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\n Poisson distribution in betting is used to calculate the frequency of any occurrence in a game. In this article, you will learn how to calculate the probability of any score in football, and how to use it to calculate who is likely to win.<\/p>\n\n

\n Hot Topics<\/b> on this page:<\/span>\n
\n \n The Poisson distribution explained<\/span>\n <\/a>\n \n How to use the Poisson formula<\/span>\n <\/a>\n \n Poisson distribution advantages<\/span>\n <\/a>\n <\/div>\n <\/div>\n<\/div>\n\n
\n
\n
\n \n
\n $\"Table$ \n Explore this page with our Table of Contents<\/b><\/span>\n <\/div>\n \n
<\/div>\n
\n $\"Table$ \n <\/div>\n <\/div>\n <\/button>\n
\n \n
\n ON THIS PAGE<\/span>\n <\/div>\n
\n
<\/div>\n
\n
<\/div>\n
\n
\n 1<\/span>\n What is Poisson Distribution in Betting?<\/a>\n <\/li>\n
\n 2<\/span>\n Why is Poisson Distribution Important?<\/a>\n <\/li>\n
\n 3<\/span>\n Calculating Football Results<\/a>\n <\/li>\n
\n 4<\/span>\n How Bookies Convert Estimated Chance Into Betting Odds<\/a>\n <\/li>\n
\n 5<\/span>\n Advantages of Poisson Distribution in Betting<\/a>\n <\/li>\n
\n 6<\/span>\n Limitations of Poisson Distribution in Betting<\/a>\n <\/li>\n
\n 7<\/span>\n How to Create Your Own Poisson Football Spreadsheet<\/a>\n <\/li>\n
\n 8<\/span>\n TPP Football Stats Centre<\/a>\n <\/li>\n
\n 9<\/span>\n Match Stats<\/a>\n <\/li>\n
\n 10<\/span>\n Betting Stats<\/a>\n <\/li>\n
\n 11<\/span>\n Profit & Loss Stats<\/a>\n <\/li>\n
\n 12<\/span>\n Streaks & Trends<\/a>\n <\/li>\n
\n 13<\/span>\n ThePuntersPage Final Say<\/a>\n <\/li>\n
\n 14<\/span>\n Poisson Distribution FAQs<\/a>\n <\/li>\n <\/ol>\n <\/div>\n <\/div>\n <\/div>\n<\/div>\n
\n
\n
\n ON THIS PAGE<\/a>\n <\/div>\n<\/div>\n
<\/div>\n\n\n
What is Poisson Distribution in Betting?<\/h2>\n \n\n
\n Poisson distribution<\/strong> was developed by 19th century French mathematician Sim\u00e9on Denis Poisson<\/a><\/strong>. It is a probability theory<\/strong> that uses historical sports data<\/strong> to predict the outcome of a sports event. It measures the likelihood of how many times an event will occur during a specific period.<\/p>\n\n
\n This may seem complicated to someone who has no background in maths, but it is actually a fairly simple method. To put it simply in terms of football betting, Poisson distribution can help you predict how likely each number of goals scored is.<\/p>\n\n
Why is Poisson Distribution Important?<\/h2>\n \n\n\n When bookies set their odds, it is important to know how likely any event is, based on past performance. Bookies do not simply come up with odds out of the blue.<\/strong> They use mathematical models. If you want to take a scientific, mathematical approach to betting<\/strong><\/a>, you should calculate for yourself how likely you think a specific game event, or set of events will be. That is the first step to finding value<\/strong>. If you have found something that is more likely to happen than what the bookies predict, that is what value is.<\/p>\n\n
\n Poisson distribution in betting is particularly relevant for games like football, where scoring happens on an incremental scale. It helps you determine the likelihood of each possible score.<\/p>\n\n
Calculating Football Results<\/h2>\n \n\n
