Implied Probability Formula for Every Odds Format

Derive implied probability for American, decimal and fractional odds, then see why Bovada's -1000/+600 pair sums to 105.19% and what that overround means.

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SonicBet Odds Bulletin

16 Oct 2026 · 08:41

6 min read

The implied probability formula turns a price into the win chance that price charges for. For decimal odds it is 1 divided by the odds. For American odds it is 100 / (odds + 100) on a plus price and odds / (odds + 100) on a minus price, using the number without its sign. Add both sides of a real market and the total lands above 100 percent. The excess is the bookmaker's margin, called the overround.

Deriving the implied probability formula from the payout

Every version of the formula is the same idea: implied probability equals the stake divided by the total return. A bet that hands back R for every 1 staked only breaks even if it wins 1 time in R, so 1 / R is the chance the price is charging for.

The American format spells out the stake and the return. As of October 2026, Bovada's help page defines it this way: on a minus price the odds show the risk to win $100, and a plus price shows the profit on a $100 stake. That gives four formulas from one definition:

Plus American (+A): stake 100, total return A + 100. Implied probability = 100 / (A + 100).
Minus American (-B): stake B, total return B + 100. Implied probability = B / (B + 100).
Decimal (D): D already is the total return per 1 staked. Implied probability = 1 / D.
Fractional (N/M): stake M, total return N + M. Implied probability = M / (N + M).

The check is the even-money price. An EVEN price wins exactly the wager, so it is +100, decimal 2.00 and fractional 1/1. Every formula returns 50 percent: 100 / 200, 1 / 2.00 and 1 / (1 + 1).

Odds implied probability in each format

Odds implied probability is the same number in every format; only the arithmetic changes. Bovada's own example pair, Celtics -1000 against Cavaliers +600, shows it on a real posted line.

Side	Format	Price	Working	Implied probability
Celtics	American	-1000	1000 / (1000 + 100)	90.91%
Celtics	Decimal	1.10	1 / 1.10	90.91%
Celtics	Fractional	1/10	10 / (1 + 10)	90.91%
Cavaliers	American	+600	100 / (600 + 100)	14.29%
Cavaliers	Decimal	7.00	1 / 7.00	14.29%
Cavaliers	Fractional	6/1	1 / (6 + 1)	14.29%

To move between formats first, use decimal as the hub. A plus American price becomes 1 + A / 100, so +600 is 7.00. A minus price becomes 1 + 100 / B, so -1000 is 1.10. Analysts working in code tend to standardize the same way: the R package implied states that its inputs must be decimal odds, because 1 / D is the cleanest form of the conversion.

Implied win probability and why the sides top 100 percent

Implied win probability for one side is half the reading. Add both sides of the Celtics and Cavaliers line and you get 90.91% + 14.29% = 105.19%, not 100%. The extra 5.19 points is the overround: the book prices the market at more than certainty, so it keeps a margin whichever side wins.

A -110 line on both teams shows the same thing in its simplest form. Each side converts to 110 / 210, or 52.38%. The pair sums to 104.76%, and the 4.76 points above 100 is the margin. Bovada describes that line as neither team favored, and the numbers agree: equal prices mean equal implied chances, 50 percent each once the margin comes out.

The overround tells you how much of each implied probability is margin rather than market opinion. A book with no margin sums to exactly 100 percent; anything above that is what the bet costs.

From implied to fair probability

The simplest fix divides each side by the market total. The CRAN implied package documents this as its basic method, dividing the inverted odds by their sum. On the Celtics and Cavaliers line that gives 86.42% and 13.58%, which add back to 100%.

That method is a convenience, not a law. A paper in the American Journal of Sports Science found that subtracting the margin in equal shares, the additive method, can produce negative probabilities, and that plain normalization ignores favorite long-shot bias. The same paper found the power method outperformed multiplicative normalization across three large datasets while keeping every probability between 0 and 1. On a two-outcome market such as a moneyline, Shin and additive removal match exactly. Shin's model, per the package documentation, assumes a fraction of insider trading and returns an estimate of that share, labeled z.

Implied probability versus true probability

Implied probability is what a price charges. True probability is what actually happens, and nobody posts it. A price only offers value to someone whose own estimate of the true chance is higher than the implied one after the margin, and even then the result of any single game stays uncertain. Read the number as information about the market, not a forecast to bank on.

Market questions

How do you calculate probability from odds?

Divide 1 by the decimal odds. For American odds, a plus price converts as 100 / (odds + 100) and a minus price as odds / (odds + 100), using the number without its sign. Bovada's +600 Cavaliers price works out to 100 / 700, or 14.29%.

What is the difference between probability and odds?

Probability is a chance between 0 and 1. Odds are a payout quote. The implied probability is the chance a price charges you for, and on a real market it includes the bookmaker's margin, so it runs slightly above the market's honest estimate.

How do you calculate the probability of winning a bet?

The price gives you the implied probability, margin included. Divide each side by the market total to strip the overround, which is the basic method in the CRAN implied package. That still gives the market's view, not a guarantee of how the game goes.

What is the formula for calculating the odds against a probability?

Run the conversion backwards. Decimal odds equal 1 / p, and fractional odds against equal (1 - p) / p. A 50 percent chance gives decimal 2.00 and fractional 1/1, the EVEN price that pays exactly the stake.