Reading Betting Odds: Decimal, Fractional, Moneyline and the Margin
Three notations describe the same price. Converting them into percentages shows what a market is really charging.
One price, three notations
A price is a statement about what a winning stake returns. Three notations dominate, and they carry exactly the same information. Decimal odds, common across Europe, give the total return for each unit staked, with the stake included. Fractional odds, traditional in Britain and Ireland, give the profit earned by staking the amount on the right of the fraction. Moneyline odds, used in North America, give the profit on a stake of 100 when the figure is positive, and the stake required to win 100 when it is negative.
The three figures below are one price written three ways. They are an illustration of the arithmetic, not a quoted market.
All three say the same thing: stake one unit, and a win returns two and a half, of which one and a half is profit.
Converting between them
Decimal to fractional: subtract one, then write what is left as a fraction. 2.50 leaves 1.5, which is 3/2. Fractional to decimal: divide the fraction out and add one. 3/2 divides to 1.5, which gives 2.50. Decimal to moneyline, for prices above 2.00: subtract one and multiply by 100, so 2.50 becomes +150. For prices below 2.00, divide minus 100 by the decimal price minus one, so 1.50 becomes minus 200. The definitions behind these conversions are set out in Wikipedia's article on odds.
From price to percentage
The step that makes prices comparable is turning them into implied probabilities. For a decimal price, divide one by the price. A price of 2.50 implies 40%. A price of 4.00 implies 25%, and a price of 1.25 implies 80%. That percentage is what the price asserts about the likelihood of the outcome, which is not the same as the likelihood itself.
Doing this once gets a reader out of several traps. Prices that look generous in one notation often look ordinary as a percentage, and a long shot quoted at a large number is still only a claim that something is unlikely, not a measure of how unlikely.
Why the percentages add up to more than 100
Add the implied probabilities of every outcome in a market. If the prices were fair, the total would be 100%, because one of the outcomes must happen. In practice the total is higher, and the excess is the operator's built-in margin, called the overround in Britain and the vigorish in American usage.
An illustration with round numbers: a two-outcome market priced at 1.90 on each side implies about 52.6% per side, or roughly 105.3% in total. The 5.3 points above 100 are the margin across the pair. Pricing both sides at 2.00 would total exactly 100% and leave the operator nothing, which is why such a market is not offered. How a book is balanced to produce that surplus is described under the mathematics of bookmaking.
What follows from this
- A smaller overround is better for the bettor in the same way a smaller house edge is. It is the cost of taking part, charged on every bet.
- The margin is rarely spread evenly. On many markets more of it sits on the less likely outcomes, so the long shots are the dearer part of the card.
- Prices in different notations cannot be compared by eye. Convert to decimal, or straight to percentages, before deciding which is better.
- Markets with many outcomes tend to carry a larger total margin than two-way markets, because there are more prices to shade.
Two habits worth keeping
The first is to write the implied percentage next to any price before acting on it. The arithmetic takes seconds and it converts a piece of jargon into a number that can be argued with.
The second is to add up the market. If the total sits far above 100%, the prices are expensive whatever the individual figures look like, and no amount of selectivity within that market removes the charge. Understanding the notation does not improve anyone's forecasting, but it does stop a price being misread, which is a cheaper mistake to avoid than to make.
Betting costs more than it returns on average, whatever the notation. If gambling is causing problems, the free help line listed on the About page is open at all hours.