QM_Project_Report.docx

7/27/2019 QM_Project_Report.docx

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Quantitative MethodProject Correlation

Analysis: Corners

won and goals scored

Submitted By:

Nikhil Sasi : PGP/16/095

Rejin Johny : PGP/16/103

Saprem Dalal : PGP/16/106

Vishwas Anand : PGP/16/118

Sruthy S :PGP

/16/113Arjun Menon : PGP/16/072

Nishant S : PGP/16/096

Arnab Kumar Saha : PGP/16/073


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ContentsPurpose and reason for choosing the project: ............................................................................................. 2

SCOPE OF WORK ........................................................................................................................................... 3

Analysis and Observation: ............................................................................................................................. 4

Correlation: ............................................................................................................................................... 4

Test for significance of correlation: .............................................................................................................. 5

A: Premier League 2011-12 ....................................................................................................................... 5

Correlation for the goal difference and corner difference ................................................................... 5

Correlation for the Home goals and Home corners .............................................................................. 6

Correlation for the Away goals and Away corners ............................................................................... 7

B: La Liga 2011-12 ..................................................................................................................................... 8

Correlation for the goal difference and corner difference ................................................................... 8

Correlation for the Home goals and Home corners .............................................................................. 9

Correlation for the Away goals and Away corners ............................................................................. 10

Chi Square Test: .......................................................................................................................................... 11

A. Premier League: .................................................................................................................................. 11

Hypothesis: ......................................................................................................................................... 12

Decision: .............................................................................................................................................. 12

B. Spanish League: .................................................................................................................................. 12

Hypothesis: ......................................................................................................................................... 13

Decision: .............................................................................................................................................. 13

Conclusions: ................................................................................................................................................ 14

Bibliography ................................................................................................................................................ 15


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Purpose and reason for choosing the project:

We had decided to do a project related to Sports statistics. Football is a sport that is very much

dependent on statistics and statistical analysis. Top football teams around the globe rely on

rigorous statistical analysis to give themselves a competitive edge over their rivals. Keeping thatin mind, we decided to do our quantitative management project for the first term in the field of

football statistics.


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SCOPE OF WORK

One of the constant features of all football match statistic is the Corner Kicks count, the

number of corner kicks that has been awarded to each of the teams. A team is awarded a

corner kick when the ball goes over the goal line outside of the goal and it is last played by thedefense. The corners (for and against) statistic finds its way to most football match reports on

the widespread belief that a greater number of corners statistic is a measure of greater

attacking intent of the team and therefore the team that has a higher corner count has a better

chance of winning the match and a higher chance of scoring goals .

We chose to explore the relevance of this assumption based on the evidence from the last

season in the English (Premier league) and Spanish league (La Liga). A total of 20 teams

compete against each other twice over the course of each season giving us a sample of 380

matches each to draw our conclusion. We have chosen the English and the Spanish leaguesbecause of the distinctive style of the game in the mentioned league. We wanted to further

explore if the statistics would be dependent on the style of play as well.


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Analysis and Observation:

For all the matches played we took a sample of both the corners won and the goals scored for

both the home as well as the away teams.

First we tried to find the percentage of matches where teams that had greater number of

corners have gone on to win the match. Based on evidence of season 2011-12, we got thefollowing results for both the leagues for the team that won the maximum number of corners.

Number of matches won: 274

Total number of matches: 380

Percentage of matches won: 72.11

Correlation:

Next, we tried to find if any correlation exists between the following,

1. No of goals scored and number of corners won by the home team2. No of goals scored and number of corners won by the away team3. The goal difference and the corner difference

And the below are the results for the correlation coefficients that we observed.

English League 2011-2012:

Data Correlation

Away Goals and Away Corners 0.03475

Home Goals and Home Corners 0.08298

Goal Difference and Corner Difference 0.13818

Spanish League 2011-2012:

Data Correlation

Away Goals and Away Corners 0.04321

Home Goals and Home Corners 0.03547Goal Difference and Corner Difference 0.11229


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Test for significance of correlation:

A: Premier League 2011-12

Correlation for the goal difference and corner difference

The value of correlation coefficient = 0.13818

Number of samples, n = 380

Degree of freedom, n-2 = 378

Step 1:

Parameter of interest is , the population correlation coefficient

Step 2:

H0 : =0

Step 3:

H1: !=0

Step 4:

= 0.05, degree of freedom = 378

Step5:

Test Statistic t = r (n-2/1-r2)0.5

Where r = correlation coefficient

Step 6:

Reject H0 if t > 1.960 or t 1.960, we reject the null hypothesis H0 : =0 and conclude that there exist a

correlation between the sample and the original population .


