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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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