# The Concept of Implied Probability and Expected Value in Sports Betting

September 12, 2021

Written By,

Brijesh Mehta

Knowledge is a key to success in sports betting. Unlike casino’s chance-based games, sports betting demands knowledge and research from your side. Sports betting is not just about accurately predicting the outcome of sporting events. There is much more than that. Also, getting accurate predictions every time is unrealistic and it’s important for you to understand that there are other variables involved in sports betting. In this article, we will discuss two important aspects of sports betting: Implied Probability and Expected Value.

You might think that if you have a high hit rate, then you will make a higher profit. But, the high rate doesn’t guarantee that you make a higher profit in the long term.

On a side note, IPL is going to start very soon and we have also written an article on free IPL betting tips. You can click the link to know the important tips to enhance your winning chances in IPL betting.

Let’s discuss the hit rate and how it doesn’t reflect the chances of winning money.

## Hit Rate in Sports Betting

Hit rate in sports betting refers to the number of bets won to the total number of bets placed. It is generally expressed in percentage. For example, if you place 200 bets and win 120 of them, then your hit rate is 60%.

High rate doesn’t indicate your profits or losses in sports betting. Just because your hit rate is high, it doesn’t guarantee that you will make a profit. Let’s understand this with an example.

Suppose, you make a total of 20 bets where you chose favourite teams on every bet instead of underdogs. Out of 20 bets, you won 15 of them and lost only 5 bets. Here, for simplicity, let’s consider you wagered ₹100 on every bet and the odds for all favourites were 1.25. If so then, the total amount you wagered is ₹(100 x 20) i.e. ₹2000 and the total return from all your winning bets is ₹(100 x 1.25) x 15 = ₹1875. From the winning bets, you make a profit of ₹ (1875 – 1500) i.e. ₹375. Also, you have lost 5 bets at ₹100 each; so your loss from losing bets is ₹500.

So, your net loss = ₹ (500 – 375) = ₹125

In this example, although your hit rate is high (75%), you still incur an overall loss of ₹125 instead of making profits.

The above example is for showing that the hit rate doesn’t reflect your chances of making profits and not for showing the pros and cons of betting on favourite teams. Hit rate only reflects how many bets you win to the total number of bets you place.

So, it is not the number of bets you win, it is more about the relative quality of bets you win for determining your financial success in sports betting. Now, what determines the quality of bets? This is where the value of bets comes into action. The value associated with bets you place determines their quality. Before we discuss the value in sports betting, let’s know what type of role probability plays in sports betting.

## Probability in Sports Betting

Probability is the measurement of the likelihood of the occurrence of an event. It is generally expressed either in decimal or percentage. In the case of decimal representation, the value of probability lies between 0 and 1 in which 0 refers that the event is impossible to occur whereas 1 refers that the event is certain to occur. In the case of percentage representation, the value lies between 0% and 100% in which 0% refers that the event is impossible to occur whereas certain events have 100% probability.

In many cases, probability can be calculated accurately. For example, in a coin toss, there are only two possible outcomes: heads and tails. So, the probability of the tossed coin coming up heads is ½ i.e. 50% and the probability for tails is only 50%. Another example is the roll of a dice where we can calculate the probability of the occurrence of any number in a dice accurately which is 1/6 i.e. 16.667%.

But, we can’t calculate the probability of an outcome in sports betting accurately or precisely since many factors are involved. Even if you try to consider all factors and apply all statistics, you are unable to come up with a definite probability and the probability you come up with is only the probability that you believe. So, that’s why the implied probability is used in sports betting by bookmakers.

## Implied Probability and Expected Value

The betting odds are set by bookmakers or sportsbooks and the probability suggested by such odds is the implied probability in sports betting. Implied probability is what a bookmaker thinks the likelihood of an occurrence of an event.

To calculate implied probability, you have to divide 1 by the decimal odds set by a bookmaker. For example, the decimal odds given for Mumbai Indians is 1.61 in an IPL cricket match between Mumbai Indians and Chennai Super Kings by an IPL betting app. The implied probability of Mumbai Indian winning the match is 1/1.61 i.e. 0.62 or 62%.

On the other hand, the expected value is related to how much you can expect to get a return from a bet you place. Expected value is a theoretical measure and it is based on the implied probability.

In the above example where Mumbai Indians is given the odds of 1.61, suppose you place a bet of ₹100 on Mumbai Indians to win at the given odds. If you win your bet, you get a return of ₹161 which includes your stake of ₹100. If you lose your bet, you lose your stake of ₹100. Considering the implied probability calculated above, you have the probability of 62% to make a profit of ₹61 by getting a return of ₹161 and you have the probability of 38% to lose your stake of ₹100.

The expected value can be calculated as:

Expected Value = (Probability of Winning x Profit Made on Winning a Bet) – (Probability of Losing x Bet Amount)

The expected value for the above example is:

Expected Value = (62% x ₹61) – (38% x ₹100)

= ₹37.82 – ₹38

= – ₹0.18 (close to ₹0)

The probability used in the above calculation is the implied probability and not the real probability. The bookmaker usually sets the implied probability to be higher than the real probability. If we consider the real probability of Mumbai Indians winning the match is 55%, then

Expected Value = (55% x ₹61) – (45% x ₹100)

= ₹33.55 – ₹45

= -₹11.45

The expected value of this bet is negative and this is considered a low-quality bet technically. Although you can make some profit by winning this bet, you are expected to lose some money in the long run.

High-quality bets or predictions have positive expected values. You are expected to win money in the long run with high-quality bets. Let’s calculate the expected value in the above case by considering the real probability of Mumbai Indians to win the match to be 70% this time.

Expected Value = (70% x ₹61) – (30% x ₹100)

= ₹42.70 – ₹30

= ₹12.70

This time, the expected value of the bet is positive.

To find the positive expected value, you have to find the bet where the real probability of an outcome is higher than the implied probability suggested by the betting odds.

The same bet can be considered a good value by one bettor and a bad value bet by another. It all depends on how well you can assess the possible outcomes of the match or game.

Final Words

We hope that by reading this article, you are clear about the important concepts of implied probability and expected value in sports betting. Hit rate doesn’t reflect your chances of making profits in sports betting. Remember that even if you have a high hit rate of 80%, you can still be at loss.

The expected value of bets matters when it comes to being successful in the betting world. The odds set by the bookmakers reflect implied probability which is close to the real probability. It is beneficial for you to place wagers on bets where you perceive that the real probability is higher than the implied ones and the expected value of bets is positive.

Last but not least, always choose a licensed, safe and trusted betting platform for any kind or form of online sports betting.

Written By,

Brijesh Mehta

Brijesh Mehta is a content writer & strategist from India providing his top-notch skills & expertise in the Sports and online casino industry for more than seven years. He is an avid reader and creative writer who is fond of words and uses them to teach others about online betting and trending sports news through his in-depth guides.