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# Fantasy Football - Maths Coursework - Statistics

Extracts from this document...

Introduction

Statistics Coursework  –  Jackie Webster

Fantasy Football – Maths Coursework – Statistics

My coursework is based on the game ‘Fantasy Football’ which is ran by the British newspaper called ‘The Sun’.

Fantasy Football is a competition based on building your own ‘dream team’ and collecting points to try and have the most points at the end of the season with your team, to win the cash prize. All the players from the English Premiership are used and a scoring system is used to see how well the players are doing and who has picked the best eleven players for their team. You are allowed to create your own team consisting of 1 goalkeeper, 4 defenders, 3 midfielders, 2 attackers and a ‘sub’ which must be either an attacker or midfielder. All the players are valued depending on how well they play and the number of points they have from last season. Competitors have a total of £40million ‘money’ to spend on their players. A scoring system is used and players can both gain and loose points. The points for all the players on your team are added up at the end of the season and the competitor who has the team with the most points wins.

I am going to find out how to pick the top-scoring team and I will do this by using last year’s scores. I will use the 2003 scores as they were at the end of the season. I will not be including goalkeepers in my investigation because they have a different scoring system to defenders, midfielders and attackers. To do this I will use two hypotheses:

Hypothesis 1

I think that attackers achieve more points than midfielders and defenders.

Hypothesis 2:

Middle

5

28

120 ≤ P < 150

|

1

29

150 ≤ P < 180

0

29

180 ≤ P < 210

|

1

30

210 ≤ P < 140

0

30

240 < P < 270

0

30

Defenders:

 Points Tally Frequency Cumulative Frequency 0 ≤ P < 30 |||| 4 4 30 ≤ P < 60 |||| 4 8 60 ≤ P < 90 ||| 3 11 90 ≤ P < 120 |||| 5 16 120 ≤ P < 150 |||| 5 21 150 ≤ P < 180 |||| 5 26 180 ≤ P < 210 | 1 27 210 ≤ P < 140 | 1 28 240 < P < 270 || 2 30 Points Tally Frequency Cumulative Frequency 0 ≤ P < 30 || 2 2 30 ≤ P < 60 ||||  |||| 9 11 60 ≤ P < 90 ||||  |||| 9 20 90 ≤ P < 120 ||||  | 6 26 120 ≤ P < 150 | 1 27 150 ≤ P < 180 ||| 3 30

Interpretation:

From my box plots I can see the following:

Attackers: There is a negative skew, which means that there are a higher number of high scores than low scores. It also has the highest median which means that the points are generally higher than midfielders and defenders. Attackers have the biggest range which means that the points are less consistent and that there is a wide range of high and low scores. However this means that attackers are unpredictable as to whether they will score very high, or very low.

Midfielders: The median is in the middle of the box, which makes this box plot symmetrical, which means that there are as many high points as low points. The median is the lowest which means that there are more low points than high points.

Defenders:  This is a positive skew which means that there are more lower scores than high scores. Defenders have the lowest range which means that the scores are all consistently low.

From my cumulative frequency graph I can see that attackers have more points than defenders and midfielders. The curve finishes further along the x axis, which means that attackers have more points.

I also found out the standard deviation for Attackers, Midfielders and Defenders to see if there were any outliers, and to see how many players had points close to the mean in their group.

Conclusion

The only problem that I encountered in the investigation was handling the data. This was because there was such a large amount of data, and different data was used in hypothesis 1 to hypothesis 2. However this problem was soon solved when I got used to using the data and organised it successfully.

In hypothesis 1 we grouped the data to make it easier to work with and to put into a cumulative frequency graph. However this changed the accuracy of the data. A problem with Spearman’s Rank was having tied ranks when ranking the points or other rating. This was easily solved by finding the mean of the rank number and using this instead.

The investigation had limitations. We could not use goalkeepers because of the different scoring system, so we could not use them in our investigation and therefore could not effectively predict a complete winning team. We also had to work with last years data, and some players such as Wayne Rooney have increased their performance dramatically since last year, just as some players have decreased their performance dramatically, perhaps through injury or lack of training. The last limitation was the fact that we only used premiership players and not players from any other divisions.

If I had the chance I would extend my investigation to cover goalkeepers. I would also use more recent and accurate data to try and pick an actual fantasy football team. It would then be interesting to actually take part in the fantasy football game and see how well my team would score.

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

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