What Is Expected Value?



In the context of probability theory, the expected value of a random variable is the average over the long-run of repetitions in the experiments that it represents. For example, the expected value of flipping a coin and having it land on heads is 50%, or alternatively, the expected value of rolling a dice and having it land on a one is 16.67%. The expected value can be derived from the law of large numbers, where the mean of the values will almost surely converge to the expected value as the number of repetitions approaches infinity. In this article, we’ll take a look at the meaning of expected value in the context of sports betting.

Benchmarking

For any type of investment, it’s important to have a benchmark to compare performance. Investors in the stock market may choose to benchmark their performance against the S&P 500, an index fund consisting of the 500 largest companies in the U.S. by market capitalization. For sports bettors, the benchmark is the odds at the time the match begins. This is referred to as the closing line. The closing line is a proper benchmark due to the assumption that the closing line has been shaped by all bets placed at sportsbooks and because they know where the rest of the market have their odds, the sports betting markets are very efficient as the match gets closer to game time.

Goal Of Sports Betting

While no one is able to accurately predict the outcome of every sporting event, this does not imply that it’s impossible to be a profitable sports bettor. The goal of sports betting is hardly to win every bet placed. Instead, the goal is to make decisions that yield a positive expected value (+EV). Over small sample sizes, anything can happen. In order words, variance will impact your results in a big way. However, over large sample sizes, variances will even out and only sports bettors who are able to consistently beat the vig-free closing lines at the sharp sportsbooks will end up profitable. In sports betting, the closing lines of sharp sportsbooks are considered to the expected value. What this means is that if you locked in your bet at higher odds than the closing line, you have made a +EV bet. On the other hand, if you locked in your bet at lower odds than the closing line, you have made a -EV bet.

Closing Lines

The odds of matches represent a reflection of the information possessed by the sports betting market. The main difference between soft and sharp sportsbooks is their payout rate and liquidity. Since sharp sportsbooks have a higher payout rate and allow larger bets to be placed on the outcome of matches, more money flows through the sharp sportsbook, with the result being that the sharp sportsbook also has more liquidity. High liquidity translates into more information, which means that the sharp sportsbook will have a better reflection of the true odds of any match. As a result, the sportsbook that consistently has the highest liquidity in a particular market will be considered the sharpest. More liquidity attracts sharper bettors, who in turn possess valuable information. Once they have placed a bet, the market will reflect the information possessed by the sharp bettors. As a result, the closing line of any match represents what the market believes to be the true odds, and thus, the probability of the outcome of the game.