Analysis of Salary of Formula 1 Driver and Pitstop Analysis

8/10/2019 Analysis of Salary of Formula 1 Driver and Pitstop Analysis

1/15

1

AAnnaallyyssiissooffSSaallaarryyOOff

FFoorrmmuullaa11DDrriivveerr&&EEffffeeccttOOffPPiittssttooppOOvveerrDDrriivveerr

PPeerrffoorrmmaannccee

IE:6210 Project Report

Submitted to : Submitted By:

Gary Wasserman, PhD Muhash Sanjofy (FK0181)


2/15

2

Satyam Quamara (FK0785)

Shreyash Poojari (FK0605)

Ashish Shadija (FJ9668)


3/15

3

Content

Introduction

Part 1 Problem Statement

Data

Regression Analysis

o Matrix Plot

o Best Subset Regression

o Stepwise Regression Model

o Backward Stepwise Regression

o Regression Model on Career Average Point and Popularity

Conclusion

Part 2 Problem Statement

Data

Data Analysis using Minitab

o Probability Plot

o Model Accuracy Check

o Regression Analysis Finishing Time versus Pit Stop

Conclusion

References


4/15

4

Introduction

Formula 1 racing is a million dollar industry and drivers are also paid heavily. Teams are

willing to pay high amounts to the drivers. There are definitely many factors that will influence

the teams decision to pay a driver his salary. In this project, In view of exploring the application

of engineering statistics we want to identify the factors that could play a key role in deciding

the drivers salary.

Moreover it's a myth that pitstop timing of a driver is an important factor that

will affect the probability of the driver winning the race. We would like to put this myth to a

test using regression to verify if that is really the case in part 2 of the project.

Part 1 Problem Statement:

The analysis for the factors deciding the drivers salary called for looking at potential variables

that might be important to consider. Researching for such factors and considering the recent

Formula1 season of 2013 we were able to highlight the following:

Score in 2013 : Every podium finish in a race, gets the driver 25 points and goes on

reducing as his finishing position goes down. This variable could be one of the important

factors for grading the drivers potential that will probably have a direct effect on thedrivers salary.

Age: We personally think that age of a driver can also play a crucial role in deciding his

salary. The younger the driver is, he has more chance of having good salary because of

his much better physical and mental Agility. Or it can be also possible that driver with

above average age can also be paid more due to his experience.

Average Career Point: The ratio of total no of win to the number of races participated in

throughout his Formula1 career. It is a clear indicator of how the drivers performance

has been so far and what can be expected from him in the future.

Average Pole Position: Average pole position or better defined as the ratio of poleposition achieved by the driver throughout his career to the number of races

participated in so far. As a head start or being first in the racing grid to start is an

advantage that will increase the possibility of the driver to win the race or indirectly the

driver has proven his potential by achieving a pole position.

Popularity: A driver represents his sponsors. The more the driver is popular the more

the brand is publicized and this could be one of the factors where the driver deserves to


5/15


6/15

6

Regression Analysis

It can be seen from the box plot that the career average point (car point) and popularity does

have some significance as a factor that can be considered over deciding the drivers salary .

Score 1Avg Pole PositionSalarypopularitycar pointage

40

30

20

10

0

Data

Boxplot of age, car point, popularity, Salary, Avg Pole Pos, Score 1

Most of the data are normally distributed though they are slightly distributed with

positive skew.

In order to check the dependency of these variables on salary of the driver, we run

several regression models. To name them Best subset model, Stepwise regression model and

Backward stepwise regression model.


7/15

7

Matrix Plot

353025 1680 20100

400

200

0

35

30

25

10

5

016

8

0 0.4

0.2

0.0

4002000

20

10

0

1050 0.40.20.0

score

age

car point

popularity

Avg Pole Position

Salary

Matrix Plot of score, age, car point, popularity, Avg Pole Pos, Salary

Best subset regression:Best Subsets Regression: Salary versus score, age, career average point (car point), popularity,

Average Pole position


8/15

8

According to the best subset model as minimum Cp value and maximum R-Sq(adj) lie on the

same line with markers pointing the variables Career average point (Car point) and the

popularity lie on the same line, indicating that both are the best suitable variables that have an

influence on the drivers salary.

Stepwise Regression Model

Stepwise Regression: Salary versus score, age, career average point (car point),

popularity, Average Pole position

Running the stepwise regression model it was inferred that career point average

and popularity are the influential variables on the drivers salary. The result was similar

to best subset regression model.

Backward Stepwise regression

Stepwise Regression: Salary versus score, age, career average point (car point), popularity,

Average Pole position (Backward)


9/15

9

It can be clearly seen that all the models suggest that career average point and the

popularity are the important factors that may be considered while deciding the drivers salary

with minimum Cp value of 0.2 and maximum R-Sq(adj) of 67.29%.


