Implied total (booksum)
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De-vig calculator
A bookmaker's odds are not its estimate of what will happen — they are that estimate with a margin baked in. De-vigging strips the margin back out, leaving the probability the book is actually implying. Enter the odds for every result in one market and compare four methods side by side.
Remove the margin
Decimal odds, all results in the same market. Add a leg for 1X2.
ResultOddsImplied
Vig / overround
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| Method |
|---|
Each cell shows the no-vig probability and, beneath it, the fair decimal odds it corresponds to. The methods disagree on purpose — they encode different assumptions about where the margin sits, and none of them is a measurement.
What the vig is
Take any market and convert each price to an implied probability with
1 / odds. Add them up. In a market that reflected genuine
probabilities the total would be exactly 1, because one of the results
must happen. In a real sportsbook market the total is always higher —
1.04, 1.06, sometimes 1.15 on an obscure competition.
That excess over 1 is the bookmaker's margin. It goes by several names — vig or vigorish (from the American side), juice, overround, or just the book's margin. It is the structural reason a bettor who picks results at exactly the rate the odds imply still loses money over time.
Booksum = Σ (1 / odds)
Vig = booksum − 1, usually quoted as a percentage
A two-way market at 1.91 / 1.91 has a booksum of
0.5236 + 0.5236 = 1.0471, so about 4.7% vig — the familiar
American −110 on both sides. The calculator reports both figures at the
top.
Why remove it
Because the de-vigged number is the closest thing available to a public estimate of what will actually happen, and you need such an estimate to judge any other price.
The standard use is to treat a sharp book — one with low margins, high limits, and a business model built on accepting winning customers rather than restricting them — as a reference. De-vig its price, and you have that book's honest probability. Then compare a softer book's price for the same result against it. If the soft book is offering odds implying a lower probability than the sharp book's de-vigged figure, that price is better than the reference thinks it should be.
This is a different activity from sure betting, and it is worth being clear about the difference. A sure bet is arithmetic: the prices either sum below 1 or they do not, and no opinion is involved. De-vigging produces an estimate, and every conclusion you draw from it inherits the estimate's error. The two approaches suit different temperaments, and mixing them up is how people talk themselves into thinking a judgement call is a certainty.
The four methods
There is no single correct way to de-vig, because the vig is not observable separately from the price. Every method is an assumption about how the bookmaker distributed its margin across the results, and that assumption is where they differ.
Multiplicative (proportional)
Divide each implied probability by the booksum.
pi = (1 / oddsi) ÷ Σ(1 / odds)
Assumes: the margin is spread proportionally — every result carries the same percentage of it. This is the default almost everywhere, because it is trivial to compute, always produces valid probabilities, and is scale-free. Its weakness is well documented: it systematically overstates the true probability of longshots, because in reality books load proportionally more margin onto long prices.
Additive
Subtract an equal share of the excess from every result.
pi = (1 / oddsi) − (Σ(1 / odds) − 1) ÷ n
Assumes: the margin is a flat amount per result rather than a percentage. This shifts probability toward longshots relative to the multiplicative method. It has a real failure mode: on a market with a big margin and a very long price, it can return a negative probability, which is a signal the assumption does not fit rather than a rounding problem. The calculator flags that case instead of hiding it.
Power
Raise each implied probability to a common exponent k, chosen
so the results sum to 1.
pi = (1 / oddsi)k, with k solved so that Σ pi = 1
Assumes: the margin scales with the price in a smooth,
non-linear way. Because k > 1 and every implied probability
is below 1, exponentiation shrinks small numbers proportionally more than
large ones — so the power method takes more margin off the longshots.
Empirically it tends to fit observed outcomes better than the
multiplicative method, at the cost of needing to be solved numerically.
There is no closed form; the calculator finds k by bisection.
Shin
Named for the economist Hyun Song Shin, whose model treats the margin as
the bookmaker's defence against a fraction z of bettors who
know something it does not.
pi = [ √( z² + 4(1−z) · qi² / Σq ) − z ] ÷ (2(1−z))
where qi = 1 / oddsi and z
is solved so that Σ pi = 1.
Assumes: the margin exists to price insider risk, and
that risk is concentrated on the results insiders would back. The solved
z is interpretable on its own — it is the model's estimate of
the proportion of insider money in that market, and the calculator reports
it. Shin's method is the one favoured in the academic literature on
favourite–longshot bias, and on three-way markets it lands between the
multiplicative and power results.
On a two-outcome market, Shin and additive give exactly the same
answer. This is not an approximation — the two formulas
coincide when n = 2, and you can confirm it in the
calculator by entering any two prices and comparing the rows. So on
two-way markets there are really only three distinct methods, and the
only one that meaningfully disagrees is power.
Which to use
| Situation | Reasonable choice |
|---|---|
| Two-way market, prices close to even | Any — they barely differ |
| Two-way with a heavy favourite | Power — Shin equals additive here |
| Three-way (1X2) | Shin, or power |
| Long lists (outrights, first goalscorer) | Shin — margin is very unevenly spread |
| You need one number and can't justify a model | Multiplicative, and say so |
The honest summary is that on a balanced two-way market the four methods agree to within a fraction of a percent and the choice does not matter. On a lopsided market they can disagree by several percent, which is larger than the edge most people are trying to detect. When that happens, the disagreement is the finding: your estimate is not precise enough to support the decision you were about to make with it.
Common questions
Why does my result differ from another calculator?
Almost always because the other one does not say which method it uses. Most default silently to multiplicative. Run the same market through the table above and you will usually find your number in one of the columns.
Should I de-vig one side or the whole market?
The whole market, always. Every method needs the complete set of results to know how much margin there is to remove. De-vigging a single price by halving its vig assumes a two-way symmetric market, and quietly gives the wrong answer everywhere else.
What about markets where a result can be void?
Push-eligible markets — a handicap that can land exactly on the line, a total that can land on the number — break the assumption that the listed results are exhaustive. The probability mass on the push is not in the prices at all, so the de-vigged figures are conditional on no push, and should be treated as such.
Does a lower vig mean a better book?
For price, yes, mechanically. But the margin is only part of it: a book with a 2% margin that limits you to a token stake after three winning bets is worth less than one with a 4% margin that takes real money. Margin is the number that is easy to publish, which is why it gets quoted most.
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