The question
"Betfair has the home side at 2.12. What is that price actually saying?"
With implied probability explained, every price on the ladder turns into a plain percentage you can compare with your own view. This is the first step in every bet and every model, and it takes one division.
The idea in one sentence
A decimal price of O says the market thinks the selection has a 1 ÷ O chance of winning.
The picture
Decimal odds tell you the total return on £1, stake included. If a price is fair and you bet on it forever, you break even. For that to happen, the selection must win exactly often enough to pay back all the losing bets. At 2.00 it must win one time in two; at 4.00, one time in four.
That's all implied probability is: the win rate at which a price breaks even. Short prices mean high percentages, long prices mean low ones. The scale isn't even: moving from 1.10 to 1.20 is a drop of about 7.6 points in probability, while moving from 10.0 to 20.0 is a drop of only 5 points.
| Decimal | Fractional | American | Implied probability |
|---|---|---|---|
| 1.25 | 1/4 | −400 | 80.00% |
| 1.50 | 1/2 | −200 | 66.67% |
| 2.00 | 1/1 (evens) | +100 | 50.00% |
| 2.50 | 6/4 | +150 | 40.00% |
| 3.50 | 5/2 | +250 | 28.57% |
| 11.0 | 10/1 | +1000 | 9.09% |
On Betfair the ladder runs from 1.01 (99.0%) to 1000 (0.1%). Use the converter to go between any of these.
Worked Betfair example
A Premier League match on Betfair's Match Odds market shows best back prices of Home 2.12, Draw 3.60, Away 3.95, and best lay prices of 2.14, 3.65, 4.0. (Illustrative prices.)
- Read the home price. 1 ÷ 2.12 = 47.17%. The market says the home side wins about 47 times in 100.
- Read the others. Draw: 1 ÷ 3.60 = 27.78%. Away: 1 ÷ 3.95 = 25.32%.
- Check the book. 47.17% + 27.78% + 25.32% = 100.26%. On the back side the percentages sum to just over 100%; on the lay side (2.14, 3.65, 4.0) they sum to 99.13%. The true market view sits between the two, and every matched bet is struck at one agreed price.
- Allow for commission. Betfair takes 2% of net winnings. A £10 back at 2.12 wins £11.20, less 2%, so £10.98. Your net odds are 2.0976, and your break-even win rate is 1 ÷ 2.0976 = 47.67%. That's half a point above the headline 47.17%.
- The lay side. If you lay the home side at 2.14, you keep £0.98 per £1 of backer's stake if it doesn't win, and pay £1.14 if it does. You break even when the home side's true chance is 0.98 ÷ (1.14 + 0.98) = 46.23%. Lay only if you think it's lower than that.
- Your decision rule. Back the home side at 2.12 only if your honest estimate is above 47.67%. Lay at 2.14 only if it's below 46.23%. Between the two, leave it.
Verdict: the price 2.12 isn't "a bit better than evens". It's a statement that the home side wins 47% of the time, and you need to believe it's nearer 48% or more before backing it.
The formula
Implied probability
- q is the implied probability.
- O is the decimal price.
In plain English: one divided by the price. 4.0 means 25%, 1.25 means 80%.
Converting other formats to decimal
- a/b is a fractional price, such as 6/4.
- A is an American price, such as +150 or −200.
In plain English: fractional shows profit per unit staked, so add 1 for decimal. American shows profit on 100 (plus sign) or the stake needed to win 100 (minus sign).
Break-even after commission
- c is the commission rate: 0.02 on Betfair.
- q back is the win rate you need to break even backing at O.
- q lay is the win rate below which laying at O makes money.
In plain English: commission shaves your winnings, so a back needs a slightly higher chance than 1 ÷ O and a lay needs a slightly lower one. At 2.12 the back break-even rises from 47.17% to 47.67%.
Try it
Type 2.12 into the decimal box and check you see 47.17%, a back break-even of 47.67% and fractional 28/25. Then try 1.01 and 1000 to see the two ends of the Betfair ladder.
Common mistakes
- Thinking in odds, not percentages. "3.5 is a big price" means nothing. "28.6%, and I think it's 33%" is a bet you can judge.
- Forgetting commission in the break-even. At 2.12 it moves you half a point. At long odds it matters less in points but still shaves your edge.
- Treating the back/lay gap as a cost. The two sides are competing offers, not a fee. Every matched bet has one price, and the only charge on it is commission.
- Assuming the implied probability is the truth. It's the market's view. It can be wrong, and finding where is the whole job (Lesson 2.5).
- Reading bookmaker prices the same way. A bookmaker book adds up to 104% or more, so 1 ÷ O overstates each chance. Strip the margin first (Lesson 2.2).
Why the price, not the sport, is what you're up against: why good models still lose money.