Expected value is the theoretical difference between the probability of the odds that the oddsmakers offer and what you perceive the probability to be. The reason why it is useful for sports bettors is that it can be used to calibrate how likely the oddsmakers reckon a bet will win, and you can then make the judgment call on whether the odds are well priced or not.
Here, we will explore the concept of probability and how you can use the knowledge to gain an edge on the house. We have plenty of betting tools (such as OddsNotifier) to help you crunch the numbers and look for good value, and we will show you how to best use them to perfect your betting strategy and turn a profit.
Expected Value Defined for Sports Betting
We can calculate the expected value for the odds on a wager, using a formula, and the value either comes out positive or negative (+EV or -EV). Positive expected value is what we are after, and many expert bettors use the value to determine how many betting units they want to stake on that specific wager. To understand expected value, we need to delve into probability.
Probability in Sports Betting
Probability is the likelihood of a bet coming through, and it is a percentage. Implied probability is the chance of a bet coming through, and you can read it directly through the odds.
Implied Probability = 1 / Decimal Odds x 100
You can use the formula, or use our Odds Calculator to quickly get the implied probability. Our calculator reads odds in all three formats (Decimal, American and Fractional), so there’s no need to convert the odds. Besides, it will display the betting odds in the other formats, and also show you how much the bet can win. More importantly, right now, it shows us the probability that the odds imply.
But we also need to come up with the actual probability of the bet to win. This can be done through statistics and various tools. There is no way to know the exact percentage, but you can gauge it on the data at hand, and this is how you calculate whether the Expected Value is worth it or not.
Calculating Expected Value
Essentially, we calculate the value of the odds based on the implied probability, given by the odds. Using those numbers, and the odds of the wager, we can find out if it has +EV or -EV.
(Potential Profit x Probability of Winning) – (Probability of Losing x Amount Wagered)
Just to define what is going on:
Potential Profit – The amount you win in profit, not counting your stake
Probability of Winning – This is the actual percentage that you have to calculate
Probability of Losing – Subtract the implied probability of the odds from 1 to get the IP of losing
Amount Wagered – Your stake
Expected Value in Real Examples
Let’s play out two scenarios – one in which you back the favorite to win and another in which you bet on the underdog. Let’s keep the stake nice and low, at only $10, and say that the chalk comes at odds of -150 and the other wager is priced at +250.
Example 1: Chalking
In the first scenario, by using our odds calculator, we find that you can win $16.67 on a $10 wager, and that the implied probability of the odds (-150) is 60%. Your potential payout is 16.67, and your stake is 10. The implied probability of hitting and losing are 0.60 and 0.40, respectively.
Let’s say that using historical data and H2H records, you give the favorite a 65% to 70% chance of winning. Let’s see how that affects the EV.
Using a 65% Actual Probability:
(6.67 x 0.65) – (10 x 0.40) = +0.335
Using a 70% Actual Probability:
(6.67 x 0.70) – (10 x 0.40) = +0.669
As you can see, even with a 65% chance of winning, you would theoretically make 33.5 cents on each $10 wager. If you think the favorites have a 70% chance of winning, you would be making approximately double that, with 66.9 cents profit on every $10 wagered.
Example 2: Betting on the Underdog
In the other example, we have a $10 wager to win $24 in total, with an implied probability of 28.57%, which means the IP of losing is 71.43%. The underdog is not expected to win, but let’s say that you think they have a 50% of winning (optimistically) and only 40% (pessimistically).
Using a 50% Actual Probability:
(15 x 0.50) – (10 x 0.7143) = 7.5 – 7.143 = +0.357
Using a 40% Actual Probability:
(14 x 0.40) – (10 x 0.7143) = 6 – 7.143 = -1.143
If you are optimistic about the underdog’s chances, then this is quite a good value bet, bringing you approximately 35.7 cents for every $10 you wager, theoretically. However, if you think they have a 40% chance of winning then this quickly becomes negative EV, and the bet should be avoided.
It is not easy to figure out the actual probability, but we will look into some techniques.
How Do I Work Out a Bet’s Actual Probability?
This is the kicker, the actual likelihood of a bet coming through cannot be counted, and you will need to assess the situation for yourself. When the BettingTools team looks at an NFL game, let’s say between the Baltimore Ravens and the Seattle Seahawks, we have to do lots of research before coming up with stuff like:
“Alex reckons the Ravens have a 60% chance of winning”
or
“The Ravens have a 55% shot at winning according to Paul“
No, this is a number that we have to determine based on the information available, but there are some useful systems such as betting bots and betting systems that can help us get a realistic probability percentage. At the very least, we can define the range of the actual percentage. So Alex and Paul can come to conclusion that the Ravens have a 55-60% chance of winning.
It is not fault-proof, but this system can help to better define the quality of the odds and find well-priced wagers that are worth a shot. But we can also use the EV formula backwards, to determine how much the actual probability is if we assume the bet is positive (or negative) EV.
