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Developing a basic poisson distribution model

Step One - Gathering Data

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 💻 - Starting Your Model

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 - Expanding Your

Dataset

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 -

Including Averages

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%.

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