Poisson distribution

Poisson distribution is a foreign term to many new bettors, and something that even many professional bettors may not utilise. Poisson distribution is, in short, a statistical technique that should help you bet more accurately on the outcome of sporting events. Poisson distribution is a model that considers the amount of times something has occurred over a specified period of time, and offers a probability for the likelihood of that happening again. The most common application of poisson distribution is to create models for football bets, commonly known as expected goals, to determine the probability of goals in a football match. You can also use poisson distribution to inform your own betting odds. Statistics such as shots on target, off target, conversion rate and areas from which shots were taken help to determine future probability.

Pros & Cons

  • Pro - Using poisson distribution can help a bettor create models that really improve their win percentage.
  • Pro - The amount of research and preparation that goes in to using such a method provides a deeper education on sports betting that looking at form tables and highlights cannot provide.
  • Con - Poisson distribution application can be incredibly time consuming, and not everyone will have the time to fit this in alongside day to day life.
  • Con - It’s a case of trial and error. Only through trial and error will you work out what is and isn’t valuable and you may well make mistakes and losses as part of the learning process.

Focusing on football, the data used to create expected goal probability comes from statistics that reflected how many shots on and off target teams have produced, how many of their chances they convert, etc.

Some models also consider where on the pitch a team are taking shots from, with closer and more central shots having more value towards an expected goals total. Naturally you may expect a six yard side foot or a penalty to have a much better chance of going in than a 30 yard screamer from near the touchline. Each shot will be assigned a value that contributes part of one goal.

How does this help you predict future performances? Unfortunately, there’s no way of being entirely accurate. There will also be anomalies, but by assessing a good sample number of past performances, you can develop a good idea of patterns that may reveal future probabilities.

If a team has taken more shots that anyone else from inside the eighteen yard box over the past 20 games, that’s no coincidence. Shot data and shot type reveals a lot about the style of a team's attacking play.

The strength of a side's defensive play is also important of course. There’s a major flaw in knowing a side is expected to score three goals if you’re unaware they’re expected to concede just as many. The defensive values and attacking values come together to offer a predicted correct score. With this score you can identify relevant betting markets.

Just because the model suggests a team will win 2-1, it isn’t gospel. As accurate as that may be in perfect circumstances, models may not know the importance of absent players, weather, or situational circumstances such as a game being a local derby. Factoring in your own opinion and knowledge is also key.

Below are the steps you’ll need to take to utilise poisson distribution on a more basic level. Not everyone has the time to collate shot data, so there is a model you can create without this data…

Step One 

You’ll need base numbers for each team in the league that reflect their attacking and defensive strength. The nice thing about basic poisson distribution is you can it by hand, spreadsheet or just in a table on Word. The choice is yours. But you will need to update the numbers each week, so knowledge of a spreadsheet would make the process easier and more efficient.  

Your base numbers will be the numbers of goals every team has scored and conceded during your sample size. It may be 20, 30, 50 games, or just the season so far. Sample size is important but it depends on your personal opinion and time constraints.

Step Two

Here’s what we do with our base numbers. We know how many goals each team has scored and conceded so far this season. Make sure you also have the breakdown of goals scored at home and goals scored away.

We want to work out the average number of goals scored at home and away. So, take the total number of goals scored home/away and divide each by the number of goals played. Let’s use the Football League as an example, where 46 games are played.

The team in focus scored 49 goals at home and 36 away. Below are the example equations of what we must do with each team's goal output to find their home and away average.

Goals scored at home (49) / Games played at home (23) = Average Home Goals (2.13)

Goals scored away (36) / Games played away (23) = Average away goals (1.56)

Step Three

Our team averaged 2.13 goals per game at home and 1.56 goals per game away from home. Offensively, we’d say that’s a pretty good output. But that’s not of much use if we fail to recognise they could be conceding a lot or keeping clean sheets regularly. We also need to know their defensive capabilities.

The same theory applies with identifying defensive averages. We want to know how many goals a team has allowed home or away. Our team has allowed 23 goals at home and just 17 away from home.

Goals allowed at home (23) / Games played at home (23) = Average Home Goals (1.00)

Goals allowed away (17) / Games played away (23) = Average away goals (0.73)

Step Four

Before you move on to calculating the expected goals output or looking at individual games, it’s a good idea to understand where each team ranks in relation to league averages. League averages can be found by adding averages of each team together and dividing by the number of teams in the league. That will be your focal point with teams ranking either above or below the league average.

Step Five - Maths and Formulas

Now we’ve come as far as predicting a goals output for two teams in a game. Our example team, Team A, are hosting Team B. We need to know how Team A perform at home and how Team B perform away from home.

To work out the attacking strength of a team, we start with our average goals at home. Team A scored an average of 2.13 goals per game at home. We then divide this number by the average number of goals scored by all home teams that season (remember the focal point we mentioned?) Let’s say the average is 1.55.

