Market maths
Overround calculator
Every bookmaker price contains a margin. Add up the implied probability of each outcome in a market and the total comes to more than 100%; the excess is what the bookmaker holds back. This calculator takes the prices of a complete market and reports that excess three ways, then strips it out to show what the prices imply about the actual chances.
It reports two figures that are both routinely called "the margin" and are not the same number. The overround is the book percentage minus 100. The expected loss per unit staked is the overround divided by the book percentage, because it is measured against the money staked rather than against a fair 100% book. A 103.22% book has a 3.22% overround and a 3.12% expected loss, and quoting one where the other is meant is how two sites end up publishing different margins for identical prices.
Inputs
Enter every outcome of the market. A partial set always looks cheaper than the market really is.
How the margin is removed. Proportional is the one you can reproduce by hand; power and Shin allow for margin being weighted towards longshots.
Result
- Book percentageSum of the implied probabilities of every outcome. A book with no margin is 100.00%.
- 103.22%
- OverroundBook percentage minus 100. This is the figure most often quoted as the bookmaker margin.
- 3.22%
- Expected loss per unit stakedOverround divided by the book percentage. Smaller than the overround because it is measured against the money staked, not against a fair 100% book.
- 3.12%
- Fair odds, outcome 1 (priced at 2.05)Fair probability 47.26%, proportional de-vig
- 2.116
- Fair odds, outcome 2 (priced at 3.60)Fair probability 26.91%, proportional de-vig
- 3.716
- Fair odds, outcome 3 (priced at 3.75)Fair probability 25.83%, proportional de-vig
- 3.871
These figures describe the prices as entered, and only hold if those prices cover every outcome of the market — a partial outcome set reports a lower book percentage than the market really has. Prices move, margin differs between markets and between leagues at the same bookmaker, and de-vigged fair odds are a model estimate of the true chances rather than the chances themselves. Commission, price boosts, stake limits and voided selections all change what a bet actually returns.
How this is calculated
book % = sum(1 / odds_i) x 100; overround % = book % - 100; expected loss % = overround % / book % x 100; fair odds_i = odds_i x book sum (proportional)
Take the reciprocal of each price to get its implied probability and add them up. On a 1X2 market priced 2.05 / 3.60 / 3.75 that is 0.487805 + 0.277778 + 0.266667 = 1.032249, a 103.22% book. Subtracting 1 gives the overround, 3.22%: the book is 3.22 percentage points heavier than a fair 100% book. Dividing the same excess by the book sum instead gives 0.032249 / 1.032249 = 3.12%, the expected loss per unit staked — the two differ because one is expressed as a fraction of a fair book and the other as a fraction of the money you put down. You can see the second figure directly: split EUR 100 across the three outcomes in proportion to their implied probabilities and every result returns EUR 96.88, a shortfall of 3.12%. The proportional de-vig then divides each implied probability by the book sum so they total exactly 1; because dividing a probability by the book sum is the same as multiplying the price by it, the fair odds are just each price times 1.032249. Power and Shin instead solve for a fair set that removes proportionally more margin from longshots than from favourites, so their fair odds will not equal price times book sum.
Worked example
A football 1X2 market at one bookmaker, compared with a second bookmaker pricing the same match.
- 01Prices: 2.05 on the home win, 3.60 on the draw, 3.75 on the away win.
- 02Implied probabilities: 1/2.05 = 0.487805, 1/3.60 = 0.277778, 1/3.75 = 0.266667. They sum to 1.032249.
- 03Book percentage = 103.22%. Overround = 103.22 - 100 = 3.22%.
- 04Expected loss per unit staked = 3.2249 / 1.032249 = 3.12%. Check it: staking EUR 47.26, EUR 26.91 and EUR 25.83 (EUR 100 split in proportion to the implied probabilities) returns EUR 96.88 whichever outcome wins, which is EUR 3.12 less than the EUR 100 staked.
- 05De-vigging proportionally divides each probability by 1.032249, giving 47.26%, 26.91% and 25.83%. The fair odds are the reciprocals: 2.116, 3.716 and 3.871 — the same as multiplying each price by 1.032249.
- 06A second bookmaker showing 2.00, 3.50 and 3.60 on the same match is a 106.35% book: a 6.35% overround and a 5.97% expected loss. That higher margin is visible in every individual price, all three of which are shorter than the first bookmaker.
Questions
Is the overround the same thing as the margin?
It depends who is speaking, which is the problem. "Margin" is used for both the overround (book percentage minus 100) and the expected loss per unit staked (overround divided by the book percentage). On a 103.22% book those are 3.22% and 3.12%. The gap grows with the size of the margin: a 110% book has a 10% overround but a 9.09% expected loss. This calculator labels both so you can see which one a given source is quoting, and the two should never be compared against each other.
Does a lower overround mean a better market for the customer?
On that market, at that moment, yes — a lower book percentage means the prices across the outcomes are collectively longer, so every outcome pays more than it would at a higher-margin book. That is why comparing bookmakers on overround is more informative than comparing them on sign-up offers: the margin applies to every bet you place there, while an offer applies once. It is a per-market measurement though, not a property of the bookmaker. The same operator can be tight on a major football league and much heavier on a lower division, on in-play prices, or on side markets, so a single headline figure should not be read as applying across the board.
Which de-vig method should I use?
Proportional is the transparent default: it divides every implied probability by the book sum, and anyone can reproduce it from published prices. Its known weakness is that it removes the same proportion of margin from every outcome, whereas real bookmaker margin is weighted towards longshots, so it tends to understate the favourite. Power and Shin correct for that in different ways. In the example above the favourite's fair odds come out at 2.116 proportionally, 2.101 under Shin and 2.096 under power — a small difference, but enough to change whether a price looks like value. Whichever you use, state the method alongside the number, because the fair odds are not comparable across methods.
Why does the real market differ from these figures?
Several ways. Entering an incomplete outcome set is the biggest one: two prices from a three-way market always sum to less than the full book, so the market looks far cheaper than it is, and can even appear to be under 100%. Beyond that, prices move, so the overround you measured is the overround at the moment you read the board; taking the best price on each outcome across several bookmakers produces a synthetic book with a lower percentage than any single bookmaker shows, which is not the margin any one of them charges; and exchanges quote no overround in this form at all because their cost is commission on winnings rather than margin in the price. Fair odds are also only an estimate of the true chances derived from one bookmaker's opinion, not a measurement of them.
Related calculators
These calculators are information tools. They describe the arithmetic of the prices you enter — they are not advice, and they do not predict outcomes. Betting involves risk. 18+ only. If gambling is causing you harm, support is available from Peluuri.