What is Positive Expected Value in Sports Betting? How to Calculate Expected Value in Betting
James Wilson
Sports Betting Analyst
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 bettor's expectations of the outcome of the event, and the sportsbook's 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 bettor's expectations and the sportsbook's expectations on the outcome of an event.
Positive EV Betting Example
Below is the bread and butter of how you can use Truepicks to become a sharp sports bettor. In this NHL example, our sophisticated models price the Under 5.5 Goals in this Predators vs. Flyers game at +130 (the "true" odds). However, we found FanDuel offering +150 for the same bet. This is a Positive EV play because we're getting better odds than what our calculations show the line should truly be.
| MATCHUP | BET | TRUEPICKS LINE | BOOK | MARKET ODDS | EV% |
|---|---|---|---|---|---|
| Predators vs Flyers | Under 5.5 Goals | +130 |  | +150 | +3.8% |
Why This Is Positive EV: Our true probability models calculate that the Under 5.5 has a 43.5% chance of happening (implied by +130 odds). However, FanDuel's +150 odds only imply a 40% probability.
This 3.5% difference in probability translates to a +3.8% expected value. For every $100 you bet on this line, you would expect to profit $3.80 in the long run - making this an attractive betting opportunity despite the individual outcome being uncertain.
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.
Example 1: Fair Coin (Negative EV)
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.
When Heads (50 times):
- Win $90 each time
- Total Profit: $4,500 (50 × $90)
When Tails (50 times):
- Lose $100 each time
- Total Loss: $5,000 (50 × $100)
Net Result: -$500 loss
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.
Example 2: Weighted Coin (Positive EV)
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 have different results.
When Heads (60 times):
- Win $90 each time
- Total Profit: $5,400 (60 × $90)
When Tails (40 times):
- Lose $100 each time
- Total Loss: $4,000 (40 × $100)
Net Result: +$1,400 profit
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?
Truepicks has built-in tools that can calculate expected value 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.
Calculating EV for our Coin Flip Examples
Example 1: Fair Coin (50/50)
(50% × $90) – (50% × $100) = $45 – $50 = -$5
This gives us a negative expected value of $5 per $100 bet, or -5% expected profit margin.
Example 2: Weighted Coin (60/40)
(60% × $90) – (40% × $100) = $54 – $40 = $14
This would be a positive expected value of $14 per $100 bet, 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 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.
Understanding Market Width
Example: First-Half Spread Market
| MARKET | SIDE 1 | SIDE 2 | MARKET WIDTH |
|---|---|---|---|
| Rams/49ers 1H Spread | -141 | +123 | 18 cents |
| Chiefs/Raiders Alt Total | -110 | -114 | 24 cents |
In the first example, 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).
In the second example where both numbers are negative, you add the last two numbers of the two lines together. So, for this market the width would be 24 cents (10 + 14).
Market Width Guidelines
- General Rule: Stay away from any markets above 25 cents market width, specifically when looking at non-player prop markets.
- Tight Markets: Anything 15 cents and below is considered a very tight market.
- Player Props: Player props are treated differently. Due to higher variance, the recommended market width limit can be up to 40 cents.
- Minimum EV for Player Props: Due to variance, it's recommended not to bet player props below 5% Positive EV.
- Risk Management: Be aware that sportsbooks are quicker to limit users who bet heavily on player props. Some sharp bettors stay away from player props entirely.