Welcome back to our comprehensive guide on sports betting. Over the series, we've laid a solid foundation covering the basics, mechanics, and strategies that every bettor needs to understand. Before we dive into the specifics of expected value (EV) betting strategies, let’s review the key concepts from the previous parts:
With this background, we now focus on integrating these concepts into a cohesive EV betting strategy, emphasizing the calculation of expected value in betting and why it is essential for long-term success.
Expected value (EV) is a statistically derived concept used to quantify the average outcome of a given scenario if it were to be repeated multiple times.
In betting, EV helps determine whether a bet offers a positive (profitable) or negative (loss-making) expectation over time.
The basic formula for calculating the EV for any given wager is:
To understand EV clearly, consider a simple coin flip. Assume a fair coin with a 50% chance for heads and a 50% chance for tails. You place a $100 bet on heads at even odds (+100), meaning you stand to win $100 if heads come up.
Using the EV formula:
This shows an EV of 0%, indicating neither a profitable nor a loss-making bet—it's perfectly balanced.
Now, suppose you have inside information that the coin is slightly biased, giving heads a 52% chance of occurring. The odds offered remain at +100.
Here, the EV is 4%, or $4 per $100 bet, signifying a positive expected value. Betting $100 on heads over 1,000 bets with this setup:
This calculation shows an expected profit of $4,000 over 1,000 similar wagers, highlighting the power of betting with a positive EV.
While this adjusted probability example is simple, these types of positive-EV sports betting opportunities come up many times each and every day. Optimal finds them for you!
This method involves creating detailed models to predict game outcomes based on team and player performance data. It requires:
While potentially profitable, the bottom-up approach is complex and resource-intensive. The largest sports gambling syndicates in the world employ tens or even hundreds of quants who build models and crunch numbers for all major sporting events in the world, every single day.
Our preferred strategy uses a top-down approach, based on the principle that all available information relevant to a wager is already reflected in the current odds. This includes contributions from numerous bottom-up bettors, along with all known injuries, lineup changes, and statistical forecasts.
Suppose a sharp sportsbook lists a no-vig price for an NBA player prop bet, Coby White’s total points (23.5), at a no-vig line of -130. A retail book offers the same bet at a no-vig line of -115. This scenario implies a higher probability at the retail book than the sharp book’s estimation, suggesting a betting opportunity.
Let’s follow the step-by-step process we learned earlier:
To calculate the expected value (EV) of betting on Coby White’s total points (23.5) based on the given odds at the sharp and retail sportsbooks, we need to first understand the implied probabilities of these odds and then apply them to our EV formula.
This means you need to bet $130 to win $100. The formula to convert negative American odds to implied probability is:
This means you need to bet $115 to win $100. Using the same formula:
To properly calculate the expected value (EV) for the bet on Coby White’s total points, using the correct formula and definitions for each term, plug these probabilities into the EV formula:
The expected value can be calculated using the formula:
Since the sharp sportsbook's odds are considered the true odds, we will use its implied probability for P and 1−P for Q. Using the sharp book’s implied probability and the payout from the retail book:
This calculation results in an expected value of $5.67 for every $100 wagered (5.67%). This positive EV indicates that, on average, you expect to profit $5.67 per $100 bet over the long term when betting under these conditions at the retail sportsbook. This makes the bet on Coby White’s total points at the retail book a long-run profitable opportunity, based on the provided odds and the discrepancy between the sharp and retail books’ pricing.
In the world of sports betting, achieving success is often perceived as picking more winners than losers. However, the true indicator of a sophisticated bettor's success is often measured by a concept known as Closing Line Value (CLV). Understanding and applying the principles of CLV can significantly enhance a bettor's profitability over the long term.
Closing Line Value refers to the difference between the odds at which a bettor placed a wager and the odds at the time the game starts, which are known as the closing odds. The closing odds are generally considered the most accurate reflection of the true probabilities of the outcomes because they incorporate all the information available up to the start of the game, including betting trends, news updates, and other factors that could influence the outcome of the event.
The primary goal in sports betting from a professional standpoint isn't just to win bets, but to consistently beat the closing line. When a bettor secures odds that are better than the final closing odds, they achieve what is known as "beating the close." This means the bettor has managed to place a wager at more favorable terms than the final consensus of the market, indicating a positive expectation on the bet.
For example, if a bettor places a bet on Team A at +150, and by game time, the odds have shifted to +120, the bettor has gained CLV. The bet was placed at better odds than where the market settled, suggesting that the bettor saw value that the market later recognized as well. This is a sign of sharp betting acumen.
The rationale behind emphasizing beating the closing line rather than solely focusing on winning the bet is based on long-term profitability. Sports betting markets, like financial markets, are influenced by the flow of information and money, which gradually leads to the most efficient market pricing (the closing line). By consistently beating the closing line, bettors demonstrate that they can identify mispricings in the market before they correct, effectively "buying low" and "selling high" in a metaphorical sense.
This approach is predictive of long-term success because it shows that the bettor is able to consistently anticipate market movements and place bets when the odds are in their favor. Over time, this edge will translate into financial profit as the law of large numbers plays out, and the variance (or luck) that can cause swings in short-term outcomes evens out.
Even when a bettor consistently beats the closing line, short-term variance can still result in losing streaks or results that do not seem to align with their perceived skill level. Variance in sports betting is the statistical fluctuation that can make outcomes unpredictable in the short term, despite having a long-term edge.
For instance, a bettor who achieves solid CLV on a series of bets might still find themselves losing more bets than they win in a particular week or month due to the random nature of sports outcomes.
Keep in mind that variance can benefit you, too. "Going on a hot streak" in the short run is almost always a function of bet variance, leading many new sports bettors to think their approach is more profitable than it actually is.
However, as the number of bets increases (reaching into the thousands), the true skill of the bettor in achieving CLV will manifest in their profitability.
The difference between the price a bettor gets (the odds at which they place the bet) and the closing line effectively represents their profit margin over the long run. If a bettor consistently gets better prices than the closing line, they are essentially securing a "discount" on each bet relative to the market's final consensus. Over a large volume of bets, the profit from these discounts will approximate the sum of the differences between the prices obtained and the closing prices.
This concept underscores why professional bettors focus on volume and maintaining a high frequency of bets where they have achieved CLV. The faster a bettor can reach a large volume of such bets, the quicker they will see their results align with the expected profit from their demonstrated ability to beat the close.
We cover the concept of variance and “volume as a strategy” in Part 9 of this series.
Now that you understand the process for identifying bets with positive expected value, the natural next question is, “Can this entire process be automated?”
YES! Optimal’s platform is purpose-built to find, analyze and rank positive-EV opportunities for you. Let’s take a look at the Optimal+ located in the app:
Optimal+ allows you to select from a list of proprietary algorithms, each designed to find and grade bets that hold positive expected value. You can select from a variety of sport/league categories, enabling you to refine your criteria.
Optimal+ is a constant, real-time stream of potential bets and it feeds you these opportunities all day, every day. And now that you understand the concepts and math behind EV betting, you’re ready to dive in, which we do in Part 7.
Incorporating a top-down betting strategy, grounded in the understanding of EV and market dynamics, enables you to exploit discrepancies in how different books price the same event.
By systematically identifying and betting on value opportunities, you can achieve long-term profitability in sports betting.