\n The Poisson distribution is commonly used to calculate the likelihood of a specific score in football, as well as a win, lose or draw. You need to first calculate your league\u2019s average goal expectancy<\/strong>, along with the attack strength<\/strong> and defence strength<\/strong> for both sides<\/strong>.<\/p>\n\n
\n How to calculate goal expectancy\n <\/h3>\n \n\n
\n Your team's goal expectancy<\/strong> depends on your team\u2019s attack strength<\/strong> and defence strength<\/strong>, and as well as that of the opposite team.<\/strong><\/p>\n\n
\n In our example, we will use the data from the 2018-2019 English Premier League to calculate a hypothetical match between Manchester City and Liverpool. Manchester is the home team, while Liverpool is the away team.<\/p>\n\n
\n
$\"Poisson$ <\/figure>\n<\/div>\n\n
\n Before calculating these, we need to know:<\/strong><\/p>\n\n
\n
\n
\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
The total home goals scored by all EPL teams<\/p>\n <\/div>\n <\/div>\n <\/li>\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
The total away goals scored by all EPL teams<\/p>\n <\/div>\n <\/div>\n <\/li>\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
The average number of home goals and away goals per match for the whole league<\/p>\n <\/div>\n <\/div>\n <\/li>\n <\/ul>\n <\/div>\n<\/div>\n\n
\n We need to calculate Manchester City\u2019s:<\/strong><\/p>\n\n
\n
\n
\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
Home goal average<\/p>\n <\/div>\n <\/div>\n <\/li>\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
Average goals allowed per home match<\/p>\n <\/div>\n <\/div>\n <\/li>\n <\/ul>\n <\/div>\n<\/div>\n\n
\n We need to calculate Liverpool\u2019s:<\/strong><\/p>\n\n
\n
\n
\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
Away goal average<\/p>\n <\/div>\n <\/div>\n <\/li>\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
Average goals allowed per away match<\/p>\n <\/div>\n <\/div>\n <\/li>\n <\/ul>\n <\/div>\n<\/div>\n\n
\n These stats are easy to find at the Premier League\u2019s official site.<\/a><\/strong><\/p>\n\n
\n Calculating Attack Strength\n <\/h3>\n \n\n
\n With these results, we can easily calculate attack strength for the home and away team. Attack Strength<\/strong> is the team\u2019s average number of goals, divided by the league\u2019s Average number of goals.<\/strong><\/p>\n\n
\n Home\n <\/h4>\n \n\n
\n Manchester City\u2019s Attack Strength:<\/strong> 3.00 \u00f7 1.53 = 1.96<\/p>\n\n
\n Away\n <\/h4>\n \n\n
\n Liverpool\u2019s Attack Strength: <\/strong>1.78 \u00f7 1.147 = 1.55<\/p>\n\n
\n Calculating Defence Strength\n <\/h3>\n \n\n
\n Calculating Defence Strength<\/strong> is just as easy. Simply divide the team\u2019s average number of goals allowed by the league\u2019s average number of goals allowed.<\/strong><\/p>\n\n
\n Manchester City\u2019s Defence Strength: <\/strong>0.63 \u00f7 1.147 = 0.55<\/p>\n\n
\n Away\n <\/h4>\n \n\n
\n Liverpool\u2019s Defence Strength: <\/strong>0.63 \u00f7 1.532 = 0.41<\/p>\n\n
\n Goal expectancy\n <\/h3>\n \n\n
\n Now that we have determined each team\u2019s Attack Strength and Defence Strength, we can calculate each team\u2019s likely score. <\/strong><\/p>\n\n
\n Manchester City goal expectancy\n <\/h4>\n \n\n
\n To determine how many goals Manchester City will likely score, we need to multiply<\/strong> Manchester City\u2019s Attack Strength by <\/strong>Liverpool\u2019s Defence Strength<\/strong> and the league\u2019s average number of home goals. <\/strong><\/p>\n\n
