author: andriev   11 May 2021Print page

Expected value and how to calculate it in sports betting

How much value in your bets? Still don’t know how to find value? Let’s calculate the expected value of the bet and find out how much it can help your betting in the long run. Read on.


expected value betting guide
IntroductionHow to calculate the expected value?Summary
 
Introduction
Many of you find the term «Expected value» quite sophisticated. However, let us show you a simple example, which will make everything much clear. Using the good old coin flip, assume that you bet only on heads staking a tenner every time and getting back £11 whenever you get it right. That would give you an expected value of 0.5, meaning if you continue wagering the same way over & over again, you can expect a win of £0.50 per each bet of £10 (on average).
 
How to calculate the expected value?

Enough of theory, let us get straight to calculations. Do not worry, finding expected value is quite easy, and nobody should have issues with that. In short, all you have to do is multiply the winning probability by the amount you can win per bet and subtract the losing probability multiplied by the amount that could be lost per bet:


(Probability of Winning) x (Amount Won per Bet) – (Probability of Losing) x (Amount Lost per Bet)


While it looks quite straightforward, let us explain to you a couple of steps you have to make prior to finding your value. First of all, you need to make sure you know the decimal odds for all the 1X2 outcomes. You need the following information to calculate your potential winnings, which you can obtain by multiplying your stake by the odds of each of the given outcomes and subtracting the stake from it. Next up, find the probability of each of your outcomes. You can do so by dividing 1 by the odds of the particular outcome. If you have properly done the steps listed above, you should be all set to proceed further with your calculations.


Sports Betting Guide: The most common match results in football


For example purposes, let us use the upcoming Premier League matchup between Leicester City and Crystal Palace. Taking the odds for the aforementioned matchup from one of our top online bookmakers, we end up with 1.44 (11/25), 4.33 (333/100), 8.50 (15/2), respectively. Assuming that we stake £10, a wager on the underdog’s (Crystal Palace) win at the odds of 8.50 (15/2) would give us the potential win of £75 (odds x stake - stake). Dividing 1 by the odds of Crystal Palace victory, we get the following: 1/8.50=0.118 or 11.8%.


On the other hand, we have to calculate the probability of losing while backing this outcome. In our case, the losing probability would the sum of 1X (Leicester City win + draw). Using the same formula, let us calculate those probabilities: 


  • Leicester City win: 1/1.44 (11/25)=0.694 or 69.4%
  • Draw: 1/4.33 (333/100)=0.231 or 23.1%


Add those up, and you get 0.694+0.231=0.925 or 9.25%. As for the amount lost per bet, this is simply our stake because what else do we lose. Well, it seems like we have all the necessary data to continue. Using our first formula, our calculations are looking the following way.


Sports Betting Tutorial: Staking. How to select the right approach?


Probability of Winning - 0.118 or 11.8%

Amount Won per Bet - £75

Probability of Losing - 0.925 or 92.5%. 

Amount Lost per Bet - £10


(0.118) x (£75) – (0.925) x (£10) = 8.85 - 9.25 = -0.4


Unfortunately, our expected value for this wager is -0.4. This means we are going to lose 40 pennies on every £10 wager on average (betting the same way). If you would like to calculate the expected value for other outcomes, simply follow the same approach.



 
Summary

Hopefully, everything is clear for you guys, and this simple and easy to use formula would help you find the best value for your wagers. Keep in mind, while EV might be negative (like in our example), it does not entirely mean that you are guaranteed to lose money. Unlike coin toss, betting odds are very subjective and can change at any time. Therefore, we also emphasize the importance of applying various approaches and techniques in order to find the edge over the bookmaker. In other words, if your EV shows undesirable numbers but using Poisson distribution or any other method we explained in our sports betting guides provides you with a better value, you might be on the winnings side. In betting terms, this means that you found some inaccuracies in the implied probability of the wager by finding your own “real” probability using another method. Hopefully, this information finds you well & remember to gamble responsibly.


Betting Guide: How do margins affect profitability in sports betting

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