What is Expected Value (EV) in Sports Betting?
Expected value in sports betting is a mathematical estimate of how much you can expect to win or lose on average per bet in the long term. Essentially, it’s the average outcome if you could repeat the same wager hundreds or thousands of times. Importantly, EV is not about predicting a single bet’s result – it’s about the law of averages over many similar bets. A positive expected value (+EV) means a bet should profit on average over time, while a negative expected value (–EV) means you’d expect to lose money on average. A bet with zero EV would break even in the long run.
Another way to think of expected value is as a measure of whether the odds you’re getting are better or worse than the true probability of an outcome. In fact, expected value is the difference between the true odds of an event happening and the sportsbook’s posted odds. If a sportsbook offers odds that pay better than the “fair” odds (true probability), your bet has positive EV. Bettors often call such wagers “value bets” – because you’re getting good value relative to the risk. On the other hand, if the odds are worse than the fair odds (as is usually the case due to the bookmaker’s margin), the bet has negative EV and will cost you money in the long run.
How to Calculate Expected Value in Betting
The expected value formula betting experts rely on is straightforward. In probability terms, expected value is calculated by multiplying each possible outcome by its probability and adding the results. For a simple win/lose sports bet, the formula boils down to this:
In other words, you weight the amount you could win by the chance of winning, and subtract the amount you’ll lose weighted by the chance of losing. (Note: Probability of losing is just 1 minus the probability of winning, for two-outcome bets.)
Let’s break down the expected value formula step by step with an example:
- Estimate the probability of winning. This could be your own estimated win probability or the implied probability from the odds. For example, say you estimate a team has a 50% chance (0.50) to win a game.
- Find the probability of losing. For a two-outcome bet, this is simply 1 minus the win probability. In our example, probability of losing = 1 – 0.50 = 0.50 (50%).
- Determine your potential profit if you win. This is based on the odds and your stake. For instance, if the odds are +120 (decimal 2.20) and you bet $100, a win would pay $120 in profit (you’d get $220 total, which is $120 profit plus your $100 stake back).
- Determine your loss if the bet loses. In sports betting, if your pick loses, you typically lose your entire stake. In this example, that would be $100.
- Apply the expected value formula. Using the numbers above:
EV = (0.50 × $120 profit) – (0.50 × $100 stake)
EV = $60 – $50
EV = $10 - Interpret the result. An EV of +$10 means on average you’d profit $10 per bet if you could make this exact wager many times. In percentage terms, that’s a 10% positive expected value (because $10 is 10% of the $100 stake). Positive EV suggests a profitable bet over the long run, whereas a negative EV would suggest a losing proposition over time.
Example: Calculating EV for a Coin Toss Bet
To illustrate expected value, consider a simple example of a coin toss bet. The true odds of a fair coin toss are 50/50 – there’s a 50% chance to win and 50% to lose. The “fair” betting odds for a 50% probability are +100 (even money) which would double your money on a win. Now imagine a friend offers you better odds: if you bet $100 on “tails”, they’ll pay you $120 profit if you win (this corresponds to +120 odds). Let’s calculate the expected value:
- Probability of winning = 50% (0.5)
- Probability of losing = 50% (0.5)
- Profit if you win = $120 (friend’s offered payout on a $100 bet)
- Amount lost if you lose = $100 (your stake)
Plugging these into the formula:
EV = 0.5 × $120 – 0.5 × $100 = $60 – $50 = +$10.
The expected value of this bet is +$10, which means it’s a +EV (positive expected value) bet. In fact, $10 is 10% of your $100 stake, so we’d say this wager has a +10% expected return. If you could play this coin-toss bet repeatedly under the same conditions, on average you’d earn $10 profit per toss over the long run. This is a great deal for you because the odds are in your favor.
For comparison, if the friend only offered +100 odds on the coin toss (a fair 1-to-1 payout), the EV would be $0 (0.5 × $100 – 0.5 × $100 = $0). That bet would essentially be a break-even proposition – you wouldn’t expect to gain or lose money over many flips. And if the odds were worse (say they only pay $90 profit on a $100 bet), the EV would be negative: you’d expect to lose money on average. This simple example shows why finding bets with positive EV is so important – those are the bets that give you an edge.
Why Expected Value Matters for Bettors
Why should you care about expected value? Because consistently betting on positive-EV opportunities is the key to long-term success in sports betting. A wager’s EV tells you whether it’s worthwhile in the long run. Even though any single bet can win or lose (luck plays a role in the short term), a bettor who always takes +EV bets will profit over time, whereas one who takes –EV bets will eventually go bust.
It’s important to realize that most bets offered by sportsbooks have a negative expected value for the bettor. Sportsbooks build in a margin (the “vig” or house edge) that tilts odds slightly in their favor. This means if you blindly bet at the going odds, you’re usually taking a small negative EV, which over many bets will eat away your bankroll. For example, a typical point spread bet at -110 odds has an implied win probability of about 52.4% for break-even, but your true chance might only be 50% – that gap is the bookmaker’s edge and your expected loss.
