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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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