Expected Value (EV) is a measure of how much a bettor should expect to win or lose per bet (or collection of bets) placed on the same odds time and time again.
Plus EV (+EV) bets are what punters need to identify in order to earn a profit longterm. These are also known as value bets. However, a typical gambler will often bet on Minus EV (-EV) odds, which eventually results in losses overall.
Calculating the Expected Value (EV) is an important, and relatively simple skill that enables bettors to ensure that their sports 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 in any single bet e.g. backing Spurs to beat Real Madrid in the Champions League in the 1×2 market. 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 theoretical price that turns the bet into positive value. It’s just a case of whether that price, or better, is actually available in the market.
For this particular fixture the fair odds could be something like 7.0 for Spurs to win. This is to say that odds below 7.0 would be negative value, and odds over 7.0 would be positive value (and therefore in your favour). You may not necessarily be able to achieve a value price on your bet — hence the importance of being selective in what odds you take and when you take them.
In the above example, betting at odds of 7.5 gives 7.5/7.0 = 1.07 = +107%. Therefore, the expected value is +7%.
Without knowing the fair odds, it’s impossible to accurately assign an expected value.
But conceiving the fair price of a sports event is a huge challenge. Most bettors fail to consistently get it right.
Currently the most accurate benchmark for the fair price is the Betfair exchange odds (and this is mathematically proven). Most of the time the correct value lies somewhere between the Back and Lay odds of a well-formed market (e.g. Match Odds for Premier League games) — usually closer to the Back side in my experience.
Bettors can also compile fair odds based on historical data and statistics. Percentages for the chance of an outcome occurring are essentially translated into odds. The Betting.com Odds Calculator is helpful for making a quick conversion.
Expected Value of a Turnover
‘Turnover’ in betting terms, is basically a set of stakes on one or more sports events.
To work out the expected value from a turnover 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.
Instead, you can establish your overall (average) profit margin for your betting strategy, and then estimate the expected value of a turnover going forward. This estimate relies on accuracy — so be sure to collect a lot of results before judging your ROI.
Let’s suppose that you consistently average +5% ROI on your betting strategy.
If you plan to bet a total of £100,000 going forward, 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 for a sport/market then you can easily estimate the amount you expect to lose over your total stakes there.
Individual stake sizes per each bet do not impact this calculation. They do however alter the variance in the results.
Expected Value of an Arb or Matched Bet
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. This can be achieved using a Matched Betting Calculator.
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 overall process +EV.
- Arbing: all bet combinations are +EV. You guarantee profit when both bets settle.
Hopefully this gives a clearer picture of how Expected Value (EV) factors into strategies and different bet types. To learn more about expected value, I recommend reading my post on Strike Rates.