Basic Probability and the Concept of Value

It would be reasonable to assume that the way to win money from sports betting is to accurately predict what will happen in sports events. While this is technically true, you might be surprised to learn that simply getting your predictions right isn’t necessarily enough to consistently make a profit.

This is because, no matter how good you are, you won’t get your predictions right every time. There are simply too many variables involved in sports events. No one is always right, not even the most successful gamblers in the world.

Although it obviously helps to be right as often as you can, a more important aspect of betting is to actually find value. Value is a term you’ll hear sports bettors use often, and it’s one that you absolutely have to understand if you are going to be successful.

On this page we explain what value is, and how it relates to probability. First, though, we must explain what your hit rate is in sports betting terms, and why it may not be enough to simply get your predictions right more often than you get them wrong.

Your Hit Rate

When betting on sports, your hit rate refers to the number of bets you win in relation to the number of bets you place overall. It’s typically expressed as a percentage. So, for example, if you place 100 bets and win 50 of them, then your hit rate is 50%.

If every single wager you placed was a winner, then you would have a hit rate of 100%, and would clearly make plenty of money. This is entirely unrealistic though, as we have already stated. You should, of course, try to be as accurate as possible with your predictions, but a high hit rate doesn’t guarantee a profit in the long term.

We’ll demonstrate this with a hypothetical scenario, based on betting on the results of tennis matches. For the purposes of this example we’re going to use the first day of the US Open in 2013. In the early round matches of a tournament, it’s reasonable to expect most of the favorites to win, so you could be pretty confident of a high hit rate if you chose to back them all.

Let’s see what would have happened if you decided to bet on all the favorites in the men’s matches taking place on the first day.

# of Matches	Favorites Won	Favorites Lost	Hit Rate
19	15	4	79%

As you can see, you would have had a hit rate of nearly 80%. On the surface, winning nearly four bets out of five seems excellent. However, the average odds for the favorites that won on that day were 1.25. Based on those odds, if you had bet $10 on each match your 15 winning bets would have returned $187.50 in total (including stake), for $37.50 in profit. You would have also lost four bets, at $10 each, for an overall loss of $2.50.

You’ve only just made a loss, and on another day the same strategy may well have returned a small profit. We haven’t used this example to discuss the pros and cons of betting on the favorites in tennis matches though, and this is a very small sample of relevant data anyway. The point we are trying to illustrate with this example is simply that a high hit rate by itself doesn’t automatically mean you’ll make a profit.

To put it another way, your hit rate doesn’t reflect your chances of winning money. It simply reflects how many wagers you win relative to how many wagers you place. As we have just shown, winning a high percentage of your wagers doesn’t necessarily equate to making money. It isn’t the number of predictions you get right which determines your success, it’s the relative quality of your predictions.

This is where value comes into play, because it’s the value associated with your predictions that determines their quality. We’ll get onto exactly what value is in sports betting terms shortly, but first we will look at the role probability plays.

Probability in Sports Betting

Basic probability is really quite straightforward. It is a measure of how likely something is to happen, and is usually expressed as a decimal between 0 and 1.0 in which 0 indicates impossibility and 1 indicates certainty. Probability can also be expressed as percentage, where 0% indicates impossibility and 100% indicates certainty.

In many circumstances, probability can be calculated precisely. Take the toss of a coin, for example. There are only two possible outcomes, and each is equally likely. The probability of the coin coming up heads is therefore 50%, and the probability of it coming up tails is also 50%. The roll of a die is another good example. There are six possible outcomes, and again each one is equally likely. So the probability of any one number being rolled is always 16.66% (100% divided by six).

Probability in sports betting is not quite so straightforward. It is impossible to calculate the precise probability of any outcome in a sport event, as there are so many factors involved. You can apply all the statistics you want, and take all the factors that can affect a result into account, but you simply cannot determine a definitively accurate probability.

All you can do is calculate what you believe the chances of any particular outcome to be. This is all the bookmakers can do too. While the odds they set do reflect the relative likelihood of the possible outcomes, they are not necessarily completely accurate representations of the probabilities involved. Ultimately they are based on the bookmakers’ assessment of what they think may happen, adjusted to make sure there is a built in margin for them.

While bookmakers do put the odds in their favor, it is possible to overcome their advantage. This is not easy to do, but it is certainly possible. Ideally you need to really know your sports, and you definitely need to understand implied probability and expected value.

