How to calculate implied probability: calculator and formulas
By George Boyle · Updated 2026-10-25 · The Sport Stack
To calculate implied probability, use the formula for your odds format. American odds: for a negative price, divide the number by itself plus 100 (-150 is 150 ÷ 250 = 60.0%); for a positive price, divide 100 by the price plus 100 (+200 is 100 ÷ 300 = 33.3%). Decimal odds: divide 1 by the price (2.50 is 40.0%). Fractional odds a/b: divide b by a + b (5/2 is 2 ÷ 7 = 28.6%). The result is the win rate the price needs to break even.
Implied probability calculator
Enter a price in any format to see it in the others, with the win rate it assumes.
- Implied probability
- 52.4%
- American
- -110
- Decimal
- 1.91
- Fractional
- 10/11
Break-even win rate at this price: 52.4%. Win more often than that and the bet makes money over time; less often and it loses.
Remove the vig from a two-way market
Enter both sides in American odds. The implied probabilities add to more than 100%; scaling them back to 100% (the proportional method) gives the no-vig price.
| Side A | Side B | |
|---|---|---|
| Implied | 52.4% | 52.4% |
| No-vig | 50.0% | 50.0% |
| Fair odds | +100 | +100 |
The two sides add to 104.8%, an overround of 4.8%; the book's theoretical hold is 4.5% of the money bet.
Implied probability formulas at a glance
One formula per odds format. Each gives the probability as a decimal; multiply by 100 to read it as a percentage.
The implied probability formula for each odds format, with a worked example
American, negative (favourite)
- Formula
- odds ÷ (odds + 100), ignoring the minus sign
- Worked example
- -150: 150 ÷ (150 + 100)
- Implied probability
- 60.0%
American, positive (underdog)
- Formula
- 100 ÷ (odds + 100)
- Worked example
- +200: 100 ÷ (200 + 100)
- Implied probability
- 33.3%
Decimal
- Formula
- 1 ÷ odds
- Worked example
- 2.50: 1 ÷ 2.50
- Implied probability
- 40.0%
Fractional a/b
- Formula
- b ÷ (a + b)
- Worked example
- 5/2: 2 ÷ (5 + 2)
- Implied probability
- 28.6%
How to calculate implied probability with American odds
American odds have two formulas, and the sign tells you which one to use. For a negative price, the favourite, take the number without its minus sign and divide it by itself plus 100. For a positive price, the underdog, divide 100 by the number plus 100.
Worked examples: a favourite at -150 is 150 ÷ (150 + 100) = 150 ÷ 250 = 60.0%. An underdog at +200 is 100 ÷ (200 + 100) = 100 ÷ 300 = 33.3%. The standard -110 on spreads and totals is 110 ÷ 210 = 52.4%, which is the win rate you need to break even on the standard bet.
A quick check on any answer: a negative price always comes out above 50%, a positive price below 50%, and +100 (even money) is exactly 50%.
How to calculate implied probability with decimal odds
Decimal odds are the total return for each unit staked, stake included, so the formula is the simplest of the three: implied probability = 1 ÷ decimal odds.
Worked examples: 2.50 is 1 ÷ 2.50 = 40.0%, 1.50 is 1 ÷ 1.50 = 66.7%, and 4.00 is 1 ÷ 4.00 = 25.0%. Any price below 2.00 is a favourite, above 50%, and any price above 2.00 is an underdog.
How to calculate implied probability with fractional odds
Fractional odds a/b pay a for every b staked. The implied probability is the second number divided by the sum of both: b ÷ (a + b).
Worked examples: 5/2 pays 5 for every 2 staked, so it is 2 ÷ (5 + 2) = 2 ÷ 7 = 28.6%. A favourite at 1/2 is 2 ÷ 3 = 66.7%, evens (1/1) is 1 ÷ 2 = 50.0%, and 10/11, the fractional version of -110, is 11 ÷ 21 = 52.4%.
Another route to the same answer: fractional a/b is decimal 1 + a ÷ b, so 5/2 is 3.50, and 1 ÷ 3.50 is the same 28.6%.
The same price in every format
American, decimal and fractional odds are three ways of writing one price, so they convert to the same probability. +150, 2.50 and 3/2 are the same bet: 100 ÷ (150 + 100) = 40.0%, 1 ÷ 2.50 = 40.0%, and 2 ÷ (3 + 2) = 40.0%.
That is why the calculator above takes any of the three, and why comparing bets across books and formats is easier in percentages than in odds.
Why do the two sides add to more than 100%?
