Expected value
The expected value is the average result we should get from the given bet. That is, if all our bets have such a value, this number as a% will win an average of 100, 200, 1,000 or 5,000 bets. This is our advantage over the bookmaker and shows our Edge.
Formula with probability
(Potential win * Real probability) – (Potential loss * Real probability) = Expected value
Let’s imagine we’re tossing a coin. The chances for Ezi and Tura are 50% and in fair color without a margin, we will get 2.00 odds for each one. Our bet is BGN 10.
(10 * 0.5) – (10 * 0.5) = 5-5 = 0 This is our expected value, our expected profit of 100, 200, 1,000 tosses, because we have no advantage.
Now let’s assume that the bookmaker has set a margin and gives us 1.95 odds for Ezi and Tura. Our bet is again BGN 10.
(9.5 * 0.5) – (10 * 0.5) = 4.75 – 5 = -0.25 This is our expected value if we make this bet every 100, 200, 1,000 rolls. If we want to see it in% we have to multiply it by 10 = 2.5%.
You will actually get this if you just bet on certain events in the bookmaker in the long run, because at some point good and bad luck equalize and you just lose your margin.
Formula with coefficient
If we are given 2 betting odds with a real odds of 1.80, our positive expected value is calculated as follows:
(Odds on which we bet / Real odds) – 1 = 2 / 1.8 – 1 = 0.11 x 100 = 11%
This means that we will win 11% on average of the total turnover of all bets we have made, ie the sum of all bets we have placed, if they all have such a value.
Bookmakers’ margin
The margin is about 3-4% of the sharp bookmakers and 6-7% of the soft ones, which is a number we take from the expected value and we will understand the real profitability we have.
Summary
Through the parameter Expected value we find the expected value according to the real coefficient for us.
Using the Edge parameter we find the value of the bets in relation to the closing odds and the margins of each of the events separately.
Through the parameter Yield (ROI) we understand the profitability of bets. If the closing odds are perfect, then in the long run this number should be close to the Edge we have. If this number is greater than Edge or the closing odds were not accurate at these events or we were lucky. If it’s less, then we were unlucky.
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