 → 29.4%

Sum = 104.8%  →  overround = 4.8%

Pinnacle runs roughly 2-3% margins. The wider market often runs higher, but no precise industry-average figure is well established.

How the proportional method works

The proportional (multiplicative) method is the standard starting point. It divides each outcome's implied probability by the total sum, distributing the margin in proportion to each outcome's weight.

no_vig_prob(i) = implied_prob(i) / sum_of_all_implied_probs

Worked example, a two-way market, favorite -180 / underdog +155:

Favorite  -180 → 180 / 280 = 64.3%
Underdog  +155 → 100 / 255 = 39.2%

Sum = 103.5%  →  overround = 3.5%

No-vig favorite  = 64.3 / 103.5 = 62.1%
No-vig underdog  = 39.2 / 103.5 = 37.9%

Check: 62.1 + 37.9 = 100%

Fair decimal odds:
Favorite  1 / 0.621 ≈ 1.61
Underdog  1 / 0.379 ≈ 2.64

Favorites absorb a larger absolute share of the margin because the division scales with each side's implied probability. That cuts both ways: it's simple to apply, but it tends to understate the underdog's true probability because it ignores favorite-longshot bias, the well-documented pattern where bettors overback favorites and books price underdogs at inflated implied probabilities.

The additive and Shin methods

The additive method subtracts the same flat amount from each outcome, rather than scaling by weight.

no_vig_prob(i) = implied_prob(i) − (overround / number_of_outcomes)

Using the same -180 / +155 market:

Overround 3.5%, two outcomes → subtract 3.5 / 2 = 1.75 from each

Favorite  64.3 − 1.75 = 62.5%
Underdog  39.2 − 1.75 = 37.5%

Check: 62.5 + 37.5 = 100%

37.5% for the underdog versus 37.9% under the proportional method. Subtracting equally lowers the underdog more in relative terms and the favorite less, which partly corrects for favorite-longshot bias, the tendency of books to overprice underdogs in implied-probability terms.

The additive method has a practical flaw: in markets with a heavy underdog, subtracting a flat amount can push the longshot probability below zero. That makes it unreliable as a general default. Most practitioners treat it as a sanity check rather than a primary method.

Hyun Song Shin (1993) took a different approach. His method models the market as containing a fraction of informed (insider) traders and solves for the underlying probabilities that account for that structure.

The fraction, z, is estimated per market and is typically small in liquid markets, on the order of a few percent. The closed-form expression used in practice is:

π_i = [ √(z² + 4(1−z) · o_i² / Σo_i) − z ] / [ 2(1−z) ]

where o_i are the raw implied probabilities

You don't solve this by hand. The shin Python package (and similar libraries) handles the iterative estimation.

Shin works best when favorite-longshot bias matters and predictive accuracy is the goal. Studies report it can improve accuracy over simpler methods, though no fixed improvement figure applies universally.

A related option is the power method, which raises each implied probability to a constant exponent until the total sums to 100%. It keeps all results within 0-1, avoids the negative-probability problem of additive, and some practitioners treat it as a good general default where Shin isn't available.

Method choice in practice:

Proportional  →  default; fine for near-even two-way markets; understates longshots
Additive      →  simple bias nudge or sanity check; breaks on large underdogs
Power         →  bias-aware; keeps results in 0–1 range; easier to compute than Shin
Shin          →  theoretically grounded; best when bias matters and accuracy is the goal

From a no-vig probability to finding value

Once you have a no-vig probability from a sharp book, compare it to the price available at a softer book. If your probability estimate exceeds the implied probability of the offered odds, the bet carries positive expected value.

The edge formula:

Edge = (true_prob × decimal_odds) − 1

Positive = value bet

Using the 62.1% no-vig favorite from above, suppose a soft book offers that team at 1.75 decimal (implied 57.1%):

Edge = (0.621 × 1.75) − 1 = 1.087 − 1 = +0.087  →  +8.7%

62.1% > 57.1%  →  value bet

You can also express the same thing in money terms:

EV = (P_win × profit_if_win) − (P_lose × stake)

The no-vig line from a sharp book is the benchmark. The gap between that benchmark and what the soft book offers is the edge you're trying to capture. A positive edge means the bet is +EV over a large sample. It doesn't make any individual bet a sure win.