How Sportsbook Vig Works (and How to Devig a Line)
When you look at betting odds from a sportsbook, the numbers might seem straightforward. But behind every price is a hidden cost: the vig (short for vigorish, also called juice or margin). This fee ensures the bookmaker profits regardless of the outcome. If you want to compare odds across venues, hunt for value, or price bets fairly, you need to understand how vig works—and how to remove it.
This article will cover:
- What the vig is and why it exists
- How to calculate the vig baked into a sportsbook line
- Methods to "devig" (remove the vig) to estimate the true implied probabilities
- Concrete, step-by-step examples with real numbers
- How automated tools like ArbMonster account for vig when scanning markets
Let's start with the basics.
What Is Sportsbook Vig?
The vig is the built-in margin that sportsbooks add to their odds. It ensures that, in the long run, the bookmaker makes a profit regardless of which side of the bet wins. If you bet on every outcome in a market, the total amount you'd pay would exceed the total payout—this difference is the vig.
Example: A Coin Toss Line
Suppose a sportsbook offers these odds for a fair coin toss:
- Heads +100 (decimal 2.00)
- Tails +100 (decimal 2.00)
No vig here: if you bet $100 on both sides, you’d break even. But sportsbooks rarely offer even odds. Instead, you might see:
- Heads -110 (decimal 1.91)
- Tails -110 (decimal 1.91)
Now, if you bet $110 on both sides ($220 total):
- No matter which side wins, you get paid $100 profit, plus your $110 stake back = $210
- You spent $220, but get back $210: the $10 difference is the vig (really, the bookmaker's expected revenue)
How to Calculate the Vig on a Line
To see how much vig is in a set of odds, convert each outcome’s odds to its implied probability, then add them up. If the total exceeds 100%, the excess is the vig.
Step-by-Step Example
Let’s take a common NFL spread market:
- Team A -3.5 (-108)
- Team B +3.5 (-112)
1. Convert American Odds to Decimal Odds
- Team A: -108 → Decimal = 1 + 100/108 ≈ 1.9259
- Team B: -112 → Decimal = 1 + 100/112 ≈ 1.8929
2. Convert Decimal Odds to Implied Probability
Implied Probability = 1 / Decimal Odds
- Team A: 1 / 1.9259 ≈ 0.519
- Team B: 1 / 1.8929 ≈ 0.528
3. Add the Probabilities
Total = 0.519 + 0.528 = 1.047 (or 104.7%)
4. Calculate the Vig
Vig = Total - 1 = 0.047 (or 4.7%)
This means the sportsbook expects to collect a 4.7% margin on every dollar bet in this market.
How to Devig a Line
Devigging means removing the bookmaker’s margin to estimate the "true" probabilities implied by the odds.
There are a few methods, but for two-outcome markets, the simplest and most common is proportional scaling.
The Proportional Devig Formula
If the odds imply probabilities of p1 and p2, and the total is T (>1), the devigged (fair) probabilities are:
- Fair p1 = p1 / T
- Fair p2 = p2 / T
Using the NFL Spread Example
- p1 = 0.519 (Team A)
- p2 = 0.528 (Team B)
- T = 1.047
Devigged probabilities:
- Team A: 0.519 / 1.047 ≈ 0.4954 (49.5%)
- Team B: 0.528 / 1.047 ≈ 0.5046 (50.5%)
Now these add up to 100% (49.5% + 50.5%), representing the "fair" odds implied by the market, excluding the vig.
Converting Back to Odds
To see what the vig-free odds would look like:
- Decimal odds = 1 / devigged probability
- Team A: 1 / 0.4954 ≈ 2.02 (American odds: +102)
- Team B: 1 / 0.5046 ≈ 1.98 (American odds: -102)
So, if the sportsbook were not charging a margin, you’d see odds around +102 / -102 instead of -108 / -112.
Devigging Multi-Outcome Markets
For markets with more than two outcomes (like "Who will win the championship?" with 10 teams), the process is similar: sum up the implied probabilities, then divide each by the total. For more accuracy, traders sometimes use alternate methods (like the Shin method) to account for potential bias, but proportional devigging is the norm for most practical purposes.
Example: Three-Way Market (Soccer Draw)
Suppose you see:
- Team X: +150 (2.50 decimal)
- Draw: +220 (3.20 decimal)
- Team Y: +170 (2.70 decimal)
Implied probabilities:
- Team X: 1/2.50 = 0.400
- Draw: 1/3.20 = 0.313
- Team Y: 1/2.70 = 0.370
Total = 0.400 + 0.313 + 0.370 = 1.083
Devigged:
- Team X: 0.400 / 1.083 ≈ 0.369
- Draw: 0.313 / 1.083 ≈ 0.289
- Team Y: 0.370 / 1.083 ≈ 0.342
These sum to 1 (100%), giving you the "fair" probabilities implied by the market.
Why Does Devigging Matter?
- Comparing odds across venues: By removing the vig, you can compare the true implied probabilities across sportsbooks and prediction markets, apples-to-apples.
- Spotting pricing gaps: If one venue is offering higher devigged probability (better effective odds) than another, there may be an arbitrage or value opportunity.
- Evaluating market consensus: Devigged lines give a clearer view of what the market really thinks, after accounting for bookmaker profit.
Automated services like ArbMonster scan 20+ sportsbooks, Kalshi, and Polymarket, devigging every market in real time (fees included) to show net pricing gaps and potential trades. For a deeper dive into devigging, see ArbMonster Learn.
FAQ
Q: Why do different sportsbooks have different vig?
A: Bookmakers set margins based on competition, risk, and market liquidity. High-profile markets often have lower vig (2–4%) to attract volume, while niche markets may have higher vig (up to 10% or more).
Q: Can you always calculate the exact true probability from market odds?
A: No. Devigged odds estimate the consensus probability, but markets can be biased or illiquid, and prices don't guarantee "truth"—they only reflect what people are willing to bet at.
Q: Does devigging account for exchange or prediction market fees?
A: Not by itself. You must also subtract any trading or settlement fees to find the real net probability or payout. Automated tools like ArbMonster include all known fees by default.
ArbMonster is a data service. Nothing here is financial or betting advice; markets carry risk, venues have age and jurisdiction restrictions, and you are responsible for verifying everything before acting.