Value And Probability – Concepts That Are Going To Make You Rich

It may sound strange but being good at making predictions in a certain sport does not guarantee you will be earning consistent profits.

The reason is that no matter how good you are and how often your predictions are correct, there is no way you could get it right every time. The outcome of a given sporting event depends on too many variables. Nobody gets it right all the time, even the most successful bettors in the world.

Making correct predictions will help you a great deal but the most essential aspect of gambling is to find value. You have probably heard analysts and tipsters use this term a lot, and it is necessary to understand that concept in full in order to become successful.

This article looks at value and its relationship to probability. First, it introduces the concept of Hit Rate and explains why getting your predictions right may not be enough for long-term profitability.

Hit Rate

When betting on sports events, your hit rate is calculated as the ratio between the number of bets you have won and the total number of bets you have placed. It is expressed as a percentage.

If you have placed 100 bets and have predicted 60 of those correctly, your hit rate is 60%. To calculate it, simply divide the number of bets you have got right to the overall number of bets you have placed.

Keep in mind that a high hit rate DOES NOT automatically guarantee you consistent winnings. Let me illustrate that with a hypothetical scenario based on the results of tennis matches.

We are going to use the matches from the first day of US Open. In the early rounds of the tournament it is reasonable to expect the favourites to win, so you could prepare for a high hit rate.

Let us see what would happen if you betted on the favourites in the first round:

  • number of matches 19
  • favourites won – 15
  • underdogs won – 4
  • hit rate – 79%

As you see, the hit rate is nearly 80%, which is very good. However, the average odds for the favourite was 1.25 so if you staked £10 per match, at the end of the day you would have won 15 bets, which would have yielded a profit of £37.50. At the same time, you would have lost 4 matches at £10 each, so you would have ended up with an overall loss of £2.50 regardless of the high hit rate.

Let me emphasise that again: Hit rate itself does not have a direct impact on your chances of making money. It simply shows the ratio between the wagers you win and the overall wagers you place. In other words, it is not the number of correct predictions that determines your success but their quality.

Here comes the concept of Value because it is at the core of quality predictions. I am going to discuss it shortly but first I look at probability in sports betting.


Probability is used to calculate the likelihood of a given event happening. It is usually expressed either as a decimal number between 0 and 1 where 0 is impossible and 1 is certain, or as a percentage from 0% to 100%.

In many cases probability can be calculated precisely. If we take the example with the toss of a coin, there are only two possible outcomes: heads or tails, and each of them is equally likely. Hence the probability of the coin landing on heads is 50%, just like the probability of it landing on tails. (divide 1 to the number of possible outcomes, i.e. ½ = 50%).

Another example involves the roll of a die. There are 6 possible outcomes which are once again equally likely. The probability of getting any of those is 16.66% (divide 1 to 6).

Yet probability in sports betting is not so precise and easy to calculate. There are so many factors affecting the outcome of a sporting event that it is difficult to determine the precise probability.
You may use all the statistics you want, and you will still be far from the accuracy of the die or the coin.

The only thing you can do is calculate what you believe the chances are of a particular outcome happening. This is the same as what bookmakers can do. The odds they set show the relative likelihood of a given outcome so bookmakers too might not necessarily be right.

This is merely their take on what might happen, and they have made sure the odds they offer include a built-in margin for themselves (more on how bookmakers make their money is available HERE).

While bookmakers put the odds in their favour, it is still possible to overcome their advantage. It is not so easy to do but it is definitely possible.
Ideally, you need to know very well the sport you are betting on, as well as understand implied probability and expected value.

Implied Probability & Expected Value

Implied probability in sports betting is what the odds suggest the likelihood of a given outcome happening is. It is calculated by dividing 1 to the odds.

Under 2.5 goals in Manchester United vs. Tottenham
Odds 2.50
The implied probability then = (1/2.5)=0.4=> 40%

Expected Value refers to how much you can expect to win from a wager. It is a theoretical estimate based on the overall likelihood of a win. Reading the definition doesn’t tell me much either so let me give you an example with the United vs. Tottenham match that will illustrate the concept.

If you stake £10 on under 2.5 goals at a 2.50 odds, then you will win £15 net.

Let us assume that the Implied Probability, which is 40%, reflects the real probability of winning. That way you win £15 40% of the time that you make this wager, and lose £10 60% of the time.
Use this formula to calculate Expected Value:

Expected Value = (Probability of Winning Х Amount Won) – (Probability of Losing Х Stake)

Let us now calculate the Expected Value of our wager:

(40% х £15) – (60% х £10) = £6 – £6 = £0

According to this example, you may expect to break even in the long term. Generally, there will always be winning and losing streaks but Expected Value measures how much you may expect from every wager in the long term.

Assuming that the Implied Probability reflects the real probability of a given outcome happening, the Expected Value will always equal zero.

The implied probability of bookmakers’ odds is higher than the real probability of an outcome. When the under 2.5 goals odds is 2.50, it means the real probability of that happening is not 40% but less. Let us make a calculation based on the real probability which we assume to be 35%.

Expected Value = (35% x 15)-(65% x 10) = £5.25 – £6.5 = £-1.25

As the calculation shows, your wager has a negative Expected Value given this probability. This means you may expect to lose money on your wager in the long term. That is exactly one of the tricks that bookmakers use to put you at a disadvantage.

Previously I mentioned that the value you find in your predictions determines their quality. If your wagers have a negative Expected Value, these are low quality predictions and even if you get part of your wagers right, you are still going to be losing money in the long term.

High quality predictions entail wagers with a positive Expected Value. While these might be wrong sometimes, you are bound to make money according to the mathematical expectations.

In order to find positive Expected Value, it is necessary to find a wager where you are confident that the real probability of it being successful is higher than the Implied Probability offered by the odds.

If you have an odds of 2.00 for a victory on Barcelona in the match versus Atletico Madrid, and you are confident that Barcelona is going to win more than 50% of all the matches against Atletico, this is positive Expected Value (if your assessment is objective and not biased in any way).

Let me once again use the example of the match between United and Tottenham. This time you are confident the probability of under 2.5 goals is 45%.

Expected Value = (45% x £15) – (55% х £10) = £6.75 – £5.50 = £1.25

You get a positive Expected Value.

The example I am using here is rather simplified but I need it only to illustrate the concept of Value in sports betting. I would also like to emphasise a vital aspect of that concept, namely that it is a matter of personal opinion. Whether there will be few goals in a match, or whether the 2.50 odds has a good or bad value depends entirely on the assessment of the bettor.

The more you dig into sports betting and analyse the matches’ odds and probabilities, the better your insight into winning wagers and the more accurate your assessment will become.


There are three key points to take away from this article.

  1. Your hit rate is not as important as you may think. Naturally, you want to get as many of your predictions right but you always need to take the odds of your selections into consideration.
  2. The odds offered by bookmakers do not always reflect the real probability of an outcome happening. They are usually very close but you have to remember they include the bookmakers’ margin. Plus, bookmakers often make mistakes and offer odds that are higher than they should technically be.
  3. Calculating VALUE is of paramount importance for the choice and quality of your wagers. In theory, if you bet only on positive Expected Value, you may expect to be successful.

Finding wagers with genuine value is not easy. However, if you manage to do that consistently, you will reach a very good level and join the group of successful bettors.

Only when you have a thorough understanding of the concept of Value would you be able to take full advantage of your knowledge of a given sport as well as your ability to analyse statistics and use various betting strategies.