Statistică în fotbal

Introduction

The penalty shootout has been in the game of football since the sport has existed. It is used to decide a winner when the scores are tied at the end of regulation time or it is considered a free kick when a handball or a foul is made inside the box. Though it is often criticized, nobody can come up with a better alternative. The penalty kicks in football inspired many other versions of it in many other sports, like ice hockey or handball. By studying past penalty shootouts, a person can figure out where is the most successful spot to place a kick and where the goalkeeper will most likely dive.

Study Aim

For my Internal Assessment, I will be studying penalty kicks in football. I will specifically be looking at success percentage in nine different areas of the goal, middle, top middle, bottom middle, left middle, bottom left, top left, middle right, top right, and bottom right. The area of math that this topic is placed into is probability and statistics. I have been playing football since the age of 5 years old being mostly goal keeper. I chose this topic because I believe that if I learn where the highest probability of scoring a penalty kick is then I will be able to apply it to myself and improve as a player and even to help other players improve their skills through a mathematical exploration.

Reasearch Questions

1.

2. Which area of the post ensures a higher rate of scored goals in penalties?

3. Which cell should the goal keeper dive into in order to maximize his chances of catching the ball?

4. How do my results compare with the Telegraph study (cell-wise)?

Assumptions

Wind speed not taken into account

Air resistance not taken into account

Penalty trajectory is a parabola

No tricks

No crowd pressure, coach pressure

Reasearch Methodology

I have collected my data about penalty kicks through a realistic football game, FIFA 17. I have selected 2 players, one left-footed and one right-footed - both midfielders with an average rating (i.e. 82-84 %, best player having a 94 % rating). The players are called Player X and Player Y. Using a simulation module of FIFA 17, I have kicked 100 penalties for each player, using the same goal keeper for both players