What a price is really telling you
Every posted price carries a probability inside it. Strip away the format and a decimal of 2.00 is a statement: this outcome is priced as if it happens half the time. The arithmetic that recovers that statement is the single most useful calculation in betting, because it turns a payout into a probability you can compare against your own view.
The conversion runs through decimal odds. If you have a fractional or American price, route it to decimal first — the odds conversion guide covers every direction — and then the probability is a single reciprocal.
# raw implied probability from decimal price D p_raw = 1 / D # D = 2.00 to 0.500 = 50.0% # D = 1.50 to 0.667 = 66.7% # shortcuts straight from American price A minus price (−A): p_raw = A / (A + 100) # −200 to 200/300 = 66.7% plus price (+A): p_raw = 100 / (A + 100) # +150 to 100/250 = 40.0%
The word raw is doing real work here. This figure includes the book's margin. It is not the book's honest estimate of the outcome, and it is not a number you should bet against directly. It is the starting point.
Why the market sums above 100 percent
Take a clean two-way market — one where the two outcomes are exhaustive, so exactly one must happen. If the book priced both at their true probabilities, the two raw figures would sum to exactly 100 percent, and over a long run the book would break even. No business runs that way.
Instead the book shades each price a little shorter than fair. Now the raw probabilities sum to something above 100 percent. That surplus is the overround, also called the book percentage or the book sum.
| Side | Decimal | Raw implied probability |
|---|---|---|
| A | 1.91 | 1 / 1.91 = 52.36% |
| B | 1.91 | 1 / 1.91 = 52.36% |
| Sum | — | 104.71% |
The sum is 104.71 percent. The 4.71 points above 100 is the overround. On this symmetric market the fair probability of each side is obviously 50 percent, but the prices demand you buy each at an implied 52.36 percent. You are overpaying by design.
Measuring the overround
The definition is a subtraction, and it generalises past two-way markets to any number of mutually exclusive outcomes.
# book percentage = sum of every side's raw implied probability book_pct = Σ (1 / D_i) # over all outcomes i in the market # overround, in percentage points overround = book_pct − 100% # two-way at 1.91 / 1.91: 104.71% − 100% = 4.71 points # three-way at 2.40/3.30/3.10 (illustrative): # 41.67% + 30.30% + 32.26% = 104.23% to 4.23 points
The three-way line above is illustrative — the point is the method, not the numbers. On a multi-way market the same rule holds: add up the reciprocal of every price and see how far past 100 percent it lands. A soccer 1X2 market has three outcomes and so three prices to sum; an outright with twenty runners has twenty. More outcomes usually means a wider book, because the margin is spread across more prices.
Recovering the fair probability
Raw implied probability tells you what the price demands. To find what the book actually believes — its margin-free estimate — you remove the overround. The workhorse method is proportional normalisation: rescale every side so the set sums back to 100 percent.
# fair (no-vig) probability by proportional normalisation p_fair_i = p_raw_i / book_pct # asymmetric two-way, raw 54.0% and 50.7% (sum 104.7%) # fair A = 54.0 / 104.7 = 51.6% # fair B = 50.7 / 104.7 = 48.4% (now sums to 100%)
Proportional normalisation assumes the margin is applied evenly across outcomes. That assumption is weakest on very lopsided markets — a heavy favourite against a long shot — where more careful methods (such as the odds-ratio or Shin approaches) distribute the margin differently. For most two-way markets the proportional pass is close enough to be the default, and it is the method behind the vig remover tool. The vig, hold and margin guide covers what that removed margin costs you as a bettor.
Putting it to work
The full loop is short and mechanical, and it is the honest first move on any price you are handed.
- Convert to decimal. One reciprocal gives raw implied probability, no sign branching.
- Sum the market. Add every side's raw probability to get the book percentage; subtract 100 for the overround.
- Normalise. Divide each raw figure by the book percentage to get the fair, margin-free probability.
- Compare. Set your own probability estimate against the fair figure, not the raw one — that comparison is where value is found or ruled out.
None of this predicts a result. It only makes the price legible: what it demands, how much margin it carries, and what the book's own view underneath the margin appears to be.