What is Expected Value - A Complete Guide

Where to bet, how to find the best odds and how to become a successful bettor are questions often asked, and they also go hand in hand. What it all boils down to at the end of the day is how profitable we can be with certain parameters in place and we are obviously looking for the best return possible, who isn’t? In this article we will cover how the expected value of betting with a certain operator affects your bottom line and variance, but to get going we have to look at the basics first. So, what is expected value, or EV as it is often referred to as?

What is Expected Value?

The concept of EV is a very common term no matter if we are talking about betting, poker or investing. In its essence it refers to a measure of how much a player/investor can expect to win or lose with a bet placed on the same odds time and time again. Bets with an edge will lead to a positive EV and long term profit, while bets placed with a negative EV will be losing over time. It might sound either simple or complicated, but don’t worry, we will explain it more in-depth, but also expand on how we can use this to our advantage.

The easiest way to explain how the math behind EV works out, is to imagine a coin toss. Assuming all things are fair and the probability of the coin landing on either heads or tails, the outcomes would have an equal probability of 50%. As such the real odds for this bet would be 2.0, fair and square. If we now move on to calculate the EV of such a bet we simply use this formula:

(Amount won per bet X probability of winning) - (Amount lost per bet X probability of losing)

If our bet for each coin toss would be €10 it would look like this:

  • (€10 x 0.5 = 5) - (€10 x 0.5 = 5) = 0

This would mean that our bet over an infinite amount of time would result in a long term breakeven bet, no matter which side we have chosen. This does however not mean that we can expect that result to stand true over a short period of time and that is what we call variance, but more about that later.

This example is clearly very simplified and things change quickly as we start moving around the parameters of the bet and the probabilities of winning. Before we move on to more practical ways of using this information to improve our actual betting results, let’s imagine another scenario. This time we have got a better deal - we are getting 2.20 odds to bet on tails. Sounds good right? It obviously is, but time to find out how good the numbers say it is.

  • (€12 x 0.5 = 6) - (€10 x 0.5 = 5) = 1

As you can see, the only variable that changes is our expected return on our wins, which goes from winning €12 instead of €10. This leaves us with a profit of €1 for each bet, theoretically. With such a bet we have reached a positive EV and in the betting world that would be a value bet. Another way to put it is: the odds we have received are better than the true odds of the bet. This is an important calculation for every successful bettor, as we have to both know what we are betting on well enough to:

1. Find odds with a positive EV.

2. Beat the bookmakers/exchanges cuts

If we once again look at our example above, it is important to realise a betting site would never offer you even odds on an outcome. They will always take a cut through offering odds lower than the true odds. On a bet with both outcomes being an even 2.0 would be changed to 1.9 on both outcomes, and that is the best case scenario. At bookies with a bigger cut or on certain markets it could be as low as 1.8. That means we have to be very knowledgeable and have a great understanding of what a value bet truly is, since we have to beat more than one obstacle to become profitable.

Implied Odds & Probability

We have established that a bettor who can find value bets constantly will be profitable in the long run, due to a positive EV. Next, let’s look at how we can use these calculations to determine if odds offered on certain games fall into this category. The easiest way to envision what odds actually mean in a simpler way is to turn our odds into probabilities. Betting.coms odds calculator helps you do this in an instant, as you can insert your odds in decimal, fractional or american form and quickly see the implied probability. Let’s look at an example from a game between Brighton and Liverpool from the Premier League.

Odds offered by bookmaker

  • Brighton: 5.75
  • Draw: 4.20
  • Liverpool: 1.57

Implied Probability

  • Brighton: 17.39%
  • Draw: 23.81%
  • Liverpool: 63.69%

If we would place a €10 bet on Liverpool in this game with odds of 1.57 and assume their actual probability of winning is 63.69% we can work out our long term expected value of this bet as follows:

  • (€5.7 x 0.6369) - (€10 x 0.412) = -€0.49

As we can see this bet would lose €0.49, or 4.9%, per bet in the long run. This loss comes from the house edge and nothing else, since we are assuming the odds are correctly set. This means we will need to beat the bookie by more than just an inch, we simply need to outperform them more than that. Don’t worry though, that is more than possible, but this is important to keep in mind as we start looking at what bookies we should be using. To find the best odds available is, and will always be crucial to our success and even the smallest difference has a massive effect on our bottom line.

Bookmakers Expected Value

When it comes to choosing what bookie to use the questions are abundant - where am I allowed to play? Who has the best bonus? Who has the best markets for me? Who has the best payment options? The list could be made incredibly long, but one point often gets forgotten - What bookmaker can offer you the best odds? This often gets left aside, since it’s easy to point out that you should be using as many bookmakers as possible to find the highest available odds for every bet. While this is true and we recommend this approach heavily the reality is also that various bookmakers might not suit everybody. There are country limitations, maybe they don’t have bonuses or none that suit you. Again, that list could be made very long. If you are choosing one or a few bookmakers to bet with it becomes absolutely crucial to understand that not all bookmakers are equal when it comes to their payouts.

