Probability plays an essential role in sports betting. Everything related to a possible outcome of a sporting event can be boiled down to the seemingly simple concept of probability. When we speak of expected value (EV) it is paramount to understand how betting odds work and all the different variables that go into the process of oddsmaking.
I will show you the ropes of finding markets with positive EVs, discuss the relationship between (implied and true) probability and EVs, and provide the formula for estimating it in sports betting.
Expected Value in Sports Betting
Expected value is, plainly speaking, the difference between what you think the probability is for an outcome against the probability (odds) assigned by the bookmaker. What you want to look for are discrepancies between the given odds and the actual likelihood of those odds. More specifically, to target outcomes with a higher actual probability of winning than the one given by the betting site i.e. with positive EV (+EV), and avoid negative EV (-EV) markets.
Working out the likelihood of an outcome based on the odds given by the betting site can, at times, be misleading. This is where EV comes into play. It enables you to estimate the value of the market with more accuracy and return a profit, even a small one if you recognize a positive EV (higher than 50%).
Implied Odds and True Odds
As I said, probability and expected value are closely knitted together, so to understand EV, you must understand probability. Betting sites employ oddsmakers to create betting lines and assign odds (probability values) on various outcomes of the game, whether to win, cover the spread, or something else, based on thorough statistical analyses.
But odds from betting sites are not always 100% accurate and may not actually reflect the true probability of the outcome. This is what we call implied probability i.e. implied odds. On the other hand, you have the true probability, which offers a more accurate representation of the probability of a given outcome. Implied probability is what the bookmaker believes the probability (odds) should be.
You can use the BettingTools odds calculator to see the implied odds of a given betting market. Input the odds in the required field and our calculator will show you the implied odds as a percentage value. For instance, a bet with 11/10 odds, has an implied probability of 47.6%.
Positive and Negative EV
Understanding implied odds can help you better grasp the concept of positive and negative expected value. When bookmakers assign (implied) odds to an event, they use a trove of resources at their disposal and usually manipulate the odds in their favour to collect vigorish (vig). The vig is a form of commission the operator takes from every betting market.
In an NFL game where the favourite has 10/13 odds to win and the underdog 11/10 (+110), the implied odds are 56.5% for the favourite and 47.6% for the underdog, coming to a total of 104.1%. The extra percentage (4.1%) is the vig.
For example, if you come across a betting market offering 10/9 odds, the implied odds are approximately 47.4%. However, using your insight, EV formula, and data analysis, you can work out the true probability to be higher than 50% and assign a +EV, indicating a favourable market.
Conversely, if you reason that a market with 20/21 odds (51.20% implied odds) is unrealistic and estimate the win probability comes to less than 50%, you will assign negative EV (-EV) and need to steer clear of such markets.
Calculating Expected Value
Knowing the implied odds of winning, probability of losing, and variables like potential payout can help you work out whether you can expect a positive or negative EV in the long run. Below, we look at the formula for calculating EV, and I’ll explain the variables and factors for determining EV and how the formula works in practice.
Key Factors for Determining EV
To understand how the EV formula works, you must first familiarise yourself with its key variables.
- Implied odds (probability) of winning – You can see the implied probability of winning a given market based on its odds (you can use the BettingTools odds calculator for that). But you must still do your own research into historical performances, result stats, and team and player stats to estimate a probability as accurately as possible.
- Probability of losing – Knowing the probability of losing is key to calculating if you have a +EV or -EV. In single bets, the loss probability is simply the difference from the win probability. On the other hand, in combined bets, you must work out the loss probability for each selection.
- Amount staked (potential loss per bet) – The amount staked, sometimes listed as the (potential) loss in the EV formula, is a key variable in the formula for determining EV.
- Potential payout – Your potential payout is closely tied to how much you bet (amount staked) and the odds from the bookie. It is important to note, that for the formula, you should only calculate your potential profits (returns – amount staked).
EV Calculation Formula
Now that you know the main variables for determining EV, I will present the formula for estimating it. The formula is as follows:
(Potential Payout * Probability of winning) – (Probability of Losing * Amount Staked)
If, for example, you place a single bet of £20 on events with odds of 11/13, the implied probability of winning (which you can see using a betting calculator) is 54%, with a potential payout of £36.95. The probability of losing is, logically, 46%.
Potential Payout = £26.95
Amount Staked = £20
Probability of Losing = 46%
Now let’s draft up two scenarios. In one, you reckon the favourite has a good 60% chance of running away with a result. In the other, you doubt them and think that they only have a 50% chance of winning.
Probability of Winning = 60% and 50%
We can apply those hunches into the formula and crunch some numbers for EV.
Assuming a 60% Chance of Winning
(16.95 * 0.60) – (0.46 * 20) = +0.97 EV
Assuming a 50% Chance of Winning
(16.95 * 0.50) – (0.46 * 20) = -0.725 EV
If you are positive about the team’s chances of winning and assume they win 60% of games of this calibre, then the EV is nearly +1. Assuming that they can only win 50% of the time in the given scenario, the EV is negative, meaning the profit margin is just not enough to justify the 50% chance of winning.
Analysing and Finding Positive EV in Sports Betting
Once you learn how to put the EV formula into practice, you can train yourself to identify and calculate potentially profitable markets with a positive expected value (+EV).
You may come to a point where you can roughly recognise if a market has a positive or negative EV in the long run. But this is much easier for single bets. However, given the popularity of accumulators and other combined bets, a calculator is often necessary to get as close to the accurate EV as you can.
One way to identify markets with positive EV is to go line shopping i.e. compare odds and probabilities among established bookmakers. Of course, each bookie has its in-house oddsmakers who generate market probabilities based on complex data analytics.
If you compare the regular-time/moneyline markets in the images above from DraftKings and bet365, you’ll see odd variations between some events. Tracking betting lines and odds movements is key to catching positive-value markets.
Yet, the odds the bookmaker assigns have a vigorish (vig), a commission the bookie charges that distorts the true odds. For instance, if we take a football game between Southampton and Manchester United, the odds for the home team to win would be around 7/2 (22.22% implied odds for winning); 31/10 for a draw (24.39% implied odds), and 20/27 (57.45% implied odds) for United to win.
Man United to Win: 20/27 (57.45%)
Southampton to Win: 7/2 (22.22%)
Draw: 31/10 (24.39%)
The total implied odds come to 104.06%, which is in practical terms, impossible. That extra 4.06% is the juice, that the bookie has to add to make its money.
Estimating the true odds is difficult but not impossible, and it helps you come closer to identifying +EV markets. By estimating the vig, you can see the bookie’s markup and come to the true probability. But odds are pliable metrics and can change, underscoring the importance of keeping up to date with the latest market values across many sportsbooks.
Why Understanding EV Matters in Sports Betting
EV is a metric not for calculating the current profitability of a market, but its long-term value, hence the ‘expected’ qualifier.
It is comparable to what shareholders and venture capitalists do when evaluating different investment avenues, looking to find stocks and other assets whose future (long-term) value has a positive return on investment (ROI).
It is the same with finding positive EV in sports betting. You work out the true probability yourself by following the established formula, your own market analysis strategies and by following credible market-makers.
But take notice, finding a positive EV is all about making it count in the long run. Losses should be expected at first. After all, sports betting is a volatile enterprise, and the (true) probability of outcomes shifts based on a broad spectrum of factors, highlighting the need to stay up to date with market shifts from reliable sources.
