Calculating odds is a science, and statisticians/analysts, who can do the job competently, receive good annual salaries (GBP 50k-80k; €60k-95k: Quantitative Analyst).

These jobs are paid so well because the results form the backbone of each bookmaker’s business. The better an analyst understands his job, the bigger the potential profit margins for the bookmaker. In order to make long-term profits, a good understanding of odds calculation is therefore also essential for any bettor.

### Probability of Football Match Results

Odds are based on the probability that a certain event occurs: for example a home win, a draw, or an away win in football games based on historical data. But what is the current probability of each of these outcomes and how are percentages computed? Also, from where does one get the data from?

The following diagram shows the distribution of results for the English Premier League for home win, draw, and away win during the last five complete seasons:

Looking at the graph, one can see that the distribution of results is rather similar for each year.

Without considering factors such as matches between strong or weak teams, teams under new management, rain affected games or anything else one can think of, fixtures in the English Premier League, according to the statistics, show on average 24.46% of all games were drawn, 27.35% ended in an away win and 48.16% were won by the home team:

Only twice (of 15) did results fall outside of ± 2% **residual** from the average figures, being drawn games in 2005/2006 (-4.2%) and away wins in 2009/2010 (-3.4%):

### Comparison of the expected results with observations

Now, it is time to compare the expected results (based on the average results of 5 years) with the observed results of the current 2010/2011 season up to 19 February 2011:

There are quite large differences from the expected values (averages or means) to the observed results (actual results for 2010/2011) in both the drawn matches and away wins categories. However, I am pretty sure that by the end of the season, the figures will adjust themselves more in line with the 5-year average figures and that the differences showing now can be explained by having compared only two-thirds of the current season with the average results of a full-year. However, this indicates that there is an uneven distribution of home wins, draws and away wins at different times over the season, which should balance out by the close.

So, if the odds of a single match are calculated, this seasonal effect must be considered, but for this article and for your general understanding, I shall not complicate matters by touching on it further.

### Mean (average value), Errors and Residuals (relative and absolute deviation)

For those of you with difficulties understanding what **arithmetic mean** and **errors/ residuals** are, herewith a few additional explanations with examples:

**Arithmetic Mean**

The arithmetic mean, often referred to as simply the**mean**or**average**when the context is clear, is a method to derive the central tendency of a sample. In probability theory, the mean is also called expected value (or expectation, or mathematical expectation, or the first moment).

The mean (average value) is avalue and can therefore be used as an**known**value.**expectancy**

Simply speaking, one can use the mean to predict future events (e.g. the distribution of football results) quite accurately.

**Example using the 5-Year English Premier League table above for home games:**

(50.53% + 47.89% + 46.32% + 45.29% +50.79%) divided by 5 = 48.16% (= mean/ average)

Therefore, it “is expected” that the 2010/2011 season will produce 48.16% home wins.**Errors and Residuals (relative and absolute deviation)**Statistical errors and residuals are two closely related and easily confused measures of the deviation.

The**error**of a sample (e.g. observed football results for a certain period of time) is the ‘relative’ deviation from the function value (mean), while the**residual**is the difference (absolute deviation) between the sample and the function value (mean).**For example, the****RESIDUAL**(absolute deviation) for home wins during 2005/2006:

50.53% (2005/2006 home wins) minus 48.16% (average value for 5-years) = 2.37% (= residual)**For example, the ERROR (relative deviation) for home wins during 2005/2006:**

2.37% (residual) divided by 48.16% (mean) = 4.92% (= error)The error (relative deviation) is the proportional deviation between the observed value (the actual results) and the expectancy value (the mean/ average of all years). The

**error**(relative deviation) puts**residuals**into relation to each other.

Hey. i wanna know how I can use probability to predict the putcomes of football bets. Mind showing me how?

Hi Derrick, we’ve got a course that teaches probabilities to predict outcomes in detail: The Science of Football Predictions

The course has already helped many people; so it will probably also be of great help to you. Good luck! 🙂

Hello

I have been using some data like

1. Average Home Team goals,

2. Avereage Home team conceeds

3. Average scored by Away Team

4. Average Conceedes by away Team

I also use:

1. Attacking rating

2. Defensive Rating

How can I combine these statistics to get me an idea of expected result.

I am aware that per chance things can change

Erny

Hi Erny,

I’ll have to think about that and add your question to the 1×2 course I have been planning to write for a long while, especially the attacking/ defensive rating… No idea, to be honest, because I don’t even know where I could get enough data from to analyse it properly.