The goal for a smart bettor is to find those rare bets where the expected value is zero or positive despite the vig. These occur when you have reason to believe an outcome’s true probability is higher than what the odds imply. In the long run, consistently identifying and wagering on positive expected value bets can produce steady profits. This is often referred to as “value betting” – you’re effectively capitalizing on discrepancies between the sportsbook’s odds and the true odds.
Another benefit of understanding EV is better decision-making and bankroll management. When you calculate the EV of potential wagers, it helps you identify which bets are better than others, leading to better bankroll management and potentially higher profits. You can avoid throwing money at long-shot parlays or bad lines that carry huge negative EV, and focus on bets where you have an edge. Even if positive-EV bets don’t win every time (and they won’t), you know that over a large sample those bets should yield a profit. This knowledge can keep you disciplined and patient, rather than chasing quick wins.
In summary, expected value is the ultimate measure of a bet’s quality. Bettors who internalize this concept start thinking in terms of probability and long-term outcomes, much like a casino does. You’ll begin to ask not just “Who do I think will win?” but also “Is this bet priced right?”. When you consistently wager on outcomes where you have the edge (positive EV), you essentially become the “house” in the long run, and the odds tilt in your favor. That is the path to sustainable betting profits.
Using an Expected Value Calculator and BetRocket’s EV+ Lab
Calculating EV by hand as we did in the example is useful for understanding the concept. However, doing the math for every bet can be time-consuming – especially when dealing with different odds formats or multiple outcomes. This is where an expected value calculator betting enthusiasts use can save the day. An EV calculator is a simple tool where you input your stake, the odds, and the win probability, and it will instantly compute the expected value and even the expected return on investment for that bet. In essence, it automates the formula we described earlier. Bettors can use an EV calculator to double-check that they are only placing bets with positive expected value, thus avoiding negative-EV wagers that will cost them money over time.
BetRocket offers a free, user-friendly expected value calculator for betting that makes these calculations a breeze. You don’t have to be a math whiz – just enter the odds for your bet (American, decimal, or fractional), the amount you plan to stake, and either the implied win probability or your own estimated probability of winning. The calculator will output the EV in dollars and as a percentage. This helps you quickly see whether a potential bet is +EV, 0 EV, or -EV. For example, if you input a $100 stake, +120 odds, and a 50% win probability, the calculator will show an expected value of +$10 (a 10% return), confirming the profitable edge we calculated earlier.
Beyond the basic calculator, BetRocket’s platform also features the EV+ Lab – an innovative space for testing and refining your betting strategies. The EV+ Lab allows you to simulate betting scenarios and experiment with different strategy ideas in a risk-free environment. For instance, you can test how a strategy of only taking underdogs with a certain positive EV would perform over a season, or compare the long-term outcomes of two different staking plans. The lab uses real odds and probability inputs to calculate the hypothetical expected value and variance of a series of bets, so you can see the potential long-term results of a strategy before you put real money on the line. It’s like a sandbox for bettors to fine-tune their approach using solid data and math.
Some key benefits of using BetRocket’s EV tools include:
- Instant EV calculations: The expected value calculator gives you quick answers on any single bet’s profitability, so you can make informed decisions on the fly.
- Strategy simulation: In the EV+ Lab, you can simulate multiple bets and even entire betting portfolios to gauge their cumulative expected value and risk. This helps in discovering truly profitable systems and weeding out flawed strategies.
- Better bankroll management: By quantifying the expected value, you’ll know which bets are worth the risk. The tools encourage a disciplined, data-driven approach, preventing impulsive wagers on hunches or overly risky parlays with negative EV.
- Education and confidence: For beginners, seeing the numbers can be eye-opening. Using the calculator and EV+ Lab not only gives you answers but also helps you learn – you’ll develop an intuition for odds and probabilities, and gain confidence in spotting value bets.
In short, BetRocket’s expected value calculator and EV+ Lab take the guesswork out of finding +EV bets. They empower you to apply the probability math without hassle, so you can focus on strategy and enjoy the game knowing you have the statistical edge on your side.
Conclusion
Expected value is the fundamental concept that separates smart betting from just gambling. By understanding the EV formula and thinking in terms of probabilities, you can evaluate bets not just on gut feeling, but on their true long-term merit. Always remember: a bet is “good” or “bad” not just by whether it wins, but by whether it had a positive expected value. Even a bet that loses can be a smart play if it was +EV, and even a winning bet can be foolish if it had negative EV (it was a bad bet that got lucky). Keeping the focus on expected value will guide you toward bets that make money in the long run and steer you away from traps set by sportsbooks.
The great news is you don’t have to crunch the numbers all by yourself. Tools like BetRocket’s EV calculator and EV+ Lab are there to help you find and test profitable opportunities with ease. Ready to boost your betting strategy with the power of math? Try BetRocket’s expected value calculator and jump into the EV+ Lab today to start placing smarter bets. By consistently betting with positive expected value, you’ll be well on your way to long-term success in sports betting – and BetRocket is here to help you get there. Good luck and may all your bets be +EV!