Expected Value in Betting
What is Expected Value (EV)?
Expected Value (EV) is one of the most fundamental concepts in sports betting. It is a measure of what a bettor can expect to win or lose on a bet in the long run. In simple terms, it is the difference between the true probability of an outcome and the probability implied by the sportsbook's odds. A positive expected value (+EV) indicates a profitable bet in the long term, while a negative expected value (-EV) indicates an unprofitable one.
Thinking in terms of expected value is what separates casual bettors from sharp, successful bettors. Casual bettors often focus on trying to pick winners, while sharp bettors focus on finding value. A bet with positive expected value is a value bet. It doesn't guarantee you will win that specific bet, but it means that if you were to make the same bet over and over again, you would come out ahead.
How to Calculate Expected Value
The formula for calculating expected value is straightforward:
EV = (Your Winning Probability * Potential Profit) - (Your Losing Probability * Stake)
Let's break down the components:
- Your Winning Probability: This is your assessment of the true probability of the bet winning, expressed as a decimal.
- Potential Profit: This is the amount of money you would win if the bet is successful.
- Your Losing Probability: This is your assessment of the true probability of the bet losing (1 - Your Winning Probability).
- Stake: The amount of money you are risking on the bet.
A Simple Example: The Coin Toss
Imagine you are offered a bet on a fair coin toss. You can bet $10 on heads. If it lands on heads, you win $11. If it lands on tails, you lose your $10.
- Your Winning Probability: 0.5 (since it's a fair coin)
- Potential Profit: $11
- Your Losing Probability: 0.5
- Stake: $10
EV = (0.5 * $11) - (0.5 * $10) EV = $5.50 - $5.00 EV = +$0.50
This bet has a positive expected value of $0.50. This means that for every $10 you bet, you can expect to make an average profit of 50 cents. In the short term, you will either win $11 or lose $10, but over a large number of coin tosses, you will be profitable.
Finding Positive EV in Sports Betting
To find positive EV bets in sports betting, you need to be able to do two things:
- Accurately assess the true probability of an outcome. This is the most difficult part and requires a deep understanding of the sport, statistical analysis, and the ability to create your own odds.
- Compare your probability to the implied probability from the sportsbook's odds.
Implied Probability
Implied probability is the probability of an outcome as suggested by the sportsbook's odds. You can calculate it from the odds using the following formulas:
- For positive American odds: Implied Probability = 100 / (American Odds + 100)
- For negative American odds: Implied Probability = |American Odds| / (|American Odds| + 100)
Example: NFL Game
Let's say the New England Patriots are playing the Miami Dolphins. The Patriots are listed at -150 odds to win.
- Implied Probability: 150 / (150 + 100) = 150 / 250 = 0.60 or 60%
The sportsbook's odds imply that the Patriots have a 60% chance of winning. Now, you need to do your own analysis to determine if you agree with this assessment.
Let's say your analysis suggests that the Patriots actually have a 65% chance of winning. Now you can calculate the expected value of a $100 bet on the Patriots.
- Your Winning Probability: 0.65
- Potential Profit: A $100 bet at -150 odds wins $66.67.
- Your Losing Probability: 0.35
- Stake: $100
EV = (0.65 * $66.67) - (0.35 * $100) EV = $43.34 - $35.00 EV = +$8.34
This bet has a positive expected value of $8.34. This is a bet you should make.
The Importance of Shopping for the Best Lines
Not all sportsbooks offer the same odds. A small difference in the odds can have a significant impact on the expected value of a bet. This is why it is crucial to have accounts at multiple sportsbooks and always shop for the best line.
Let's say another sportsbook is offering the Patriots at -160 odds.
- Implied Probability: 160 / (160 + 100) = 160 / 260 = 0.615 or 61.5%
If your assessment of the Patriots' chances is still 65%, the bet still has positive EV, but it is lower.
- Potential Profit: A $100 bet at -160 odds wins $62.50.
EV = (0.65 * $62.50) - (0.35 * $100) EV = $40.63 - $35.00 EV = +$5.63
By taking the time to find the best line, you have increased your expected profit on this bet by almost 50%.
Conclusion
Expected value is the cornerstone of a successful sports betting strategy. It is the mathematical principle that allows you to identify profitable betting opportunities. To be a successful bettor, you must stop thinking about who is going to win the game and start thinking about the probability of each outcome. By consistently making positive expected value bets, you are giving yourself the best possible chance of being profitable in the long run.