Add the implied probabilities of both sides of a -110 / -110 market and you get 52.4% + 52.4% = 104.8%. Real outcomes can only sum to 100%, so the excess is the book’s margin, often called the vig or the overround. The bigger the sum, the more the book is charging.
Because of that margin, an implied probability is always a little higher than the book’s actual estimate of the outcome. The simplest way to remove it is to divide each side by the total: a -150 / +130 market implies 60.0% + 43.5% = 103.5%, which scales to 58.0% and 42.0%. Removing the margin is called devigging, and it is the step between reading a price and judging one.
What does implied probability tell you?
It is the win rate you need to break even at that price, which makes it the yardstick for every bet. If your own estimate of an outcome is higher than the price implies — after the margin has been removed — the bet has positive expected value; if it is lower, no amount of confidence in the pick makes the price right.
It is also the input every sizing rule needs. The Kelly criterion, for instance, sizes a bet from the gap between your probability and the market’s, so the conversion above is the first line of that calculation too.
Odds to implied probability chart
Every common American price from -1000 to +1000, with the same price in decimal and fractional odds and the win rate it implies. These are raw implied probabilities — the book's margin is still in them, so the two sides of a real market add to more than 100%.
| American | Decimal | Fractional | Implied % |
|---|---|---|---|
| -105 | 1.95 | 20/21 | 51.2% |
| -110 | 1.91 | 10/11 | 52.4% |
| -115 | 1.87 | 20/23 | 53.5% |
| -120 | 1.83 | 5/6 | 54.5% |
| -125 | 1.80 | 4/5 | 55.6% |
| -130 | 1.77 | 10/13 | 56.5% |
| -135 | 1.74 | 20/27 | 57.4% |
| -140 | 1.71 | 5/7 | 58.3% |
| -145 | 1.69 | 20/29 | 59.2% |
| -150 | 1.67 | 2/3 | 60.0% |
| -155 | 1.65 | 20/31 | 60.8% |
| -160 | 1.63 | 5/8 | 61.5% |
| -165 | 1.61 | 20/33 | 62.3% |
| -170 | 1.59 | 10/17 | 63.0% |
| -175 | 1.57 | 4/7 | 63.6% |
| -180 | 1.56 | 5/9 | 64.3% |
| -185 | 1.54 | 20/37 | 64.9% |
| -190 | 1.53 | 10/19 | 65.5% |
| -195 | 1.51 | 20/39 | 66.1% |
| -200 | 1.50 | 1/2 | 66.7% |
| -210 | 1.48 | 10/21 | 67.7% |
| -220 | 1.45 | 5/11 | 68.8% |
| -230 | 1.43 | 10/23 | 69.7% |
| -240 | 1.42 | 5/12 | 70.6% |
| -250 | 1.40 | 2/5 | 71.4% |
| -260 | 1.38 | 5/13 | 72.2% |
| -270 | 1.37 | 10/27 | 73.0% |
| -280 | 1.36 | 5/14 | 73.7% |
| -290 | 1.34 | 10/29 | 74.4% |
| -300 | 1.33 | 1/3 | 75.0% |
| -325 | 1.31 | 4/13 | 76.5% |
| -350 | 1.29 | 2/7 | 77.8% |
| -375 | 1.27 | 4/15 | 78.9% |
| -400 | 1.25 | 1/4 | 80.0% |
| -425 | 1.24 | 4/17 | 81.0% |
| -450 | 1.22 | 2/9 | 81.8% |
| -475 | 1.21 | 4/19 | 82.6% |
| -500 | 1.20 | 1/5 | 83.3% |
| -550 | 1.18 | 2/11 | 84.6% |
| -600 | 1.17 | 1/6 | 85.7% |
| -650 | 1.15 | 2/13 | 86.7% |
| -700 | 1.14 | 1/7 | 87.5% |
| -750 | 1.13 | 2/15 | 88.2% |
| -800 | 1.13 | 1/8 | 88.9% |
| -850 | 1.12 | 2/17 | 89.5% |
| -900 | 1.11 | 1/9 | 90.0% |
| -950 | 1.11 | 2/19 | 90.5% |
| -1000 | 1.10 | 1/10 | 90.9% |
| American | Decimal | Fractional | Implied % |
|---|---|---|---|
| +100 | 2.00 | 1/1 | 50.0% |
| +105 | 2.05 | 21/20 | 48.8% |
| +110 | 2.10 | 11/10 | 47.6% |
| +115 | 2.15 | 23/20 | 46.5% |
| +120 | 2.20 | 6/5 | 45.5% |
| +125 | 2.25 | 5/4 | 44.4% |
| +130 | 2.30 | 13/10 | 43.5% |
| +135 | 2.35 | 27/20 | 42.6% |
| +140 | 2.40 | 7/5 | 41.7% |
| +145 | 2.45 | 29/20 | 40.8% |
| +150 | 2.50 | 3/2 | 40.0% |
| +155 | 2.55 | 31/20 | 39.2% |
