Understanding decimal vs fractional odds

Odds do two jobs. They tell you what you get paid if you win, and they tell you what the bookmaker thinks the chance is, with a margin built in. Decimal and fractional odds carry exactly the same information in different clothes. Once you can switch between them and read the probability underneath, you can see what you are really being offered.

Decimal odds: the total return

Decimal odds show the total amount you get back for each 1 staked, and that total includes your stake.

At 2.50, a £10 bet returns £25. Take away your £10 and the profit is £15. At 1.40, a £10 bet returns £14, a £4 profit. Anything under 2.00 is odds-on: you win less than you risk. Anything over 2.00 is odds-against.

That is the whole system. Multiply stake by odds for the return, subtract the stake for the profit.

Fractional odds: the profit

Fractional odds show the profit relative to the stake, and the stake is not included.

At 3/2, you win £3 for every £2 staked. A £10 bet wins £15 profit, and you get your £10 back, so £25 in total. That is the same bet as 2.50 decimal.

Evens is 1/1: win £10 for a £10 stake. Odds-on prices put the smaller number first. At 4/6 you have to stake £6 to win £4.

Converting between the two

Fractional to decimal: divide the first number by the second, then add 1. So 5/2 is 2.5 + 1 = 3.50, and 10/11 is 0.909 + 1 = 1.909, usually shown as 1.91.

Decimal to fractional: subtract 1, then write what is left as a simple fraction. So 3.25 becomes 2.25, which is 9/4. And 1.80 becomes 0.80, which is 4/5.

Some decimal prices do not map to tidy fractions, and some fractions give long decimals. 4/6 is really 1.6667 and 10/11 is really 1.9091. Screens round them. For a single bet, the rounding is pennies. Across hundreds of bets, it is worth knowing which number you actually got.

Implied probability

Every price implies a probability. It is the chance at which the bet would break even in the long run, ignoring the bookmaker's margin for a moment.

From decimal: divide 1 by the odds. At 2.50, that is 1 ÷ 2.50 = 40%.

From fractional: divide the second number by the sum of both numbers. At 5/2, that is 2 ÷ (5 + 2) = 2/7 = 28.6%. Check it the other way: 5/2 is 3.50 decimal, and 1 ÷ 3.50 = 28.6%. Same answer.

This is the number that matters. If you think a team wins 45% of the time and the price implies 40%, the price is too big for your view. If you think 35%, it is too short, however much you fancy them. We build our confidence grades on exactly this comparison.

The overround: where the margin hides

Add up the implied probabilities for every outcome in a market and you will get more than 100%. The extra is the overround, and it is how the bookmaker is paid.

Here is a worked example with a football match result market:

The book adds up to 104.81%, so the overround is 4.81%.

What does that mean in money? Suppose you backed all three outcomes so that each one returns £100. You would stake £47.62 on the home win, £29.41 on the draw and £27.78 on the away win, a total of £104.81. Whatever happens, you get £100 back. You lose £4.81 on £104.81 staked, which is 4.59% of your money. That 4.59% is the bookmaker's theoretical margin on this market.

To strip the margin out, divide each implied probability by 1.0481. That gives the fair probabilities in the fourth column, which add up to 100% (allowing for rounding). Turn those back into odds with 1 ÷ probability and you get the fair prices in the last column. The home win priced at 2.10 would be about 2.20 in a market with no margin.

Two-way markets work the same way. A price of 1.91 on both sides implies 52.36% each, a total of 104.71%. To break even at 1.91, you need to win 52.36% of your bets, not 50%.

Why we use decimal odds

We publish every tip in decimal odds, for three practical reasons.

• The maths is quicker. Implied probability is 1 divided by the price. No adding numerators and denominators.
• Expected value is one line. Multiply your probability by the odds and subtract 1. At a true 50% and odds of 2.10, that is 0.50 × 2.10 − 1 = +5% per unit staked.
• Accumulators multiply. Four legs at 1.90 is 1.90 × 1.90 × 1.90 × 1.90 = 13.03. Try doing that with 9/10 in your head.

If you are more used to fractions, keep the conversion table above handy. After a few weeks the common prices become second nature.

Whichever format you use, the discipline is the same: turn the price into a probability, compare it with your own view, and remember the margin you are paying on every bet.