July 29, 2020

What is Expected Value (EV) Betting?

Have heard about expected value betting but are wondering what it actually is? Is it some new fad or is it a genuine way to make money from sports betting? And how does it compare to arbitrage betting or matched betting?

In this definitive guide to value betting, I will show you the pros and cons of value betting, as well as how you can use this unique technique to exploit inaccurate bookmaker odds and return an average profit of 7% per bet!

However, value betting isn’t all roses and sunshine. There is a genuine risk of losing your entire bankroll, unlike in arbitrage betting. We will use mathematics to minimise these risks, but ultimately it’s up to you as to whether the increased risk is justified by the increased reward!

Read on to find out more!

What is Expected Value Sports Betting?

Expected value sports betting involves identifying situations where a bookmaker has priced odds that do not reflect the true probability of an event. Particularly they have priced odds that imply a probability lower than the true probability.

What does this really mean? Let’s remember our formula for calculating the implied probability from the odds:

Value Betting Formula

So the probability of an outcome is the inverse of the odds. Higher odds mean lower probability of an outcome occurring. This makes sense right? If a horse is running at odds of 201, it makes sense that the bookmaker thinks that they have virtually no chance of winning.

Considering this, if a bookmaker has set odds of 1.80 for Manchester United to win an EPL match against Chelsea, what probability are they implying by setting these odds?

Value Betting Equation

Note: The bookmaker actually thinks that Manchester United have a lower probability of winning than this (say 50% chance), but they set the implied probability higher (and odds lower) than this to build in a profit margin of a few percent.

However, what if we somehow knew that the true probability of Manchester United winning was actually 60%?

This would mean that we could bet on Manchester United with this bookmaker and have an edge over them! Even with their built-in profit margin, we know that the bookmaker is giving us a better price than they should.

But how much of an edge do we have? Well, it comes back to the concept of expected value.

value betting

What is Expected Value (EV)?

Expected value is a mathematics concept that describes what the expected outcome is for an event which has multiple possible outcomes.

Basically, you multiply the probability of each potential outcome by the payout associated with that outcome, then sum this up for each of the outcomes.

For an event with 2 possible outcomes, it looks like this:

What is Value Betting

Where A and B are the 2 possible outcomes.

Let’s consider the classic example of flipping a coin.

Coin Flip

We are offered to bet $1 on the outcome of a coin flip. If we get it right, we win $2 (our $1 stake plus $1 winnings). If we get it wrong, we lose our $1 stake. Assuming a fair coin, there is a 50% chance of getting it right each time.

So, the expected value of this bet is:

EV Betting

So we have a 50% chance of profiting $1 and a 50% chance of losing $1. If we were to do this bet many times, our expected value would be $0. We don’t expect to win or to lose in the long run, but to break even.

What about another example, this time with dice. We are offered a gamble whereby when we roll a die, we win based on the number that we roll ($1 for a 1, $2 for a 2 etc.). It costs $3 to play each time. Would you play this game?

Dice roll

Let’s calculate the expected value to find out!

what is value betting

The calculation above may seem confusing but remember that if we roll a 1, we actually lose $2, as we staked $3 but only received winnings of $1.

So we will expect to win $0.50 each time we roll the dice. Note that this is our expected profit (or value), not a guarantee of what will happen each time.

In reality, it is impossible to win $0.50 in this game, but over the long run, our profits will tend towards $0.50 multiplied by the number of times we rolled the die.

If we rolled the die 10 times, we would expect to have a profit of $5, although our actual result could range anywhere from -$20 to +$30.

The more rolls of the die, the wider the possible range of values, but also the likelier it is that we will be near our expected value.

In fact, I graphed the various outcomes from this dice game below. Here is the probability distribution after each roll, simulated for 3 rolls.

As you can see, the range of possible outcomes is increasing each roll, but the centre of the distribution is slowly moving to the right. This means that a higher fraction of possible outcomes are profitable, the more we play.

As the number of dice rolls gets larger and larger, the graph above approaches a bell curve distribution.

How does this apply to sports betting?

Well if we go back to our original example (wow that was a long segway), a bookmaker has given us odds of 1.80 for Manchester United to win a match.

This implies a probability of 55.6%, but we know that the true probability of them winning is actually 60% (we’ll come back to how we know this later).

So what is our expected value from staking $100 on this bet:

Value Betting Calculation

We have a 60% chance of profiting $80 and a 40% chance of losing our $100 stake, which gives us an expected value of $8 (or 8%)!

In the long run, we would expect to profit $8 multiplied by the number of times we placed this bet! However, you can see that our variance is large (as low as -$100 or as high as +$80 multiplied by the number of bets we place).

This is one of the major downsides of value betting. While the expected profits are high, the variance is huge and you need to use a careful staking plan to ensure that you don’t lose your bankroll.

Find Value In Betting

How Do We Know Whether a Bet has Value?

After reading everything above, the question you are probably asking yourself is ‘how do we know that the true probability of Manchester United winning was 60%?’ or in other words ‘how do we know when a bet has value?’

Excellent question.

If you have read my article on sharp and soft bookmakers, you will know that sharp bookmakers differ from soft bookmakers by:

  • Having very low profit margins (<5%)
  • Changing their odds very quickly when news breaks

The sharp bookmaker business model relies on high turnover to make money. The high turnover makes up for the tight profit margins they operate.

Sharp bookmakers invest a lot of money in having excellently priced odds that very accurately represent the true probability of an outcome occurring. This is what lets them accept such high bets.

