'Expected value' is the name given to the expected ROI of a value bet. The EV is how much you could expect to make by betting on this value bet an infinite number of times, letting variance play its part.
If the EV is +7%, you would expect to make £70 after £1000 (theoretically). The same works for negative EV. If the EV was -5% you would expect to lose £50 after staking £1000.
Therefore, in theory, taking bets with a positive EV will result in profit over the long term. But how do we calculate it?
Step 1 - Convert True Odds to Probabilities
Suppose we put £100 on Newcastle to win at evens (2.00) on a bookmaker as our value bet, and we wanted to calculate EV:
The 'true' odds are the odds on the exchange, as this removes the bookmaker profit margin. For example, Newcastle are 1.8 on the exchange to beat Aston Villa:
'True' odds of Newcastle win = (1/1.8)*100 = 55%
'True' odds of Newcastle NOT to win = (1-0.55) = 45%
Step 2 - Use Expected Value Formula
The expected value formula is as follows:
EV = (Profit if bet wins * Probability of bet winning) * (Loss if bet loses * Probability of bet losing)
Using our true probabilities we calculated, we can plug these values in:
Profit if bet wins = £100 * 2.00 - £100 = £100
Probability of bet winning = 0.55
Loss if bet loses = £100
Probability of bet losing = 0.45
Plugging these values in, we get an EV of +10%, meaning, if we staked £10 over and over, in the long run we would make a £1 profit from every £10 we stake.
There's nothing more to it!