Expected Value (EV) and Variance

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 which includes the variance.

Let’s take an example with a coin toss:
The probability of a coin to land on Heads is 50%. But assume you were to bet €10 on Heads at odds of 2.10.

  • 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 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 is particularly high when the sample size is small, for instance at the start of your value betting career. If you place a couple of thousand bets, the variance will have far less effect and your results will over time move closer and align with your expected value.

Key takeaway: 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.

You can read more about the variance and expected value of value betting on the Pinnacle blog.

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