Decimal, Fractional, American: Reading a Price and Finding the Margin
Three notations for the same number, and a fourth number the notation is designed not to show you.
· 9 min read
A price is a probability with a margin folded into it. The three notations in common use — decimal in Europe and Australia, fractional in Britain and Ireland, American in the United States — express exactly the same number in three different dialects, and none of them shows you the margin. Finding it takes one addition.
The three notations
Decimal odds state the total return per unit staked, including the stake. A price of 2.50 returns $2.50 on a $1 bet: $1.50 profit and your dollar back. This is the easiest form to compute with, which is why almost every model and every exchange uses it.
Fractional odds state profit against stake. 6/4 means six units of profit for every four staked. Anything above evens is odds-against; anything below is odds-on and is written the other way up, as in 4/6. To convert to decimal, divide and add one: 6/4 = 1.5, + 1 = 2.50.
American odds use a positive number for the profit on a $100 stake and a negative number for the stake required to profit $100. +150 and −150 are not the same price: the first returns $250 on $100, the second returns $166.67.
| Decimal | Fractional | American | Implied probability |
|---|---|---|---|
| 1.20 | 1/5 | −500 | 83.33% |
| 1.50 | 1/2 | −200 | 66.67% |
| 1.91 | 10/11 | −110 | 52.36% |
| 2.00 | 1/1 (evens) | +100 | 50.00% |
| 2.50 | 6/4 | +150 | 40.00% |
| 3.00 | 2/1 | +200 | 33.33% |
| 5.00 | 4/1 | +400 | 20.00% |
| 11.00 | 10/1 | +1000 | 9.09% |
Implied probability is 1 ÷ decimal price. These are conversions, not offers — no operator is being quoted here.
Implied probability, and why it is not the real one
Turning a price into a probability is a single division: 1 ÷ decimal. A price of 4.00 implies 25%. This number is doing two jobs at once, and only one of them is honest — it contains both the bookmaker’s view of the event and the profit they intend to make. It is always higher than the probability they actually believe in.
1 ÷ price
Implied probability from a decimal price. Add the implied probabilities of every outcome in a market and a fair book totals exactly 100%
The book, and the overround
Here is the whole trick. Take a football match with three outcomes and price it fairly at evens the home win, 2/1 the draw, 5/1 the away win. Implied probabilities of 50%, 33.3% and 16.7%: a book of exactly 100%, and a bookmaker who expects to make nothing at all.
Now shorten every price while keeping the same ratios — 4/6, 6/4 and 4/1. The implied probabilities become 60%, 40% and 20%. The book now totals 120%, and that extra 20 points is the overround. Stake in proportion across all three and you put up £120 to collect £100 whatever happens.
Price converter and book calculator
Enter up to three decimal prices for the outcomes of one market. The table converts each to fractional and American notation and shows the implied probability; the total is the book.
| Decimal | Fractional | American | Implied |
|---|---|---|---|
| 11/10 | +110 | 47.62% | |
| 5/2 | +250 | 28.57% | |
| 14/5 | +280 | 26.32% | |
| Book total (3 outcomes) | 102.51% | ||
| Overround | 2.51% | ||
A fair book totals exactly 100%. Anything above that is the bookmaker’s margin. Leave a field blank or set it below 1.01 to price a two-way market.
What a normal margin looks like
Two-way markets are the cleanest comparison. The standard American price on both sides of a point spread is −110, which is 1.91 in decimal and implies 52.36%. Two of those add to 104.71%, so the book runs at a 4.71% overround. In football, published analysis of English markets puts Premier League three-way margins around 4% and lower-division margins around 6%, with Premier League margins having fallen from roughly 9% to 4% between 2005 and 2018.
| Market | Prices | Book | Overround |
|---|---|---|---|
| Two-way, standard US spread | 1.91 / 1.91 | 104.71% | 4.71% |
| Two-way, sharp price | 1.95 / 1.95 | 102.56% | 2.56% |
| Three-way, competitive league | 2.05 / 3.45 / 3.75 | 104.43% | 4.43% |
| Three-way, lower division | 2.00 / 3.40 / 3.75 | 106.08% | 6.08% |
| Fair book, no margin | 2.00 / 4.00 / 4.00 | 100.00% | 0.00% |
Book totals computed from the prices shown. The typical margin ranges are from the Wikipedia article on the mathematics of bookmaking; the prices are illustrative examples, not quotes from any operator.
Why accumulators are the expensive product
Margins compound. Combining two selections multiplies the prices, which multiplies the overround along with them. Two markets carrying about 9% each produce a double carrying roughly 19%. Four legs at 5% each end up near 22%. This is arithmetic, not a conspiracy — and it is also why free-bet promotions cluster around multiples rather than singles.
The one habit worth forming
Before evaluating any price, convert it to a percentage and add up the market. If the book comes to 112%, you now know that you are being asked to accept a twelve-point handicap before any opinion about the event enters the picture. That is not a reason to bet or not to bet. It is simply the price, stated the way a price should be stated, and it takes about ten seconds to work out.