Implied Probability and Expected Value

In sports betting, implied probability is what the odds suggest the likelihood of an outcome happening is. It is calculated by dividing one by the decimal odds. So, if the Chicago Bears are given odds of 2.50 to win a match, their implied probability of winning is 0.4, or 40%. If they are given odds of 1.50 to win a match, their implied probability of winning is 0.67, or 67%.

To easily convert odds, in any format, into implied probability, you can use our odds converter tool.

Expected value relates to how much you can expect to win from a wager. It is a theoretical measure that is based on the overall probability of it winning. Let’s use an example of betting on the Chicago Bears at 2.50 to illustrate expected value.

If you placed a $10 wager on the Bears to win at odds of 2.50 then you stand to make a return of $25, including your stake. Assuming the implied probability of them winning (which we’ve already established is 40% based on these odds) is an accurate reflection of their real probability of winning, you will be paid $25 40% of the time that you make this wager. You will lose $10 60% of the time that you make this wager.

The calculation for expected value is as follows.

Expected Value = (Probability of Winning x Amount Won Per Bet) – (Probability of Losing x Stake)

Let’s use this calculation to work out the expected value of this wager.

(40% x $15) – (60% x $10) = $6.00 –$6.00 = $0.00

The expected value of this wager is therefore zero, meaning it should break even in the long run. Obviously it will always win or lose in practice, but expected value is basically used to measure how much theoretical value a wager offers over the long term.

The expected value of a wager is in fact always zero when you assume that the implied probability is an accurate reflection of real probability. However, the implied probability that bookmakers’ odds suggest is usually higher than the real probability. When the odds are 2.50 on the Chicago Bears winning a match, then the real probability on them winning is actually likely to be less than 40%.

Let’s do some sums based on the real probability of the Bears wining being 35%, and the real probability of them losing being 65%.

(35% x $15) – (65% x $10) = $5.25 – $6.50 = -$1.25

We can see that, based on these probabilities, a wager on the Bears winning at 2.50 actually has negative expected value. This means that you would expect to lose money on this wager in the long run.

We mentioned earlier that it’s the value associated with your predictions that determines their quality. If a prediction involves making a wager where the expected value of a wager is less than zero, then it’s technically a low quality prediction. You may be right sometimes, but the expectation in the long run is that you will lose money.

High quality predictions involve making wagers with positive expected value. These might be wrong sometimes, but the expectation is that you will win money in the long run. To find positive expected value, you have to find opportunities to place a wager where you believe the real probability is higher than the implied probability that the odds suggest.

Let’s use the example of betting on the Chicago Bears to win at 2.50 again. This time we’ll do the sums based on you believing the real probability of them winning to be 45%.

(45% x $15) – (55% x $10) = $6.75 – $5.50 = $1.25

We can see that a wager on the Chicago Bears at 2.50 now appears to offer positive expected value.

The examples we’ve used here are somewhat simplified. We have used them purely to illustrate the concept of value in sports betting. We have also demonstrated one very important aspect of value – that it is ultimately a matter of opinion.

The fact is that a bet on the Chicago Bears to win a match at odds of 2.50 might be a good value bet in the eyes of one bettor, and a bad value bet in the eyes of another. It basically depends on how you assess the relative probabilities of the possible outcomes. This is very much an individual thing, and there is no particularly right or wrong way to do it.

Summary

There are three key points that you should take away from this article. The first is that your hit rate is not as important as some would have you believe. Of course you want to get as many of your predictions right as you can, but you have to consider the odds of your selections. It’s no good winning 80% of your wagers if you still lose money overall.

The second point is that the odds that bookmakers set do not necessarily accurately reflect the real probability of possible outcomes. They are usually pretty close, but you must remember that there is always the built in margin to consider. It is also quite possible for bookmakers to make mistakes, and offer odds that are actually higher than they technically should be.

The third point is that assessing the value of any particular wager is an excellent way to decide which bets to place, but offers no guarantee of success. In theory, if you only ever place bets that have positive expected value then you should make money overall. It is important to recognize, though, that value is subjective. Making bets that you perceive to offer value will only prove to be profitable if your perception is correct.

Identifying opportunities which do offer genuine value is not easy. If you can do it consistently though, then you stand a very good chance of becoming a successful bettor. This is where sports knowledge, an ability to analyze data and statistics, and an understanding of various betting strategies are all useful.