YES plus NO is more than a dollar: reading price as probability

One YES contract plus one NO contract on the same event pays exactly $1 at settlement, whatever happens. So if you could buy both for 96¢ you would have riskless profit, and someone would keep doing it until you could not. What survives is the opposite: the two asks sum to slightly more than $1, and the surplus is what the market charges for immediacy.

Betting calls this the overround or the vig, and it is the same quantity, sitting in a different place. A bookmaker builds it into the odds deliberately as a margin. On an exchange nobody sets it — it emerges from the gap between the best bid and the best ask, and it shrinks when more people compete to be at the front of each queue. Either way, the arithmetic a reader has to do is identical.

Concretely: YES at 64¢, NO at 40¢, sum 104¢. There are four cents of overround here, which is the same information as saying the market has a four-point spread. Reading YES as “the market says 64%” therefore overstates the probability by roughly half the spread, because the ask sits above the midpoint by exactly that much.

The convention is proportional: divide each side by the sum of both. For the market above, 64 ÷ (64 + 40) = 64 ÷ 104 = 61.5%, and the NO side is 40 ÷ 104 = 38.5%. The two now add to 100% by construction, which is the property that makes the number usable.

This site uses that formula everywhere it prints an implied probability, and it is worth naming it as a convention rather than a truth. Proportional de-vigging assumes the overround is distributed evenly in percentage terms across both sides. Other conventions exist — some assume it falls more heavily on the longshot, which is a real effect in fixed-odds betting — and they produce slightly different numbers. What matters more than the choice is applying one choice consistently, because a comparison between two differently-adjusted numbers is meaningless regardless of which method is better.

One case is not a de-vigging problem at all. If YES and NO sum to less than $1, no adjustment makes that coherent: it is riskless profit, which does not persist on a live book. In practice it means one of the two quotes is stale, and the right response is to discard the pair rather than to publish an arbitrage. Our own quote pipeline rejects sums below $1 for exactly that reason.

Take the same event on two venues. Venue A quotes YES 64¢ / NO 40¢. Venue B quotes YES 62¢ / NO 41¢. Read raw, the YES prices are two points apart and the obvious conclusion is that one venue is cheap.

De-vig both and the picture changes. Venue A gives 64 ÷ 104 = 61.5%. Venue B gives 62 ÷ 103 = 60.2%. The genuine disagreement is 1.3 points, not 2.0 — a third of the apparent gap was never a disagreement about the world, only a difference in how much overround each venue’s book happened to be carrying at that moment.

That shrinkage is the whole reason the adjustment matters. A cross-venue gap only means something if it survives the cost of acting on it, and the cost of acting includes crossing a spread on both legs plus whatever each venue charges. A 2-point “edge” that is really 1.3 points of disagreement, against maybe 2 points of round-trip cost, is not an opportunity — it is a rounding error dressed up as one.

The excess is worth keeping rather than throwing away once you have divided by it, because it says what kind of fact the price is. A quote de-vigged from a market with a one-point spread and a quote de-vigged from a market with a fourteen-point spread are both probabilities, and they are not the same quality of probability.

Above roughly eight points, we stop treating the midpoint as a consensus at all: the two sides of the book are far enough apart that the number between them is not a price anyone has agreed to. It still gets displayed, with the spread alongside it, but it does not feed a cross-platform comparison. Showing a probability without showing how wide the market behind it was would be the more misleading of the two options.