What is Positive Expected Value in Sports Betting? How to Calculate Expected Value in Betting

Most bettors have probably heard of the term expected value, but not all of them know what it actually means, and even fewer actually apply it to their bets. 

What is Expected Value? 

The exact definition of Expected Value is the predicted value of a variable. The way expected value is calculated is: the sum of all possible values and then multiplied by the probability of its occurrence. Expected value applies to much more than just sports betting as well. It can be in terms of an investment, or anything regarding probabilities. 

In the sports betting world, it is essentially a way to measure the probability gap between a bettors expectations of the outcome of the event, and the sportsbooks expectations for the same event. It places an actual percentage to that probability gap, and the goal of a sports bettor is to only bet on bets that are positive expected value, or mathematically profitable. The higher the percent profit margin the better.

This probably sounds very confusing, so let’s detail it in regards to Positive Expected Value betting.

What is Positive EV Betting?

Positive EV betting, as explained earlier, is betting on a play that has a positive probability gap, or Positive Expected Value, between the bettors expectations and the sportsbooks expectations on the outcome of an event. 

This screenshot above is the bread and butter of how you can use OddsJam to become a sharp sports bettor. The OddsJam Perfect Line, as you see it labeled with the logo above, prices the Under 5.5 Goals in the Predators vs. Flyers game at +130. Using the OddsJam line shopping tool and Positive EV betting tool, we were able to find this bet at +150 on FanDuel. That is a Positive EV play because we are getting better odds than what the “true” line is calculated to be from the OddsJam Perfect Line. 

Why is Expected Value Important to Bettors?

So now that you know what Expected Value is, and, more importantly, Positive Expected Value, let’s talk in detail about why it is so important. 

The easiest way to explain this is using a coin flip and probabilities. 

The unfortunate part of sports betting is that when a sportsbook deems a bet a 50/50 bet, the odds will be priced at -110 on each side. This is the vig that sportsbooks charge. So, using a coin flip example, both sides would be priced at -110 odds, which has an implied probability of 52.38% each for heads and tails. 

Let’s say you flipped the coin 100 times, and bet $100 on heads every time at -110 odds ($100 bet wins $90). Statistically speaking, the results would be heads 50 times and tails 50 times. So, for every time it was heads you would have profited a total of $4,500 (50 * $90), and for the 50 times it was tails you would have lost a total of $5,000 (50 * 100) leaving you with a net loss of $500. What we have learned is that just because it might land on heads one individual time, you know that in the long run you would not be able to profit with this strategy. This is an example of a negative expected value bet.

Next example: now let’s say we discovered that we are using a weighted coin, and that heads actually has a 60% chance and only 40% for tails. In this case, for 100 coin flips we would profit a total of $5400 on heads (60 * $90) and only lose $4000 on tails (40 * $100), profiting $1400. Again, just because one flip of the coin might land on tails, you would know that over time you will make money with this strategy. This is what positive expected value betting is. 

As a sports bettor it is important to determine what the expected value of a bet is, because that is the difference between profiting over time betting on sports or losing money doing so. 

How do I Calculate Expected Value in Sports Betting?

Luckily, OddsJam has an expected value calculator that can do this for you. But, if you want to know the math behind it, then please see below. 

The formula is: Expected Value = (Winning implied probability %  * profit if bet won) – (Losing implied probability % * stake). 

If the calculated number is positive, that means the bet has a positive expected value and if we simulated that event an infinite number of times you would always net a profit.

So, going back to the original 50% coin flip scenario, let’s see how much of a negative EV bet that was.

(50% * $90) – (50% * $100) = -5%. Meaning that bet has a negative expected value of 5% or a negative 5% expected profit margin.

Now, let’s see what it would look like with the weighted coin example.

(60% * $90) * (40% * 100) = 14%. So, this would be a positive expected value bet of 14%, or a 14% expected profit margin.

Vig and Expected Value

We mentioned it earlier, but vig/juice, plays an important role in expected value. Sportsbooks are going to charge a vig on every bet, so when you calculate the implied probability associated with those odds, it is important to do so with the vig removed. These are what are called the “fair odds” or “no-vig odds”. 

When we calculated the expected value for the coin flip the winning/losing percentage was 50% despite getting -110 odds. This is because the -110 odds are juiced, and the true % was 50/50 each way. Knowing the implied probability of -110 odds is 52.38% adding both probabilities together would equal 104.76%. That 4.76% is the juice. Removing that would make the “fair odds” +100, implying a 50% probability on either side.

Positive Expected Value Betting Strategies

Positive EV betting is a great way to evaluate sports bets, but, with that said, that doesn’t mean all Positive EV bets should be wagered on blindly. There are still strategies and best practices involved.

The most important strategy is to look at the market width of the OddsJam Perfect Line. Market width can be used as an indicator of the confidence in the betting lines of that market. It is essentially the difference on the two opposite betting lines.

In the above screenshot the odds are -141/+123 for this first-half spread market in the Rams/49ers game. The way you calculate market width is to subtract the two lines. So, in this case the market width would be 18 cents (141-123). 

You will also see situations such as the above where both numbers are negative. In this case, you would add the last two numbers of the two lines together. So, for this market the width would be 24 cents (10 + 14). 

The general rule of thumb is to stay away from any markets above 25 cents market width, specifically when looking at non-player prop markets. We’ll get to player props later. Anything 15 and below is considered a very tight market.

Player props, as mentioned above, are treated differently. There are a couple reasons for this. First of all – player props have a much wider variance than game props. So, the recommended market width limit can be up to 40 cents, because there are almost never any player props under 25 cents. But, with that said, because of the variance of player props it is recommended to not bet any that are below 5% Positive EV. Ultimately it’s up to your risk tolerance as a sports bettor to determine your market width target.

Sportsbooks are also quicker to limit users that bet heavily on player props. So, the best rule of thumb for betting player props is to bet them in moderation. There are some sharp bettors, though, that stay away from player props entirely. It is a matter of preference, and we also have some bettors who like player props, but the most important thing is to follow the strategies above.