\n That gives us: <\/strong><\/p>\n\n
\n 1.96 \u00d7 0.41 \u00d7 1.532 = 1.23<\/p>\n\n
\n Liverpool goal expectancy\n <\/h4>\n \n\n
\n To determine how many goals Liverpool will likely score, we need to multiply<\/strong> Liverpool\u2019s Attack Strength<\/strong> by Manchester City\u2019s Defence Strength<\/strong> and the league\u2019s average number of away goals.<\/p>\n\n
\n That gives us: <\/strong><\/p>\n\n
\n 1.55 \u00d7 0.55 \u00d7 1.147 = 0.997<\/p>\n\n
\n Average goals scored in the match\n <\/h4>\n \n\n
\n Manchester City:<\/strong> 1.23<\/p>\n\n
\n Liverpool:<\/strong> 0.997<\/p>\n\n
\n Using the Poisson Formula to calculate the likelihood of each possible score\n <\/h3>\n \n\n
\n Now that we have each team\u2019s home and away defence and attack strengths, we can easily use them with the Poisson formula<\/strong> to calculate the probability of any possible outcome<\/strong>.<\/p>\n\n
\n The Poisson Formula\n <\/h4>\n \n\n
\n The Poisson Formula is:<\/p>\n\n
\n P (k events in interval) = <\/strong>(\u03bbk e \u2013\u03bb) \/ k!<\/strong><\/p>\n\n
\n In this formula:<\/strong><\/p>\n\n
\n
\n
\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
P<\/strong> is the probability<\/p>\n <\/div>\n <\/div>\n <\/li>\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
k<\/strong> is the number of occurrences in the interval (number of goals)<\/p>\n <\/div>\n <\/div>\n <\/li>\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
\u03bb <\/strong>is the expected number of goals<\/p>\n <\/div>\n <\/div>\n <\/li>\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
e<\/strong> is Euler's number (e = 2.71828…)<\/p>\n <\/div>\n <\/div>\n <\/li>\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
k!<\/strong> is the factorial of k<\/p>\n <\/div>\n <\/div>\n <\/li>\n <\/ul>\n <\/div>\n<\/div>\n\n
\n Poisson Calculator\n <\/h4>\n \n\n
\n Using this formula, you can calculate the probability for any number of goals<\/strong>. However, there are plenty of online calculators<\/strong><\/a> which will make the job simpler.<\/strong> To use the calculator, fill in each possible score<\/strong> (limit yourself from 1 to 5) separately in the top in \u201cEvent occurrences\u201d<\/strong>, and the expected average goals score per match<\/strong> in the bottom, in \u201cExpected event occurrences\u201d.<\/strong><\/p>\n\n
\n That gives us the following probability for Manchester City Goals:<\/p>\n\n
\n
$\"Manchester$ <\/figure>\n<\/div>\n\n
\n That gives us the following probability for Liverpool City Goals:<\/p>\n\n
\n
$\"Liverpool$ <\/figure>\n<\/div>\n\n
\n Predicting the match outcome based on these probabilities\n <\/h3>\n \n\n
\n To get each possible score, simply multiply the probability of each possible score by each team by the probability of each possible score by the other team. This gives you the following distribution:<\/p>\n\n
\n
$\"Goals\"$ <\/figure>\n<\/div>\n\n
\n As you can see, the most likely score is 1 \u2013 1, or 1 \u2013 0 followed by 0 \u2013 0 or 0 – 1. Given the defence averages of both teams, it is easy to see how these would be very likely scores.<\/p>\n\n
How Bookies Convert Estimated Chance Into Betting Odds<\/h2>\n \n\n
\n Bookies use Poisson distribution to calculate betting odds for outcomes in various markets. You can do the same by converting your calculated probabilities into odds. The calculations are quite simple<\/strong>.<\/p>\n\n
\n
\n
\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
