Expected Value (EV) and Variance
Expected Value (or EV) is a measure of what you can expect to win or lose per bet placed in the long run. Expected Value is without variance.
Variance measures the difference from the expected value. (How far a set of numbers are spread out from their average value.)
Real value is your actual result (profit), which depends on the outcome of the matches. Includes the variance.
Coin toss example
The probability of a coin to land on Heads is 50%. But assume you get the odds 2.10 on Heads and bet €10.
- If you win you profit €11
- If you lose you lose €10
To calculate the expected value of the bet you can use this formula:
(profit per bet * probability of winning in decimals) – (loss per bet * probability of losing in decimals).
In this case: (€11 * 0.5) – (€10 * 0.5) = €0.5
Therefore you would expect to make an average profit of €0.5 (or 5%) for each €10 bet, because the odds offered are better than the implied odds of the coin toss.
However, after only one toss you would have either lost €10 or earned €11, not won €0.5. So if you only place 1 bet, the variance will be huge.
Variance will be higher in the beginning
Variance is particularly high when the sample size is small, for instance at the start of your value betting career.
The more bets you place, the variance will have far less effect and your results will over time move closer and align with your expected value. Note that we’re not talking about a few hundred bets, it may require a couple of thousand bets. Read more about statistical significance in sports betting.
The importance of thinking long-term
It’s important to see value betting as a long-term way to profit. The number of bets, as well as using a staking and max bet strategy, play an important role to reduce variance. Here are some tips on how to reduce variance when value betting.
Downswings are temporary
If you’re having a downswing, there’s no need to panic. Your results will over time get closer to the expected value. This is because of two statistical tendencies: the law of large numbers and regression to the mean.
The law of large numbers explains that the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.
This explains why your results tend to, over time, move closer and align with your expected value.
Regression to the mean is all about how data evens out. It basically states that if a variable is extreme the first time you measure it, it will be closer to the average the next time you measure it.
Large downswings from the expected value (a losing streak) is an extreme outcome and will tend to revert back to EV.
So if you have an expected value of 3%, your actual results will, over time, even out to 3% yield (profit per dollar spent). Once again, have patience and think long-term.