ib math sl internal assessment

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IB Math SL Internal Assessment: What is the relationship between the direction of a penalty kick and success rate?

By: Sam Borgel 1/20/14 Mrs. Wicks

What is the relationship between the direction of a penalty kick and success rate? Introduction: The penalty shootout has been in the game of soccer since the sport has existed. It is the means of deciding a winner when the scores are tied at the end of regulation time. Though it is often criticized, nobody can come up with anything better. So, it will be around for years to come. By studying penalty shootouts, a person can figure out where the best spot to place a kick is and where the goalkeeper will most likely dive. Purpose: For my Internal Assessment topic I will be studying penalty kicks in soccer. I will specifically be looking at success percentage in nine different areas of the goal, middle, top middle, bottom middle, left middle, top left, bottom left, middle right, top right, and bottom right. The area of math that this topic is placed into is probability and statistics. I choose 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.

Data: Penalty Shots Taken Made

131

Saved

59

Total

190

This data shows the total number of penalty shots taken, and out of those how many were made and how many were missed.

Top

Middle

Bottom

Top

Left

Left

Left

Middle

Made

18

18

30

10

Saved

4

6

19

Total

22

24

49

Middle

Bottom

Top

Middle

Bottom

Middle

Right

Right

Right

5

3

3

16

28

1

0

7

2

3

17

11

5

10

5

19

45

This data shows the positioning of the data, the total number of shots aimed in a certain position, how many were made, and how many shots were saved.

Graphs:

Top Left 18%

Made 82%

Saved

This data shows the percentage values from the penalty shots aimed at the top left of the goal. Out of the twenty-two shots taken at the top left, 82% of them were successful, and 18% of them were unsuccessful.

Middle Left

25%

Made 75%

Saved

This data shows the percentage values from the penalty shots aimed at the middle left of the goal. Out of the twenty-four shots taken at the middle left, 75% of them were successful, and 25% of them were unsuccessful.

Bottom Left

39% 61%

Made Saved

This data shows the percentage values from the penalty shots aimed at the bottom left of the goal. Out of the forty-nine shots taken at the bottom left, 61% of them were successful, and 33% of them were unsuccessful.

Top Middle 9%

Made 91%

Saved

This data shows the percentage values from the penalty shots aimed at the top middle of the goal. Out of the eleven shots taken at the top middle, 91% of them were successful, and 9% of them were unsuccessful.

Middle 0%

Made Saved 100%

This data shows the percentage values from the penalty shots aimed at the middle of the goal. Out of the five shots taken at the middle, 100% of them were successful, and 0% of them were unsuccessful.

Bottom Middle

30%

70%

Made Saved

This data shows the percentage values f