Sports betting using the Poisson probability distribution.

The basis of my system is a Probability Distribution, which can be used to determine the probability of the outcomes of a random experiment (Poisson Distribution). This sounds complicated at first, but I’ll give you a simple example.

A post office is entered by an average of 20 people per hour. With the help of the Poisson distribution, we can now predict the probability of none, one, 20 or 30 people entering the post office. In football we have similar conditions. A game lasts 90 minutes. On average, the home team scores x goals and the away team y goals.

Using the Poisson method, we can now determine the probability of scoring less than 3 goals (Under 2.5) and compare it with the bookmaker’s probability

The whole thing then looks practically like this: The results that let us win an Under 2.5 goals bet:

 – 0-0: =((x^0/FAULT(0))*EXP(-x))*((y^0/FAULT(0)*EXP(-y)))
 – 1-1: =((x^1/FACULT(1))*EXP(-x))*((y^1/FACULT(1)*EXP(-y)))
 – 1-0: =((x^1/FAACULT(1))*EXP(-x))*((y^0/FAACULT(0)*EXP(-y)))
 – 0-1: =((x^0/FACULT(0))*EXP(-x))*((y^1/FACULT(1)*EXP(-y)))
 – 2-0: =((x^2/FACULT(2))*EXP(-x))*((y^0/FACULT(0)*EXP(-y)))
 – 0-2: =((x^0/FACULT(0))*EXP(-x))*((y^2/FACULT(2)*EXP(-y)))

Don’t be alarmed! I have prescribed the formulae for each outcome. That way, if you want to try my betting strategy, you can just copy the formulas into Excel. x represents the average number of goals scored by the home team (per match) and y represents the average number of goals scored by the away team (per match).

Let’s look at the example: Bayern – Dortmund
We determine the number of goals for Bayern’s last 6 home games: 11 goals.
We then divide this number by 6: 11/6=1.83
That would be our x

Then we find the number of goals for Dortmund’s last 6 away games: 12 goals
Divided by 6 that makes: 12/6=2
That is our y

We now put x and y into the formulas above and get

 – 0-0: 0,022 = 2,2%
 – 1-1: 0.079 = 7.9%
 – 1-0: 0.04 = 4%
 – 0-1: 0.043 = 4.3%
 – 2-0: 0.036 = 3.6%
 – 0-2: 0.043 =4.3%

The probability of scoring less than 3 goals in the match is therefore: 2.2+7.9+4+4.3+3.6+4.3= 26.3%.

The probability for more than 2.5 goals is therefore: 100%-26.3%=72.7%

If the bookmaker gives us odds of 1.5 for over 2.5, we can check whether the bet is “worth it”:
1/1,5 = 0,67 = 67%
72,7% ☻ 67%

So we have a Valuewager!!

Expansion:

To ensure an even more accurate value for the average number of goals scored by the home team, it is useful to take into account how many goals the away team concedes per game. Or, to ensure an even more accurate value for the average number of goals scored by the away team, it should be taken into account how many goals the home team concedes per match.

Let’s look again at the fictitious example Bayern vs. Dortmund:

To get an accurate value for Bayern’s average number of goals per game take Bayern’s last 6 home games and Dortmund’s last 6 away games.

Example Bayern has scored 11 times in their last 6 home matches. Dortmund has conceded 5 goals in the last 6 away games. Then the average value for Bayern goals per game is:
(11+5)/12=1,33
This is our new exact x.

To determine the value for Dortmund’s away goals, we proceed accordingly: Dortmund have scored 12 times in their last 6 away games and Bayern have conceded 5 goals at home in their last 6 games:
(12+5)/12=1,42
This is our new exact y.

Finally, the excel formulas for Under 3.5 and Under 1.5:

Formulas for Under 1.5:

 – 0-0: =((x^0/FACULT(0))*EXP(-x))*((y^0/FACULT(0)*EXP(-y)))
 – 0-1: =((x^0/FACULT(0))*EXP(-x))*((y^1/FACULT(1)*EXP(-y)))
 – 1-0: =((x^1/FAACULT(1))*EXP(-x))*((y^0/FAACULT(0)*EXP(-y)))

Formulas for sub 3.5:

 – 3-0: =((x^3/FAULT(3))*EXP(-x))*((y^0/FAULT(0)*EXP(-y)))
 – 0-3: =((x^0/FACULT(0))*EXP(-x))*((y^3/FACULT(3)*EXP(-y)))
 – 2-1; =((x^2/FACULT(2))*EXP(-x))*((y^1/FACULT(1)*EXP(-y)))
 – 0-0: =((x^0/FACULT(0))*EXP(-x))*((y^0/FACULT(0)*EXP(-y)))
 – 1-1: =((x^1/FACULT(1))*EXP(-x))*((y^1/FACULT(1)*EXP(-y)))
 – 1-0: =((x^1/FAACULT(1))*EXP(-x))*((y^0/FAACULT(0)*EXP(-y)))
 – 0-1: =((x^0/FACULT(0))*EXP(-x))*((y^1/FACULT(1)*EXP(-y)))
 – 2-0: =((x^2/FACULT(2))*EXP(-x))*((y^0/FACULT(0)*EXP(-y)))
 – 0-2: =((x^0/FACULT(0))*EXP(-x))*((y^2/FACULT(2)*EXP(-y)))
 – 1-2: =((x^1/FACULT(1))*EXP(-x))*((y^2/FACULT(2)*EXP(-y)))

The whole procedure needs some work, of course, but if you copy out the formulas and process them with Excel, the effort is manageable.