To calculate the chance of a Manchester City win<\/strong>, we add all the red squares <\/strong>from the table above: that gives us an estimated chance of 0.4142, or 41.42%<\/p>\n <\/div>\n <\/div>\n <\/li>\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
To calculate the chance of a Liverpool win<\/strong>, we add all the green squares<\/strong> from the table above: that gives us an estimated chance of 0.29867, or 29.87%<\/p>\n <\/div>\n <\/div>\n <\/li>\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
To calculate the chance of a draw<\/strong>, we add all the yellow squares<\/strong> from the table above: that gives us an estimated chance of 0.286118, or 28.61%<\/p>\n <\/div>\n <\/div>\n <\/li>\n <\/ul>\n <\/div>\n<\/div>\n\n
\n To convert each of these chances into odds, we use the following formula:<\/p>\n\n
\n Odds = 1\/ (probability)<\/em><\/p>\n\n
\n That gives us the following odds:\n <\/h4>\n \n\n
\n
\n
\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
Manchester City win: <\/strong>1\/ (0.4142) = 2.4390<\/p>\n <\/div>\n <\/div>\n <\/li>\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
Liverpool win:<\/strong> 1\/ (0.29867) = 3.3333<\/p>\n <\/div>\n <\/div>\n <\/li>\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
Draw: <\/strong>1\/ (0.286118) = 3.4483<\/p>\n <\/div>\n <\/div>\n <\/li>\n <\/ul>\n <\/div>\n<\/div>\n\n
\n You can convert these to American or fractional odds, but decimals are easier to work with<\/strong>. The calculator on our page about implied probability<\/strong><\/a> should help you do the maths faster.<\/p>\n\n
Advantages of Poisson Distribution in Betting<\/h2>\n \n\n
\n Using Poisson distribution<\/strong> in betting has many advantages<\/strong>. First of all, it helps you understand how odds are set <\/strong>in the first place. By adding up the likelihood of various possibilities, bookies are able to set up relatively accurate odds. You can do the same and compare your result to what the bookies are presenting. Betting lines are not only set by using these equations<\/strong>. Popular matches in particular often see the odds offered (betting lines) change, as more money comes in on a particular outcome.<\/p>\n\n
\n That is one example of how you can use Poisson distribution to beat the bookies<\/strong><\/a>. Comparing your own odds to the ones offered<\/strong> by the bookies is part of a sound betting strategy.<\/p>\n\n
Limitations of Poisson Distribution in Betting<\/h2>\n \n\n
\n Poisson distribution is a mathematical formula that offers estimated probabilities, not certainties<\/strong>. The more data<\/strong> it has to rely on, the more accurate<\/strong> it can get. On the other hand, no squad is the same for each match of the year.<\/p>\n\n
\n A player\u2019s injury or absence can make a huge difference in how the entire squad will perform. At the beginning of the season, most teams also have a different line-up than the year before. This makes setting odds using data from a previous season problematic. Still, that does not necessarily put you at a disadvantage, since the bookies also have fewer data to rely on.<\/p>\n\n
\n As the season goes longer, it becomes easier to predict, since there is more current data available<\/strong>.<\/p>\n\n
How to Create Your Own Poisson Football Spreadsheet<\/h2>\n \n\n
