Calculating the Expected Value (EV) is an important, and relatively simple skill that enables you to ensure that your bets have a player advantage or ‘edge’. I’ll explain how it works.
Expected Value (EV) Explained
► Expected Value (EV) of a Single Bet
Let’s suppose that you wanted to calculate the value of any single bet e.g. backing Spurs to beat Real Madrid in the Champions League. Precisely how much value is there in doing this?
Jokers out there would say “none!”. But in actual fact it depends on the price. There is always a price that’s positive value. For this particular fixture the fair odds could be something like 7.0. This is to say that odds below 7.0 would be negative value, and odds over 7.0 would be positive (commission aside). You may not necessarily be able to achieve a value price on your bet.
In the above example, betting at odds of 7.5 gives 7.5/7.0 = 1.07 = +107%. Therefore, the expected value is +7%.
Conceiving the fair price of a sports event is a challenge. Currently the most accurate benchmark for a fair price is Betfair, and this is mathematically proven.
► Expected Value of a Turnover
‘Turnover’ in betting terms, is basically a set of stakes on different sports events.
To work out the expected value you can assess every bet individually, using the method shown in the above example. However this isn’t always practical on a large data set. But if you’re able to establish your overall [average] profit margin on your betting strategy, then you can estimate the expected value of a turnover (total amount of stake) going forward. This estimate relies on accuracy — so be sure to collect a lot of results.
Let’s suppose that you consistently average +5% ROI on your betting stakes. If you plan to bet a total of £100,000, then you can predict that you’ll earn £100,000 x 5% = +£5,000.
Equally, if you average -5% ROI, then you’ll expect to lose -£5,000 over every £100,000 staked. Therefore, if you know a Bookmaker’s edge then you can easily estimate the amount you expect to lose over your total stakes.
Individual stake sizes do not impact this calculation. They do however alter the variance in the results.
► Expected Value of an Arb or Matched Bet
To ensure that your Arb or Matched Bet will earn you money you can calculate the expected value. The expected value isn’t so much an estimate in these cases because you know beforehand what you will earn from the combination of bets you make. Usually the stakes are sized in a way that guarantees the same profit regardless of any outcome.
Here’s how the expected value factors in:
- Matched Betting: the “qualifying bet” is typically -EV, meaning you lose money. You do however earn from using the free bets, making the whole process +EV overall.
- Arbing: all bet combinations are +EV. You guarantee profit when both bets settle.
I recommend also reading my post on Strike Rates. This will help to improve your understanding of the expected value.