Generally speaking, from a statistical perspective, football matches do not occur frequently enough. For example, looking at a single league such as the German Bundesliga with only 306 matches per season, a relevant sample size is never going to be large.

The plain truth is that any football league is simply not large enough to generate a significant amount of completed match statistics per season. This means that the standard deviation (margin of error) is always going to be relatively large…. and attacking/ defensive rating… it’s only the last few matches, isn’t it?

I probably wouldn’t burn my fingers with it.

If odds are 2.0 and 3.12 what is possible outcome

Hi Kelvin,

Odds and ‘possible outcomes’ are really connected. Bookmakers seldom price ‘true’ probabilities.

Here’s an article on this topic: How Bookmakers’ Odds Match Public Opinion

If you prefer videos, here are a few:

Over Under Clusters Cluster Tables – Calculate ‘Fair’ Odds

1X2 Home — Draw — Away: Expected Odds Calculation & Setting of Market Prices

if the home team have advantage in the odds ?

for example odds are 2 but this home team get 1.75 ?

Hi erez, I don’t understand your question. Sorry!

Generally speaking, home favourites are mainly overpriced, meaning that bookmakers price them at a higher chance to win than their true chances are. For example, odds of 1.75 stand for a 57.1% chance to win, whilst odds of 2.0 for a 50% chance. If bookmakers offer 1.75 odds for a team which should be actually priced at 2.0 then they are ensuring that they have the mathematical advantage on their side.

You may be interested into our

HDA Simulationtables. Just have a look.Hey,

I just came across an app that offers the chance to win 50,000 to correctly predict the odds of two entire leagues.

As an example it says if I can correctly predict 100% premier league results this weekend (10 games) + (10 games of the Spanish League)

What is the average chance per game or the chance winning the 50,000?

Do you have to predict the expected odds (antepost), or predict the actual results which will be played? These are two completely different things.

The minimum odds are computed as follows:

Home win: 2.08 calculated odds multiplied by (1 minus ‘error’ 4.14%) = 1.99

The maximum odds are computed as follows:

Home win: 2.08 calculated odds multiplied by (1 plus ‘error’ 4.14%) = 2.17

am i just being really stupid beacuse i cant seem to get these same answers when i do this sum??

many thank!

scott

Hi Scott, here’s the calculation a little bit more in detail. Hope it helps.

2.08 calculated odds multiplied by (1 minus ‘error’ 4.14%) = 1.99

1 minus ‘error’ 4.14% >> 1 – 0.0414 = 0.95862.08 × 0.9586 = 1.9939

(rounded: 1.99)2.08 calculated odds multiplied by (1 plus ‘error’ 4.14%) = 2.17

1 plus ‘error’ 4.14% >> 1 + 0.0414 = 1.04142.08 × 1.0414 = 2.1661

(rounded: 2.17)Best wishes,

Soccerwidow

hi soccerwidow

i m getting into sportsbetting,i figured out that i might bet on soccer becouse its the sport that i know more than the others,so far so good. when i started to surch on the internet information for betting i get a lot,and i mean a looot confused,there is no precise information, everyone says diffrent shit and i m far away from descovering hot all this works

i found your blog and strarting to read it,you talk about the analysis of the match,analysis for the odds and other things,is this the way professional sports bettors bet? for me to bet do i need this tools? if i have to,can i find this tings on the internet and learn them? when you find a site with odds,isn t it the same as you do you r own odds,saves so much time..so,how can i learn all this things on internet? and what are the really main thing i have to learn in order for me to bet? please help me cuz i m a lot confused and i see you are truly an expert in this so thanks if you answer my questions

Hello guys! I am looking for the acceptible methods to calculate probability chances “1 x 2” on football matches. I read a lot of articles, but there are no useful information that can help me. I started to investigate probability theory myself and I freezed after some calculations.

Let imagine we have match between Chelsea and Liverpool. I understand how calculate probabilitly for each team. I took last ten Chelsea’s home matches and last ten Liverpool’s away matches. After simple calculations(win/10; draw/10; lose/10) I received:

P(Chelsea win at home) = 0,55;

P(Chelsea draw at home)=0,35;

P(Chelsea lose at home) = 0,10;

P(Liverpool win away) = 0,20;

P(Liverpool draw away)=0,55;

P(Liverpool lose away) = 0,25;

But I could now understand how to use this calculated data to predict match Chelsea – Liverpool. I tries to apply sum and multiplication theorems, but there could be incredible result, for exmaple over 1. I definetly understand that this calculation would be very approximatly and that there are a lot of parameters that affect on football result, but I think that it could be useful to predict match. Thank you for any help!