Team A’s Goals per home game (2.13) / League average home goals (1.55) = 1.37

Team A’s attacking strength is 1.37

We also want to know how strong Team B is defensively. We will be using example numbers here for Team B, but we’ve already demonstrated above how to determine a team's goals output or goals against ratio for home and away games above.

Our Team B has averaged 1.10 goals away from home, whilst the league average is 1.61.

Team B’s Goals against per away game (1.10) / Average away goals allowed (1.61) = 0.68

Team B’s defensive strength is 0.68

You might expect you’d need a higher number to reflect strength, but you’ll see in the next sum why that 0.68 number is very useful to identifying their defensive strength. The following formula allows you to calculate the home team, Team A, expected goal output for this game.

Team A attack strength (Home) x Team B defence strength (Away) x Home goals average

1.37 x 0.68 x 1.55 = 1.44

The home side are expected to score 1.44 goals on average. We would then apply the same process to the away side to determine their attacking strength. Using the same method as above, we discover that the away side, Team B, have averaged 0.98 goals per away game. We also work out the home side's defensive strength is 0.75. The league average of away goals is 1.18.

0.98 x 0.75 x 1.18 = 0.86

The away side are expected to score 0.86 goals on average. The predicted outcome we have is Team A 1.44, Team B 0.86. That shows us that Team A are almost nailed on to score a goal in nearly every game, Team B could fail to score often, and there is a predicted 0.58 goals between the team.

One of the issues with some of the data the method puts out is that it is nothing more than averages. Averages aren’t necessarily what will occur every game, as several lopsided scores could balance out several low scoring games. So how do we deal with that?

Step Six - Correct Score probabilities

You can use the data you get to predict the likelihood of the most probable correct scores. You can do this yourself, but it’s already a long enough process. Using a simple online calculator will give you the probability for each correct score.

The data you need to input is the number of outcomes you are considering (let’s say we are working up to four goals) and the expected event occurrences, which is the team's attacking strength.

 

Goals

0

1

2

3

4

Team A

23.69%

34.81%

23.84%

10.88%

3.70%

Team B

42.31%

36.39%

15.64%

4.48%

0.009%

Each number is a separate value, so by taking the most probable goal output for each teams, you can pick out the two standout most likely scores as…

Team A 1 (34.81%) - Team B 0 (42.31%)

Team A 1 (34.81%) - Team B 1 (36.39%)

Step Seven - Find the exact probability

That highlights the most likely correct scores, but it fails to show you the exact probability of them. By multiplying the two percentages together (expressed as decimals) you can find the exact probability if that correct score.

For 1-0, it’s 34.81% vs 42.31%. As a decimal sum, that’s 0.3481 x 0.4231 = 0.1472. You convert any decimal to a percentage simply by shifting the decimal point two places to the right, so 0.1472 is 14.72%. The same method is used to determine the likelihood of a 1-1 draw, which is 12.66%.

Piecing it all together…

You can use your most probable outcomes to play the percentages and identifying asian handicap, match and total goals betting market. You can also pit your probability against the best bookmakers probability by converting best odds to implied probability, or your implied probability to betting odds. There are many simple calculators online that will allow you to do this. Online betting odds conversion calculators will give you an implied probability percentage when your enter decimal betting odds and vice versa.

We established that a 1-0 home win is deemed mathematically to be outcome14.72% of the time. You can also work out the probability of 2-0, 2-1, 3-0, 3-1, 3-2 and so one. Add together the probability for each score in favour of the home team, the away team, or the draw. Each will give you a percentage.

Let’s say the total home outcomes added together equal 51%. 51% implied probability converted to decimal odds is 1.96. You can also convert a percentage to decimal odds for the away win and also a draw. Once you have your own betting odds, you can compare them to the bookmakers.

Doing this will help you identify value when sports betting, which you can read all about here.

There’s no reason why a casual bettor couldn’t use poisson distribution, but the simple fact is that it takes a lot of time and a solid understand of the maths behind it. It’s not a straightforward method, and so it’s mainly professional bettors who use it due to having fewer time constraints in their lives. Even then, it’s not for everyone.

So poisson distribution is deemed the most accurate way of identifying scores of a match, and therefore helping bettors to be able to place relevant football bets relating to the full time score, match result and goals betting market. It helps to provide a much deeper insight than just assessing a team will beat another team based on their form, and helps bettors work towards understanding the true meaning of value also. If you have the time to play around with this method, then do so. It may take a lot of education in excel and other supporting tools and methods along the way, but it’ll go a long way to improving the way bettors look at the game in a statistical and mathematical sense, and it should certainly improve the win percentage for any bettor. You will essentially get out of this betting strategy what you put into it.