This presentation explains how a stats concept as simple as Poisson Distribution can help us predict stuff based on previous records. This shows interesting application of statistics, the subject which otherwise seems boring to a lot of students. CONTENTS Poisson Distribution Basic Example Calculation Analysis Limitations Better Version? References

1. Using Statistics to
Predict Scores in
Football
Shakeeb Ahmad
VITP U N E

2. Poisson Distribution
• Probability of a given number of events occurring in a fixed interval of
time or space
• Examples that may follow a Poisson distribution:
1. Number of phone calls received by a call center per hour
2. Number of pieces of mail received in a day

3. Basic Example
• Ugarte and colleagues report that the average number of goals in a
World Cup soccer match is approximately 2.5
• Is Poisson model appropriate?

4. Calculations
• Because the average event rate is 2.5 goals
per match, λ = 2.5.

5. Analysis
k P(k goals in a World Cup soccer match) Probability in %
0 0.082 8.2 %
1 0.205 20.5 %
2 0.257 25.7 %
3 0.213 21.3 %
4 0.133 13.3 %
5 0.067 06.7 %
6 0.028 02.8 %
7 0.010 1 %
Probability for 0 to 7 goals in a match

6. Limitations
• If the data is too long the data would be irrelevant, and if it’s short,
outliers might skew the data.
• Doesn’t consider external factors like
• Transfers, coach change
• Home and away from ground
• Weather
• Chance vs Skill
• Skill rather than chance dominates the game.
• Missed scoring opportunities, dubious offside decisions and shots hitting the
crossbar can obviously drastically affect the result

7. Better version?
• To make the results better, Maher[1] has used Bivariate Poisson
distribution.
• Bivariate Poisson distribution X 1 , X 2
• takes three independent Poisson distributions Y 1 , Y 2 , Y 3
• with means λ1 , λ2 , λ3

8. References
1. Modelling Association Football Scores by M. J. Maher
[Link]
2. Using Statistics to Predict Scores in English Premier
League Soccer by John S. Croucher [Link]
3. How Football Betting Odds Work Using Poisson
Distribution by Arpit Mishra [Link]
4. Statistical Association Football Predictions [Link]

9. THANK YOU