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Correlation for the Home goals and Home corners




Step 1:


Step 2:

H0 : =0

Step 3:H1 : !=0

Step 4:

= 0.05, degree of freedom = 378

Step5:



Step 6:

Reject H0 if t > 1.960 or t


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Correlation for the Away goals and Away corners




Step 1:


Step 2:

H0 : =0

Step 3:H1 : !=0

Step 4:

= 0.05, dof = 378

Step5:



Step 6:



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B: La Liga 2011-12

Correlation for the goal difference and corner difference




Step 1:


Step 2:H0 : =0

Step 3:

H1 : !=0

Step 4:

= 0.05, dof = 378

Step5:Test Statistic t = r (n-2/1-r

2)0.5


Step 6:

Reject H0 if t > 1.960 or t 1.960, we reject the null hypothesis H0 : =0 and conclude that there exist a

correlation between the sample and the original population .


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Correlation for the Home goals and Home corners




Step 1:


Step 2:

H0 : =0

Step 3:

H1 : !=0

Step 4:

= 0.05, dof = 378

Step5:

Test Statistic t = r (n-2/1-r2

)0.5


Step 6:



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Correlation for the Away goals and Away corners




Step 1:


Step 2:

H0 : =0

Step 3:H1 : !=0

Step 4:

= 0.05, dof = 378

Step5:



Step 6:



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Chi Square Test:

Chi Square test is done to as to test whether the Goals Scored and Corners won for a team is

dependent on whether the match is played at Home or Away.

A. Premier League:

The below table below shows the observed values

Home Away Total

Goals 604 457 1061

Corners 2445 1877 4322Total 3049 2334 5383

The expected values are shown below,

Home Away Total

Goals 600.964 460.036 1061

Corners 2448.036 1873.964 4322

Total 3049 2334 5383


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Chi Square test for the data,

Observed Expected O-E [(O-E)^2] / E

604 600.964 3.036039 0.015337917

457 442.4135 14.58654 0.480923667

2445 2401.413 43.58654 0.79111172

1877 1748.587 128.4135 9.430483846

Chi

square10.71785715

Hypothesis:

Ho: Total number of goals and corners scored is independent of where the match is played

H1: Total number of goals and corners scored is not independent of where the match is played

Decision:

Reject Ho if chisquare calculated chi square (=0.05,=1)

Calculated chisquare, 20 = 10.71785715

Threshold 2 = 3.481

Since, 20 > 2, We reject the null hypothesis that number of goals and corners scored is

independent of where the match is played and conclude that the number of goals and corners are not

independent on whether the match is played at Home or Away in the English Premier league .

B. Spanish League:

The below table below shows the observed values

Home Away Total

Goals 638 412 1050

Corners 2371 1779 4150

Total 3009 2191 5200


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The expected values are shown below,

Home Away Total

Goals 607.5865 442.4135 1050

Corners 2401.413 1748.587 4150

Total 3009 2191 5200

Chi Square test for the data,

Observed Expected O-E [(O-E)^2] / E

638 607.5865 30.41346 1.522381725

412 442.4135 -30.4135 2.090756098

2371 2401.413 -30.4135 0.385180918

1779 1748.587 30.41346 0.528986483

Chi

square4.527305225

Hypothesis:

Ho: Total number of goals and corners scored is independent of where the match is played

H1: Total number of goals and corners scored is not independent of where the match is played

Decision:

Reject Ho if chisquare calculated chi square (=0.05,=1)

Calculated chisquare, 20 = 4.527305225

Threshold 2 = 3.481

Since, 20 > 2, We reject the null hypothesis that number of goals and corners scored is

independent of where the match is played and conclude that the number of goals and corners is not

independent on whether the match is played at Home or Away in the Spanish league .


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Conclusions:

From our study we conclude the following.

1. Team that wins the majority of the corners wins majority of the matches2. There is only a weak correlation between the Goal difference and Corner difference3. Both the number of goals as well as the number of corners depends on where the match is

played and the number is observed to be significantly higher for the home team

4. There are no significant differences in the correlation data for the English and the Spanishleagues, even though the number of corners is higher in the English league.


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Bibliography

Applied Statistics in Business and Economics http://soccernet.espn.go.com/results/_/league/eng.1/english-premier-league?cc=4716 http://soccernet.espn.go.com/fixtures/_/league/esp.1/spanish-la-liga?cc=4716
http://soccernet.espn.go.com/results/_/league/eng.1/english-premier-league?cc=4716http://soccernet.espn.go.com/results/_/league/eng.1/english-premier-league?cc=4716

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QM_Project_Report.docx