| +160 | 2.60 | 8/5 | 38.5% |
| +165 | 2.65 | 33/20 | 37.7% |
| +170 | 2.70 | 17/10 | 37.0% |
| +175 | 2.75 | 7/4 | 36.4% |
| +180 | 2.80 | 9/5 | 35.7% |
| +185 | 2.85 | 37/20 | 35.1% |
| +190 | 2.90 | 19/10 | 34.5% |
| +195 | 2.95 | 39/20 | 33.9% |
| +200 | 3.00 | 2/1 | 33.3% |
| +210 | 3.10 | 21/10 | 32.3% |
| +220 | 3.20 | 11/5 | 31.3% |
| +230 | 3.30 | 23/10 | 30.3% |
| +240 | 3.40 | 12/5 | 29.4% |
| +250 | 3.50 | 5/2 | 28.6% |
| +260 | 3.60 | 13/5 | 27.8% |
| +270 | 3.70 | 27/10 | 27.0% |
| +280 | 3.80 | 14/5 | 26.3% |
| +290 | 3.90 | 29/10 | 25.6% |
| +300 | 4.00 | 3/1 | 25.0% |
| +325 | 4.25 | 13/4 | 23.5% |
| +350 | 4.50 | 7/2 | 22.2% |
| +375 | 4.75 | 15/4 | 21.1% |
| +400 | 5.00 | 4/1 | 20.0% |
| +425 | 5.25 | 17/4 | 19.0% |
| +450 | 5.50 | 9/2 | 18.2% |
| +475 | 5.75 | 19/4 | 17.4% |
| +500 | 6.00 | 5/1 | 16.7% |
| +550 | 6.50 | 11/2 | 15.4% |
| +600 | 7.00 | 6/1 | 14.3% |
| +650 | 7.50 | 13/2 | 13.3% |
| +700 | 8.00 | 7/1 | 12.5% |
| +750 | 8.50 | 15/2 | 11.8% |
| +800 | 9.00 | 8/1 | 11.1% |
| +850 | 9.50 | 17/2 | 10.5% |
| +900 | 10.00 | 9/1 | 10.0% |
| +950 | 10.50 | 19/2 | 9.5% |
| +1000 | 11.00 | 10/1 | 9.1% |
Common questions
What is the implied probability formula?
It depends on the odds format. American odds: the number ÷ (the number + 100) for a negative price, ignoring the minus sign, and 100 ÷ (odds + 100) for a positive one. Decimal odds: 1 ÷ odds. Fractional odds a/b: b ÷ (a + b). Each gives the win rate the price needs to break even.
What is an implied odds calculator?
In sports betting, an implied odds calculator is the same tool as an implied probability calculator: it turns a price into the win rate that price assumes. Poker uses "implied odds" for something different, the money you expect to win on later streets, which is not what a betting price measures.
How do you convert odds to a percentage?
Work out the implied probability and multiply by 100. For American odds use odds ÷ (odds + 100) on a negative price and 100 ÷ (odds + 100) on a positive one; for decimal odds use 1 ÷ price; for fractional a/b use b ÷ (a + b). -150, 2.50 and 3/2 come out at 60.0%, 40.0% and 40.0%.
What is the implied probability of -110?
About 52.4%. Divide 110 by 110 plus 100 and you get 0.524. It is the standard price on point spreads and totals, so 52.4% is the win rate a bettor needs to break even on the standard bet.
Does implied probability equal the true probability?
No. It is the probability the price assumes, which includes the sportsbook’s margin and whatever bias the book’s customers have introduced. The two sides of a market always add to more than 100%, so each side is overstated; the market’s real opinion only appears once that margin is removed.
Why is the break-even win rate 52.4% at -110?
Because at -110 you risk 110 to win 100. Win 52.4% of the time and the 100-unit wins exactly cover the 110-unit losses, leaving nothing. Anything below that rate loses money over time even if you pick more winners than losers.
How do you convert a probability back to American odds?
Above 50%, the price is negative: multiply the probability by 100 and divide by one minus the probability, so 60% becomes -150. Below 50%, it is positive: 100 times one minus the probability, divided by the probability, so 25% becomes +300. Exactly 50% is even money, +100.
Written by George Boyle, who builds The Sport Stack — the models, the public ledger and these explainers. Corrections and questions: hello@thesportstack.io. Who runs this.