book-vig-overround draft

Sportsbooks make money by quoting prices that, taken together, sum to more than 100% in implied-probability space. That extra slice is the vig — also called juice, the cut, or the take — and it's the book's compensation for warehousing risk on both sides of an event. A "true" market would have implied probabilities that sum to exactly 1.0; a real market sums to something a bit higher, and the difference is overround.

You compute it by converting each side's posted odds to implied probability and summing. For a binary (two-sided) market: overround = qA + qB − 1, where qA = 1 / decimal_odds_A and likewise for B. Kairos exposes both the absolute overround (s − 1) and a "vig percent" defined as overround / s × 100 — the share of the market's implied-probability mass that's vig rather than belief. The two are close at low vig but not identical; pick a convention and stick with it.

The vig matters because it sets a floor on edge: any bet you place against a book with vig V needs your true win rate to exceed the no-vig fair rate by enough to clear V before you start making money. A bet at no edge in a 5% vig market loses 5% of stake on average over a long run.

Worked example

Take a sportsbook moneyline: Side A at +150, Side B at −180.

• Decimal odds A = 1 + 150/100 = 2.50, so qA = 1/2.50 = 0.4000
• Decimal odds B = 1 + 100/180 ≈ 1.5556, so qB = 1/1.5556 ≈ 0.6429
• Sum of implied probabilities: 0.4000 + 0.6429 = 1.0429
• Overround: 1.0429 − 1 = 0.0429 (4.29%)
• Vig percent (Kairos convention): 0.0429 / 1.0429 × 100 ≈ 4.11%

So the book has built ~4% of margin into this market. Devigging (see devigging) backs out their actual fair belief.

Typical magnitudes

• Sportsbook moneylines: ~4–5% overround on standard sides; thinner on showcase markets, fatter on obscure props.
• Spreads / totals: typically posted as −110 / −110, which sums to ~1.0476 → ~4.76% overround. Sharper books may post −105 / −105 (~4.6%) or even reduced juice.
• Prediction markets (Kalshi, Polymarket): implicit overround is often very small or near zero on liquid contracts because prices come from order-book matching rather than a bookmaker setting both sides. The "vig" in those venues shows up as taker fees, not as wide quotes.

Gotchas

• Overround is sum-minus-1, not the difference between sides. A common error is thinking +150 / −180 has "30 cents of vig" because the absolute prices look 30 apart. The actual overround is computed in probability space, not American-odds space.
• Two definitions of vig percent are floating around. Kairos uses overround / sum (share of total implied mass). Other sources use just overround directly, or overround / (1 + overround). They're all close at small vig but diverge for fat markets — match definitions before comparing numbers across tools.
• Multi-way (3+) markets compound vig. A futures market with 30 outcomes may show overround of 30%+ even though "per-side" vig feels modest. Don't reason about a futures market the way you reason about a moneyline.
• Asymmetric vig is real. Books sometimes load more vig onto the favorite or the dog. The sum tells you the total, but the devig method determines how it gets redistributed back to fair probabilities — see devigging.
• Prediction-market "vig" is partly fees, not quote width. A Kalshi market with Yes 0.55 / No 0.46 looks like 1% overround, but you also pay maker/taker fees on every trade. Total cost-of-trade includes both.

Open questions

• Kairos exposes vig_pct = (overround / s) * 100 (share-of-implied-mass). Some books / industry conventions use plain overround as the headline number. Confirm which convention Mimir treats as canonical when surfacing "the vig" to a downstream consumer.

Cross-references

• mimir: american-implied-probability
• mimir: devigging
• mimir: consensus-fair-line