10/15

10

Regression model on career average point and popularity


11/15

11

Running the model accuracy check it was seen that Almost all of the points are close to the

straight line, so the normality assumption is satisfied. In time sequence, the plot of residuals

scatter at the two sides of the zero line which implies the independent assumption is

supported. Hence the model adequacy is satisfied.

The analysis of regression model, based on career average point and popularity, we got the

following regression equation as

Salary = - 1.44 + 0.671 popularity + 1.02 car point

It was also seen that P-value of regression model is very low, thus we can say that career

average point and popularity does have significance on salary of formula 1 drivers with the R-

Sq (Adj.) also being high (67.8 %) indicating that the model is a good estimator.

In order to check the overall contribution of the model, F0= 20.55 which is greater thanF0.05,2,17i.e 3.59 hence we reject H0where H0: Beta1 =Beta 2=0 thus it is clear that at least one o

the variable is significant.

For Career Average Point T0=2.76 which is greater than T0.025,17i.e. 2.110, thus we reject

H0 Where H0: Beta1=0 and P-value is also 0.021(less than 0.05) thus we can say that career

average point is contributing in our model. For Popularity T0=2.55 which is greater than T0.025,17

i.e. 2.110, thus we reject H0where H0:Beta2=0 and P-value is 0.014(less than 0.05) as p-value is

also very low, we can conclude that popularity is also a important fartor that might e

considered to decide upon the drivers salary.

The VIF value for Career Average Point and Popularity are 1.759 which is also very low

i.e. below 2.

Conclusion :

In perspective of a driver, it can be seen that one needs to concentrate on the his

average career point should be high and maintain the same to expect a higher salary. Logically a

driver represents its brand and in turn publicizes it amongst his fan base. Hence more the

popularity of the driver, the more the team sponsors would agree to pay the team and thedriver, the same is supported by the model presented above.


12/15

12

Part 2 Problem Statement:

The myth that pitstop timing of a driver is an important factor that will affect the probability of

the driver winning the race, will be tested if true with the following regression model.

As the data is related to the winning of a driver, the data of the present winner of the last

championship was taken, the driver being Sebastian Vettel . The idea behind analyzing the data

of the champion is to see whether or not his pit stops clock times are affecting his positions in the

race as he is one of the ideal formula one perfectionist so far with 13 wins out of 19 race in the

2013 season.

Data

As we are looking at the effects on the race time with respect to the pitstop time for sebastian

vettel, below is his data for Formula1 2013 season showing his pitstop timing and the respective

finishing times.


13/15

13

Data Analysis Using Minitab

Probability plot

In an attempt to check the properties of the data collated a probability plot was constructed.

It was seen that the data though was not properly normally distributed, there was also an

outlier in the finishing time data. The pitstop timing could be considered as normally distribute

having no outliers.

Model adequacy Check - Residual Plot


14/15

14

Data although is not normally distributed, but the variability of the data is distributed

evenly along the axis having an outlier.

Considering the limited scope of the data covered in this project as there is only one

season analyzed for a single driver, it was felt justified to consider the data to be in symmetry

which on the other hand would have been symmetrical if the data was huge.

Regression Analysis: Finishing Time versus Pit Stop

Explaining the regression output from minitab we see that the p value is too high and the Mean

square of error, with the f-statistics being 0 i.e. less than F .05,1,17 (4.45), hence we fail reject the

Hothat pitstop does not have any significance over the finishing time of the race or winning or

losing of the driver.


15/15

15

Conclusion

Analyzing the data through regression, we fail to conclude that the pitstop timings have

a direct affect on the drivers possibility of winning or losing the race. Though we fail o say that

the pitstop has a direct affect on the winning of the race, we still cannot make a comment that

pitstop does not have relevance. As the pitsop time average is just 51.46 seconds as compared

to 5585.63 seconds of average race finishing time, it can be easily covered or shadowed by

gaining some or the other advantages on the track. It can also be said that over the years of

technical advancements in formula one racing, a single pitstop time has reduced to 20 seconds

making it easier for the driver to cover up.

References :

Applied Engineering Statistics and Probability for Engineers by Douglas C.

Montgomery and George C. Runger, Fifth edition.

The main data was collected from official formula 1 websitewww.formula1.com

We also referred to following site:

o www.statsf1.com

o www.f1fanatic.co.uk
http://www.formula1.com/http://www.formula1.com/http://www.formula1.com/http://www.statsf1.com/http://www.statsf1.com/http://www.statsf1.com/http://www.formula1.com/

Date post:	02-Jun-2018
Category:	Documents
Upload:	ashish-shadija
View:	217 times
Download:	0 times

Analysis of Salary of Formula 1 Driver and Pitstop Analysis

Documents