De-vigging: getting the market's real opinion out of a price

Convert both sides to implied probability, add them, then divide each by that sum. Two prices of 52.4 and 52.4 sum to 104.8 and de-vig to 50 and 50. A 60 / 45 pair sums to 105 and de-vigs to 57.1 and 42.9.

The posted price contains the market's estimate plus the margin, and only the first half is information. Removing the margin proportionally is the simplest assumption available, and it turns two unusable numbers into the closest thing to an honest forecast anybody publishes.

Proportional removal is a convention, not a truth. Most books load more margin onto underdogs than onto favourites, so the simple method systematically flatters the long side. Methods that account for this exist and disagree with each other.

That is also the expensive part. A de-vigged wrong market gives you a precise wrong number, and precision is persuasive. The output looks like a probability and is only ever the market's guess with the fee subtracted.

What to do with it. Use the sharpest book you can find as the input. De-vigging a soft book returns a soft opinion with more decimal places.

Work it out. The no-vig calculator takes both sides of a market and returns the margin and the fair price of each.