Using the EV Betting Formula Backwards (for Actual Probability)
For example, if we put a $10 bet on odds of +180, and now see how the actual probability is calculated for when EV is +1 and -1. The potential returns are $18, the IP for winning/losing is 0.3571/0.6429 and we are calculating for Actual Probability (AP).
+1 EV
(18 x AP) – (10 x 0.6429) = 1
AP = (1+6.429) / 18 = 41.22%
-1 EV
(18 x AP) – (10 x 0.6429) = -1
AP = (-1+6.429) / 18 = 30.16%
With an EV of +1, we would assume that the team has a 41.22% chance of winning the game, and for -1 it would be 30.16%. You can then figure out which is closer to the actual probability based on stats and historical data.
Some bettors go a little further and use software such as Gruss to get their probability figures. They can serve you well, but you can also make your own value finder spreadsheets to familiarise yourself with probability and its effects on the odds.
How EV Works in Parlays
The same principle is applied, but it is a little harder because you will need to calculate the EV of every single wager in the parlay bet. You cannot simply take the EV of the parlay as a whole. You simply take the EV of every single selection in the parlay, add them, and you will get the overall EV of the parlay.
It is not easy to do this, but after some practise, you will recognise better value prices and how to get the most out of your wagers.
What is Juice in Expected Value
Implied probability, calculated from odds, is not technically speaking the exact estimation that oddsmakers have drawn. Sportsbooks have to make their money, and therefore the probability is increased a little, which, in the long run, gives betting sites their little cut of the action.
I personally prefer using DraftKings or FanDuel, as they have very little juice, which I will show in an example.
49ers vs Seahawks
63.5% (-174) + 40.65% (+146) = 104.15%
4.15% Juice
Jaguars vs Bears
48.08% (+108) + 55.75% (-126) = 103.83%
3.83% Juice
Commanders vs Ravens
29.41%(+240) + 74.68% (-295) = 104.09%
4.09% Juice
The implied probability of the moneylines add up to over 100%, which is not possible in real life. The extra % is where FanDuel takes its cut, and as can be seen above, the juice is close to 4%. Of course, it all depends on the betting market, and it can also vary between sports. Generally speaking, niche sports may have higher juice, but when you look at popular sports such as the NFL, the juice tends to be quite low.
Practicalities of EV in Sports Betting
One important thing to keep in mind when calculating EV is to make an important distinction between betting on favorites and underdogs. Your understanding of the value and expectations should be different. For any beginners, we don’t recommend mixing favorites and underdogs in a betting parlay until you get a good grasp on how betting odds work.
EV Betting on Favorites/Chalk
With favorites, we are assessing whether the odds will bring enough profit given the risk involved. It makes a big difference whether the Chiefs’ next game at home is priced -150 or -180, as the profit margin on a $10 bet is $6.67 and $5.56. The IP on the bets to win is 60% (-150) and 64.29% (-180)
Is a $6.67 profit good for a risk of 40%. The bet at odds of -180 only has an implied 35.71% of losing, but will only bring you $5.56.
Underdog EV Betting
When we look at underdog bets, the concept is reversed, as they are poised to lose, but when the profit margin is high enough, we may just take the risk. Here, we are more interested in the potential returns, and checking to see whether the underdog is seriously underestimated or not.
A UFC underdog may be priced to win at +220 at one sportsbook and +250 at another. The first sportsbook is implying there is a 68.75% chance of the underdog losing, whereas the second puts them at 71.45%. At the first sportsbook, you can make a $12 profit on a $10 bet, and at the second you would make $15 for every $10 wagered.
There is a large discrepancy between the odds here, and if we just assume the middle ground, that the actual value is closer to 70%, then the odds at the second sportsbook come at an EV of +2.855.
(15 x 0.70) – (10 x 0.7145) = 10.5 – 7.145 = +2.855
Such a difference in the odds is always a good indication that this fight may be closer than it seems. The most likely scenario is that the favorite will win, but the odds on the underdog at the second sportsbook are quite inflated and look like a good wager for any daring bettor.
Mastering EV in Sports Betting
Ultimately, there are lots of loose ends with EV, and you can never predict the exact percentage of winning. Just in the same way, we will never know the exact outcome of a game, but we can always come close by doing research and browsing the sportsbooks for more information.
But the goal here is to find out if the wagers are well priced, and check to see what the actual probability is based on the odds given. There are lots of ways in which this information is beneficial, as you can use it in tools such as the Kelly Criterion calculator to determine how much of your bankroll should go on the wager.
Or, you can use EV to gauge whether a bet is worth the risk or not. A lot of times when doing our NFL picks, or any other free betting predictions, we will avoid wagers that seem obvious, just because the odds are not worth it. Winning streaks don’t last, but they can easily lead to trap bets, whereas big losses can lend to some extremely favorable odds on underdogs.
