Why sportsbook odds add up to more than 100%
A fair coin flip should give even odds: +100 American, or 2.00 decimal. If you bet $100 at +100 and win, you get $200 back ($100 profit + $100 stake). That implies 50% probability for each side.
Sportsbooks don't offer fair odds. They add a margin — called vig or juice — that ensures they profit regardless of the outcome. In a two-outcome market like a match result, the odds are set so the implied probabilities add up to something like 105–110%, not 100%.
With vig (typical)
Home: +110 → 47.6%
Away: +110 → 47.6%
Total: 95.2%
Wait — that's below 100%?
The book overround is hidden in the -110 on each side, not in the total.
Each side separately
Home implied: 100/(110+100) = 47.6%
Away implied: 100/(110+100) = 47.6%
Real margin: 4.8% per side
The margin is baked into the odds on each side, not visible as an extra.
The no-vig formula
To remove the vig, convert all odds to implied probability, then scale each one proportionally so they sum to 100%.
1. Convert each outcome to implied probability:
P(implied) = odds / (odds + 100) [American]
P(implied) = 1 / decimal_odds [Decimal]
2. Sum all implied probabilities:
P(total) = sum(P(implied) for all outcomes)
3. Divide each by the total to get no-vig:
P(no-vig) = P(implied) / P(total)
Example: World Cup group winner
DraftKings offers World Cup Group A winner odds:
| Team | American Odds | Implied w/ vig | No-Vig Prob |
|---|---|---|---|
| Brazil | -180 | 64.3% | 61.5% |
| France | +120 | 45.5% | 43.5% |
| Draw | +350 | 22.2% | 21.3% |
| Germany | +600 | 14.3% | 13.7% |
Sum of implied = 146.3%. No-vig normalizes to 100%. The margin is distributed proportionally across all outcomes.
Why no-vig matters for cross-market comparison
When you compare a Polymarket prediction-market price to sportsbook odds, you need both expressed as the same thing — and that means no-vig probability for the sportsbook side. A Polymarket price of 0.62 should be compared against the no-vig probability, not the raw sportsbook implied that includes vig.
Without no-vig normalization, a market that's actually aligned will look like it has a 5–10% gap — which is just the sportsbook's margin, not a genuine disagreement between prediction market and sportsbook.
What no-vig doesn't tell you
Even after removing the vig, sportsbook and prediction-market prices can differ for legitimate reasons:
- Different settlement rules: A prediction market may settle on full-time result while the sportsbook uses 90-minute only.
- Prediction-market fees: Polymarket charges ~1% on-chain taker fee that slightly reduces effective payouts.
- Liquidity effects: Thin markets on either side can move prices away from fair value temporarily.
- Traders vs. bettors: Prediction-market participants may have different information and motivations than sportsbook bettors.
The market diagnostics dashboard applies no-vig normalization automatically and flags which differences survive after accounting for fees, spread, and settlement rules.