\n It is not so hard to create your own Poisson distribution calculator with Excel<\/strong>; in fact, you do not need to download one<\/strong> from an external site. This step-by-step guide will show you how to make your own.<\/p>\n\n
\n 1. Calculate your team\u2019s expected goals\n <\/h4>\n \n\n
\n First, calculate your team\u2019s expected goals. That is the team's average attack strength \u00d7 the other team\u2019s defence strength \u00d7 average goals per match<\/strong>. Below, we calculated Manchester City\u2019s expected goals at 1.23.<\/p>\n\n
\n Check out: Expected Goals Explained<\/a>.<\/p>\n\n
\n 2. Create the following table in Excel:\n <\/h4>\n \n\n
\n
$\"Manchester$ <\/figure>\n<\/div>\n\n
\n 3. Go to the square next to 0, and right click.\n <\/h4>\n \n\n
\n 4. Click on formulas> Insert Function > Poisson.Dist\n <\/h4>\n \n\n
\n
$\"Poisson.Dist$ <\/figure>\n<\/div>\n\n
\n 5. Fill in:\n <\/h4>\n \n\n
\n
\n
\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
X = B5 (or click on the number next to 0)<\/p>\n <\/div>\n <\/div>\n <\/li>\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
Mean = 1.23 (Your team\u2019s expected goals)<\/p>\n <\/div>\n <\/div>\n <\/li>\n
\n
\n
\n $\"List$ \n <\/div>\n
\n
Cumulative = FALSE<\/p>\n <\/div>\n <\/div>\n <\/li>\n <\/ul>\n <\/div>\n<\/div>\n\n
\n
$\"Cumulative$ <\/figure>\n<\/div>\n\n
\n 6. Move the cursor to the bottom right of C5 and use the plus cursor to drag the formula down.\n <\/h4>\n \n\n
\n
$\"Poisson\"$ <\/figure>\n<\/div>\n\n
\n This gives you the Poisson distribution for 0 to 5 goals of the expected goal average which is 1.23. You can combine the results of your team\u2019s probabilities to get a distribution that looks like this (the same as the above).<\/p>\n\n
\n
$\"Poisson$ <\/figure>\n<\/div>\n\n
TPP Football Stats Centre<\/h2>\n \n\n
\n Here at ThePuntersPage we have a full range of football statistics that you may also like to check out ranging across all the major countries and leagues:<\/p>\n\n
Match Stats<\/h2>\n \n\n
\n
\n $\"\"$ \n Goals<\/span>\n <\/a><\/div>
\n $\"Football$ \n Fouls<\/span>\n <\/a><\/div>
\n $\"\"$ \n Cards<\/span>\n <\/a><\/div>
\n $\"\"$ \n Total Shots<\/span>\n <\/a><\/div><\/div>
\n $\"\"$ \n Assists<\/span>\n <\/a><\/div>
\n $\"\"$ \n Penalties<\/span>\n <\/a><\/div>
\n $\"player$ \n Dribbles<\/span>\n <\/a><\/div>
\n $\"\"$ \n Goal Involvement<\/span>\n <\/a><\/div>
\n $\"\"$ \n Tackles<\/span>\n <\/a><\/div>
\n $\"\"$ \n Shots On Target<\/span>\n <\/a><\/div>
\n $\"player$ \n Clean Sheets<\/span>\n <\/a><\/div>
\n $\"player$ \n Goalkeeping<\/span>\n <\/a><\/div>
\n $\"player$ \n Offsides<\/span>\n <\/a><\/div>
\n $\"player$ \n Passes<\/span>\n <\/a><\/div>
\n $\"player$ \n Woodwork Hits<\/span>\n <\/a><\/div>
\n $\"player$ \n Interceptions<\/span>\n <\/a><\/div>
\n $\"player$ \n Dispossessed<\/span>\n <\/a><\/div>
\n $\"player$ \n Substitutions<\/span>\n <\/a><\/div>
\n $\"player$ \n Own Goals<\/span>\n <\/a><\/div>
\n $\"player$ \n Defending<\/span>\n <\/a><\/div><\/div><\/div>

\n 3. Go to the square next to 0, and right click.\n <\/h4>\n \n\n

TPP Football Stats Centre<\/h2>\n \n\n\n Here at ThePuntersPage we have a full range of football statistics that you may also like to check out ranging across all the major countries and leagues:<\/p>\n\n

TPP Football Stats Centre<\/h2>\n \n\n
\n Here at ThePuntersPage we have a full range of football statistics that you may also like to check out ranging across all the major countries and leagues:<\/p>\n\n