Hi Ineedscore, have a look at our Value Calculator: True Odds & Value Detector: League Games with H2H History as it may help you to answer your question.

There is no need to apply any sum or multiplication theorems. It’s far less difficult that this.

Hello, just to ask, how do you think chaos theory would affect the results of a soccer match? Like for example, in terms of 1) movements of the ball and 2) behavioural aspects. Thank you!

Chaos theory is very, very advanced maths, and goes far beyond the simplified explanations in this blog which are aimed at readers with more basic maths skills.

However, to answer your question: Yes, of course. If you are familiar with chaos theory and advanced statistics, then apply them to your calculations and predictions of match results! This will certainly lead to quite accurate results.

Try also search engines for the keywords chaos theory football. This will bring up a good number of academic articles on this subject.

How come you don’t include missing/injured players in the calculations?

Missing/insured player have a far less effect (if at all) on the final distribution of results than commonly believed. Football is a team sport. In professional football there are lots of players employed. All of them professionals. Bookmakers set their odds weeks, sometimes months, in advance. This should tell you something about the importance of injuries/ missing players for odds calculation.

In the “normal world” it’s only very tiny and poor companies with very few employees which suffer if a major employee is missing. In larger companies a sick note from an individual will hardly affect the overall performance of a company’s results.

Thank you for your help, those articles are very good and they have helped me clarify certain aspects. But with everything, the more you more learn the more questions you have 🙂 If you don’t mind could you give me your opinion on the following question?

Let’s say that I like to bet on certain events that have a high probability of happening (low odds), then I would have to:

– Find something to bet on that is statistically a sure thing. In other words a high probability and a small relative deviation over time (for instance backing Team A at home).

– Find an edge and only bet on over value home games by checking head-2-head statistics.

– Create a staking plan.

If we were to compare this strategy to one where we bet sistematicaly on every Team A home game, could we say that one is more reliable than the other, or more profitable in the long run, or is it just a personal preference?

Thank you for your time.

Without having calculations and numbers in front of me I cannot say which strategy is more reliable. Each strategy needs to be individually evaluated in detail before a statement can be made.

However, what I can say is that in the end it really doesn’t matter. You pick any strategy according to your personal preferences, and get your teeth into it. I promise that you will be able to make it a successful strategy if you don’t give up too early, and calculate and think everything through. Though it may take a long while.

One of the main mistakes unsuccessful bettors do is that they keep “shopping round”, trying one strategy for some time, then the next, and then again another. Your own time resources are one of the largest issues. Therefore it’s crucial to spezialise in order to succeed.

Hi Soccerwidow,

Glad to see the website is up and running again. I would like to ask you a question regarding the non arithmetical calculation of odds in the “Calculation of Odds” section.

In your example you, the calculated odds are found by using the 5-year mean of 48,16% (home wins). You therefore assume that for every game the odds to back the home team are of 2,08. You then use the found relative deviation the calculate the minimum and maximum odds.

If we were to calculate the odds based on reality, we would have to find the probability of the home team winnning, instead of using the 5-year average mean of 48,16%. Once we find the real odds we could then calculate the maximum and minimum odds (using the 5-year relative deviation), to which we would compare the market odds given to us.

Is this train of thought correct?

Hi Helder,

This article was just an intellectual game with deviation and probabilities. It was one of my first articles as I started to understand odds calculation.

Of course, you are thinking in the right direction, in practical terms using the mean for the calculation of odds doesn’t mean much. You need to look at each team individually.

Have you read these articles? They take the thinking a little further.

http://soccerwidow.com/betting-maths/case-studies/impact-overround-accumulators-multiple-bets/

http://soccerwidow.com/betting-maths/goal-distribution/

Thank you, Rick. We try our best!

Thanks for a well written an easy to follow article – something thats pretty rare on the subject of calculating football odds.

Ian, thank you for your very kind words 🙂

just corrected username and email……..lmfao

just found your blog……I am not usually prone to participating on forums or blogs, but I have been fascinated, reading your articles, and thought your efforts deserve to be acknowleged.

the stuff you publish kicks ass. thanks!