The method is proportional. Both sides of a book's own two-sided quote are converted to implied probabilities, then each is divided by their sum, so the resulting pair sums to exactly one. It depends only on the ratio of the two implied probabilities, so scaling both leaves the answer unchanged.
A one-sided quote gets no fair pair at all. There is no margin to remove from a single price, and inventing the missing side would fabricate a market that nobody published.
Prices that are not prices are refused rather than clamped. An American price smaller in magnitude than 100 is undefined, and a decimal price below 1.001 returns less than the stake, so both drop out instead of silently converting to an even-money default.
They are reported separately because they answer different questions, and collapsing them into a single figure loses the one a bettor can act on.
| Quantity | Definition |
|---|---|
| Implied probability | One divided by the decimal price. Still carries the book's margin. |
| Overround | The two implied probabilities added together. Above one for any real two-sided quote. |
| Hold | The overround minus one, in percentage points: the book's margin on its own two-sided quote. |
| Fair probability | Each side's implied probability divided by their sum, so the pair sums to one. |
When the two sides of one book's quote arbitrage each other the hold comes out below zero, and it is reported that way rather than floored at zero. It is rare within one book and ordinary across books, which is what the arbitrage tool exists to find.
Consensus is the median of the per-book fair Over probabilities on a market. The Under side is derived as one minus that figure rather than taken as a second median: two independent medians need not sum to one, and a pair that does not sum to one is not a probability distribution.
The books whose quotes went into that median are named in the response beside the number, so the figure can be recomputed by hand from the same board.
Best price and consensus are compared at different grains, and the difference is deliberate. The best published price is only ever compared among books quoting that exact same number, because a better price at a different number is a different bet. The consensus median spans a market's mainline quotes, which can sit at more than one number when books disagree, and the width of that disagreement is served as its own figure rather than hidden inside the median.
The role map carries 13 operators: BetMGM, BetOnline, BetOpenly, BetRivers, Bovada, Caesars, DraftKings, FanDuel, Fanatics, Kalshi, Novig, Polymarket, and ProphetX. Which of them quote any given market depends on what the feed returns for it.
It is what the market's own prices imply once the book's margin is removed. It is not a true probability, and it is not a projection: nothing in this calculation reads a model, a rating or an edge.
The distinction is measured, not rhetorical. On a frozen closing-line corpus of three books spanning 2023-10-24 through 2026-05-24, the de-vigged Over probability over-stated the realized over-rate by 1.68 percentage points across 57,842 matched regular-season book-rows, and by 3.74 points in the postseason. The market over-shades the Over, and a de-vig inherits that rather than correcting it.
This tool is part of the Market tier at $4.99/month. Goes live in October.
This page describes how the tool works. It carries no price, no fair-value figure and no margin: every number on it is a fixed threshold or a count read out of the product's own configuration.