While it can differ on a general level it can also be important to look at individual types of bets. Some offer higher/lower odds for pre-match odds, live bets, outright bets and so on. This also holds true depending on what sports you prefer betting on. As we previously mentioned it’s of utmost importance to find the smallest of edges as we first have to find good value bets, but also beat the bookmakers cut, the house edge.

Spending time to make sure the bookies you choose are not taking a unreasonably high cut is important, even if it on the surface might seem like most are close to equal - this simply is not true. We have taken a few examples to highlight this. Once again we will look at the game between Liverpool and Brighton, on the 1x2 market.

Bookmaker #1

  • Odds: 5.50 - 4.25 - 1.62
  • Total Payout: 96.7%

Bookmaker #2

  • Odds: 5.50 - 4.20 - 1.57
  • Total Payout: 93.6%

Bookmaker #3

  • Odds: 5.25 - 4 - 1.55
  • Total Payout: 92.1%

The main takeaway we can see here is that even if the odds might strike you as quite close on a first glance, the reality is very different. If we are consistently placing bets with a bookmaker taking a massive cut, we are losing out, A LOT. It’s once again worth reiterating that we should use the best odds available to the extent we can and we can do so by using odds comparison tools. However, with limitations due to factors mentioned we might need to pick out a few of the bookies we like best and then it is crucial to look at how their payouts usually stand against the competition. We are looking to be successful and our profit margin will go up dramatically by not using sub par odds.

It’s also important to note that these odds are from a big game in the Premier League and things would swing even more when looking at betting on lower leagues and tournaments. The same is true for outright betting, where bookies sometimes take astronomical cuts due to how inviting it can seem to bet on high odds for a team to win a league/tournament for an example.

Another area we have to highlight when it comes to bookies taking a cut that is too big to fight against, or at least a situation that only hurts ourselves by trying to do so - Livebetting. It is not unusual to see an outcome where the real odds are 2.0, go down as far as 1.80. This means we are looking at a 23% HOUSE EDGE. Is this really somewhere we want to place our bets? Long story short, no.

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Improving Our Expected Value

It might seem obvious that our goal with betting should always be to find the best value, increase our EV and maximize our profits, but most punters don’t have a clear path HOW to do it. In the sea of things we can do to improve our research, using tools, follow tipsters and so on it’s easy to forget to always get the best value we can get. As we have mentioned it is always good to use odds comparison tools and make sure we get the highest odds available, but the bookmaker offering the highest odds might not always suit us, for a bunch of reasons. As such it is always a good idea to know which bookmakers offer high quality odds and payouts on a general level.

With the amount of different sports, markets and bet types it’s close to impossible to draw definitive answers to this though. Each and every sport has different EV for each bookmaker, as does their individual leagues and tournaments. Smaller leagues for any sport will almost exclusively have lower payouts and as such it’s crucial we find out what’s best for us individually.

Finding great welcome bonuses and offers is always fun and it can be very profitable. EV at the bookmakers is however something that often gets overlooked when making these choices though, as the focus is only on the size of the bonus and the wagering requirements. However, the EV at the specific bookmaker will play a role here too. Imagine yourself consistently wagering a bonus with 2% house cuts compared to 10%. Over the usually long time of wagering needed this will determine our success just as much as how big the rollover is.

As we now have a better overview of how expected value impacts our betting decisions, our long term results, but also how our choice of bookmaker might change, it’s important to truly implement this form of thinking and strategy to our arsenal. Betting is a long term investment and should be treated as such. That means every edge available should be maximized and having the EV of every decision in mind will always be beneficial.

As for choosing bookmakers with their EV in mind, I still want to emphasize how important it is to not only look at percentage based numbers overall for each bookie alone. This will lead you to false information as they might have good odds for the types of bets you are not making. This could be in the form of pre-match betting, livebetting or outrights having different payouts overall, or maybe they offer good odds for sports or leagues/tournaments that you aren’t utilizing. There simply is more than meets the eye here. Long story short - don’t stare yourself blind with overall payout numbers, but what’s important to YOU.

To find new bookmakers that suit your needs you can check out Betting.coms recommended bookies, where we provide honest reviews of all of them. Besides that you can obviously also find the best bonuses and offers on the market from the same section. With this article in mind, go ahead and find a great bonus on a site who offers the best EV on your favourite sport, league and bet type. When we do that, we are maximizing our EV in a straight forward, but surprisingly simple way!

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Janne has over 10 years of experience with sports betting in various forms, but mainly on football, ice hockey and esports. A lifelong passion for traditional sports, CS:GO and Dota 2 makes his ultimate goal to share knowledge with other betting enthusiasts through written content. Janne is a deeply analytical person with a competitive mind, and the chance to challenge the bookies "at their game" was from the get-go an interesting prospect. With years of knowledge in the field he likes sharing his expertise through different avenues on our site, such as game previews, long term predictions, but also articles in the betting university. As long as the topic revolves around betting, then Janne will have something valuable to say about it.

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