Pinnacle (a sharp bookie) accepts bets with stakes up to $50k for NBA and NFL for example. They go even higher on popular events.

As a value bettor, we can take advantage of the sharp bookmakers’ hard work in setting excellent odds. Because we know that the sharp bookmakers are so accurate, we use their odds to work out the ‘true’ probability of an outcome.

If a soft bookmaker’s odds deviate from these odds (which they often do), then you have a potential value bet!

Every arbitrage bet contains a value bet in it. For a 2 leg arbitrage bet, we have the sharp leg and the soft (value) leg.

We might expect to lose 4% on the sharp leg (this is the sharp’s profit margin), and gain 6% on the soft leg. So we would get a guaranteed profit of 2%.

Value betting basically involves not betting on sharp leg, and taking the 6% profit rather than 2% but with much, much higher variance.

To calculate the expected value, just use the formula that we discussed previously. Calculate the true probability using the sharp odds, then calculate the expected value of the soft bet.

Expected value sports betting
ev betting

Which can be simplified to the following formula:

Value Betting Formula

If this formula returns a value of 0.08, for example, it means that there is value of 8% in this bet.

If you want to get fancy, you can even try to account for the small profit margin built into the sharp odds, by calculating their overroundness. We’ll keep things simple for now though.

How to Find Value Bets?

Now you know what value betting is and you know how to determine whether a bet has value, so the next thing you will be wondering is: how do we find value bets?

Search

To answer this, I suggest that you read my detailed guide on how to find value bets. In a nutshell, there are basically 3 methods:

Read the guide to find out how to use each method effectively and access a limitless source of value bets.

I highly recommend that you use some form of software to help you find your value bets, as this will speed up the process immensely.

Those of you who have done arbitrage betting will know how long you can spend trawling through bookmaker websites before you find a single suitable bet.

Keeping track of all of your value bets is another important aspect of value betting and the software can do this for you virtually effortlessly.

How Much Can You Profit From Value Betting?

This is a great question and it really comes down to a few factors:

  • How much your initial stake is
  • How aggressive you are willing to be with your staking plan
  • The number of value bets you place
  • How quickly you get limited by the soft bookmakers

Most value bets have an expected value of say 6-8%, so your monthly profit will be a function of the formula below.

How much can you profit from value betting

As I have already mentioned many times, please don’t expect a smooth profit curve. You will have great months with incredible profits and months with either no profit or losses.

What are the Pros and Cons of EV Betting?

So, as a way of summarising everything, what are the pros and cons of value betting?

Pros

Higher profits than arbitrage betting in long run

As mentioned before, arbitrage betting involves both a value bet and a regular bet. We might expect to lose 4% on the sharp leg (this is the sharp’s profit margin), and gain 6% on the soft leg. So we would get a guaranteed profit of 2%.

Value betting basically involves not betting on sharp leg, and taking the 6% profit rather than 2%.

With value betting, you can expect to make 2-3x the money you would make with arbitrage betting (in the long run).

Doesn’t require bonuses like matched betting

Even after you have run out of promotions or have been promo banned by a bookmaker you can continue doing value betting.

Only place one bet, no laying required, simpler

Arbitrage and matched betting requires you to place two bets in quick succession. Arbitrage betting in particular requires you to be very quick, as if the odds move against you, you may be exposed to potential losses.

With value betting, you simply place a single bet and you are finished. It is much simpler to execute in this regard.

Cons

Higher variance in profits

With value betting, you have fantastic months where all of your bets go in your favour, and terrible months where you may lose a large fraction of your bankroll.

There are no smooth profits like you get with arbitrage or matched betting.

Requires Discipline

A month with many losing bets can lead to frustration and anger, and it can lead some people to start placing bets that no longer represent value, which is dangerous.

You must have good discipline, control over your emotions, and the ability to stick to your staking plan.

Can be difficult to know when to withdraw profits

Due to the variance associated with value betting, it can be difficult to know when to withdraw your profits.

You don’t want to pull out too much money when you have a bad period, as this can make it difficult to get back to where you were.

Gubbings

As with arbitrage and matched betting you will get gubbed by soft bookmakers eventually, with your stakes reduced down to only a few dollars.

Expected Value Betting - Conclusion

Expected value betting is an excellent way to profit from sports betting. You can make substantially more money than with arbitrage betting and it doesn’t require continuous promotions to be profitable, like matched betting.

However, it is not without risk. There is a real (although small) possibility of losing your starting bankroll.

Before getting started, you need to come up with a value betting strategy and staking plan, set your starting bankroll (only bet what you can afford to lose!) and then stick to it!

Investing in some value betting software will pay off immensely and allow you to place many, many more bets than you would have been able to if manually searching for value bets (remember that volume is key to successful value betting).

The software will also automatically keep track of your value bets for you, which can quickly become an enormous time sink if you don’t keep on top of it.

I hope you have enjoyed this detailed guide to expected value (EV) betting!

If you have any questions about value betting, please leave them in the comments below and I will get back to you as soon as possible!

Disclaimer: This post may contain affiliate links. I will earn a commission if you choose to purchase a product or service after clicking on my link. This helps pay for the cost of running the website. You will not be disadvantaged in any way by using my links.

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Louis


I'm an Australian guy who has used sports arbitrage betting to provide a decent side income (thousands of dollars per month!) for myself while working full-time. I've set up the The Arb Academy to teach others how to do the same and achieve financial security through a second income stream!

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