## How do bookmakers set odds and manage risk?

17 June 2019

*Oddschecker selections for the next UK Prime Minister*

Betting is a risky business, not only for the customers, but also for the bookmakers. In order to stay in business, they must be profitable. To do so, they must mitigate risk in real-time. Often, this can be a labour-intensive, manual process that can be automated in many scenarios, minimising errors, enabling operators to quickly respond to market forces and saving on labour costs.

We will touch on some of the methods on how this can be automated in our next article. But first, let’s take a look at bookmaking practices and how bookmakers set odds.

## How do bookmakers make a profit?

This will require some maths.

Bookmakers make a profit by pricing their betting markets (a market is a specific event that you can bet on, e.g Manchester United to win, Ronaldo to score the first goal etc). so that the odds offered are lower than the statistical probability of the event.

Odds are in effect a % chance of something occurring and can be converted into % chance with the following formulae:

- Decimal Odds – 1/decimal Odds, Eg 1.66 = 1/1.66 = 60%
- Fractional Odds – (Denominator/ (Numerator + Denominator))*100, Eg 4/6 = (6/(4+6))*100 = 60%
- Manchester City are priced around 1.66 (Decimal) or 4/6 (Fractional) to win next year’s Premier League

Using either of the above formulae equates to a 60% chance of winning the League.

In bookmaking terminology, the percentage sum of all the prices is known as the book percentage. The value over 100% is the over-round. To make a profit, they price all selections within a market to go above 100%, creating an edge in their favour. The deviation of the price offered from the ‘true odds’ is the bookmaker's margin, otherwise known as the over-round.

For example, betting on a coin toss statistically represents a 50/50 chance (2.0 in decimal odds) on either outcome – heads or tails. You bet £10 to win £10, making this a 100% market, otherwise known as a round market. For the coin toss, bookmakers would offer heads or tails at odds below 2.0, meaning you would have to bet more to win £10. If the odds were offered at 10/11 (1.91 in decimal odds) for heads and tails each, you would have to bet £11 to make £10 on either selection. To calculate the book percentage on a two-way market, you need to use the following equation to convert the decimal price into a percentage and sum them together.

(1/Decimal Odds option A) + (1/Decimal Odds option B) = Book percentage

Using the bookmaker’s odds for 1.91 for heads and 1.91 for tails, we get the following formula:

(1/1.91) +(1/1.91) = 104.7%

In the example above:

- Book percentage is 104.7%
- Over-round is 4.7% (104.7%-100%)

In a five-horse race, a bookmaker may choose to price up each horse at odds of 4/1 (5.0 decimal). In such a scenario, were they to take an equal amount of money on each runner, they would break even, as each horse would have a 20% chance of winning. In that, the five runners have combined implied "probabilities" of winning of 100%. This is a "round" book.

However, if the bookmaker was to price up each runner at 3/1 (4.0 decimal), the implied probability of each runner winning would change from 20% to 25%. If they were again to take an equal amount on each runner, they would receive five units and pay out four.

The over-round or "juice" is what gives the bookmaker profit. If the book percentage is 120%, the bookmaker will expect to pay out £100 for every £120 they take, yielding an expected profit of 20/120 = 16.7%.

This process is known as “making a book”. This term originates from the practice of recording such wagers in a hard-bound ledger (the 'book') and gives the English language the term “bookmaker” for the person laying the bets, thus 'making a book'.

## How are betting markets determined?

A market is anything that allows the trading of goods or services. Bookmakers only allow their customers to buy or accept a price on the outcome of a future event (ignoring exchanges like Betfair).

A market is formed once odds are set by the bookmaker, based on the perception of the relative chance of each outcome in the event. In reality, very few bookmakers price up markets in-house. Instead, they receive prices from third-party feed providers. They either apply complex algorithms, using the relative strength of participants, historical data and expectation of where money will be placed, or scrape all bookmakers’ odds and aggregate their prices. This gives the bookmaker the option to place odds within the marketplace on the competitive and less competitive scale. They take more bets along with a smaller % profit (competitive) or fewer bets along with a higher profit (less competitive).

The more uncertainty surrounding an outcome, the less confidence the bookmakers have in the result. Bookmakers incorporate a larger over-round into the price when setting the market odds for a more uncertain outcome.

## Mitigating risk in bookmaking

As the event approaches, some of the uncertainty built into the initial pricing can be dismissed, resulting in increased confidence and lesser over-rounds. A bookmaker confident in their initial assessment could choose not to move the odds. However, in a changing market, this could result in them being out of line with other operators and overly exposed on a given outcome. In other words, a potential loss larger than they are willing to risk. Rather than taking that risk, bookmakers normally adjust the odds based on the flow of money. More money coming in for an outcome results in the odds shortening and the alternatives lengthened.

**Limits/Grades**

As another preventative measure, the bookmaker can also opt to set limits on bets based on the confidence in pricing of the event. These limits could be set against sport, tournament, event, market, selection and customer level.

Events could be tagged with grades usually relative to the quality of the event. Premier league football, for example, would have the highest grade, Grade A. Whereas, lower league football would have a lower grade, Grade C. Each grade has a limit set against it. Markets can be given a factor by percentage of the parent event. This way, limits are easier to manage, and once set, do not need adding every time new events or matches are added to the system. Functionality is required to override these settings specific to any market that falls out of this model. For example, a match towards the end of the season may be meaningless and therefore less competitive, so a lower limit would need to be set.

**Progressive Limits**

The time prior to the event start also needs to be factored in when calculating limits. The closer the event is to kick off, the more the markets will have settled down. Factors like team news and weather can be better quantified or known and therefore more confidence can be given towards the prices and a higher exposure or limit will be applied to the event. Time metrics prior to kick off could be assigned a factor by % and again these could be manually calculated taking the tedious, labour-intensive process out of the equation.

Operators use other trader software to manage all the data and risk calculations. We’ll talk about this in more detail in our next blog.