To what extent is there a Correlation between strike rate of batsman & height of the batsman?

I love sports from a very young age. When I was a kid, I remember my dad taking me to parks every day to play to game of cricket. I guess this is how my relation with sports strengthened. Though I have grown up now, I have an active participation in sports. My studies have never been an excuse to skip games. "All work and no play make Jack a dull boy"- I abide by the statement.

I do not play only for recreation; I follow sports religiously. I am into my school's cricket team. I take coaching classes and practice even after school. I love to play Cricket. I love being a batsman and captain of a team.

Recently, it was announced that players will be selected to be a part of the interschool cricket tournament. I was super excited and wished to grab the opportunity. When surfing the net for some tips, I read various resources, got to know many interesting facts but a statement about height being a factor of selection caught my eyes.

Being the captain of my school team, selecting players to an extent was my responsibility. I looked for confirmation everywhere but could not get a satisfactory answer. I could not decide on the players as I thought their heights should not overshadow their performances. It was a matter of their hard work as well as the name of the school.

Heaped with worries, I decided to research and find the answer to my query. This IA is about the same. In this IA, I have tried to find out if the height of a batsman determines his strike rate. I will also try to find how much height of a batsman act as a deciding factor in the result of the cricket match. This research will help me convince myself on selecting players for the competition.

The main motive of this IA is to study whether or not there exist a correlation between the strike rate of batsman and their height in the game of cricket. Furthermore, this IA will provide a brief information about the benefit or disadvantage a batsman has by default due to his height in scoring runs at a faster rate, i.e., his strike-rate. This exploration will help the team management and selection committee to sign contract with players.

What is the relationship between strike rate of batsman and the height of the batsman?

Strike rate1 is one of the most important parameters which measures the performance of any batsman in the game of cricket. It analyses how much the batsman has scored runs with respect to the number of balls he played. The formula of calculation of strike rate is shown below:

\(Strike\ Rate=\frac{Runs\ Scored}{Number\ of\ balls\ played}\times100\)

Height of players could be a benefit for any player in several games. For example, in games like football and basketball, taller players often stand a better chance in the gameplay with respect to performance over the players with comparatively shorter height.

In the game of cricket, taller batsman could have a better chance while playing short balls which will allow then to score a lot of runs in difficult deliveries also.

Regression correlation coefficient is a tool to measure the strength of the correlation between the independent variable and the dependent variable. The set of values (x₁,y₁), (x₂,y₂), (x_n,y_n) are used to find the value of r as stated by the formula below:

\(r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2-(\sum x)^2][n\sum y^2-(\sum y)^2]}}\)

In the above-mentioned formula, x is the value of independent variable of each observation, y is the value of dependent variable of each observation, xy is the value of the product of the independent and the dependent variable of each observation, n is the number of observation and ∑ denotes the sum of all the observation of the mentioned variable.

By squaring the value of r, the value of the regression coefficient (r² ) will be achieved. The value of r² lies between 0 and 1 where 1 signifies maximum correlation whereas 0 signifies null correlation.

Pearson’s correlation coefficient is a tool to measure the strength of the correlation and also the nature of correlation between the independent variable and the dependent variable. The set of values (x₁,y₁), (x₂,y₂), (x_n,y_n) are used to find the value of \(\mathfrak{R}\) as stated by the formula below:

 \(\mathfrak{R}=\frac{\sum (x-\bar x)(y-\bar y)}{\sqrt{\sum(x-\bar x)^2\times\sum (y-\bar y)^2}}\)

In the above-mentioned formula, x is the value of independent variable of each observation, y is the value of dependent variable of each observation, \(\bar x\) is the arithmetic mean of all the observations of the independent variable, \(\bar y\) is the arithmetic mean of all the observations of the dependent variable and ∑ denotes the sum of all the observation of the mentioned variable. The value of \(\mathfrak{R}\) lies between -1 and 1. A positive value of Pearson’s correlation coefficient implies a direct relationship the independent and the dependent variable whereas, a negative value of Pearson’s correlation coefficient implies a indirect relationship the independent and the dependent variable. If the value of the correlation coefficient is close of 1 or -1, it signifies the correlation exists true. On the other hand, if the value of the correlation coefficient is close to 0, it signifies the correlation does not exist.

T – test is a kind of analysis which predicts the existence of any correlation between an independent variable and a dependent variable. The T – value of any given set of data is firstly calculated. Now, based on the type of data, for example, paired data or independent data, the T- value is checked in the T – table which further predicts the existence of any correlation. The formula of T – value is given below:

\(T\ value=\frac{|\bar x-\bar y|}{\sqrt{\frac{v_x^2}{n_x}+\frac{v_y^2}{n_y}}}\)

Here, \(\bar x\) is the arithmetic mean of all the observations of the independent variable, \(\bar y\) is the arithmetic mean of all the observations of the dependent variable, v_x is the variance of independent variable, v_y is the variance of dependent variable, v_x is the number of observation of independent variable, and v_y is the number of observation of dependent variable.

Now, the T – value is checked in T – table which predicts the existence of any correlation. The T – table is shown below:

It is assumed that there does not exist any correlation between strike rate of batsman and the height of the batsman.

It is assumed that there is a correlation between the strike rate of batsman and the height of the batsman.

The strike rate of different batsman with respect to their height has been collected from the very recently organised cricket tournament, Indian Premier League 2020 . Indian Premier League or abbreviated as IPL T20 is a domestic cricket tournament organized by BCCI (Board of Council for Cricket in India). Eight teams each representing a particular city/ state in India competes in a two – three months long tournament where players across the globe are signed contract and assigned in each team. As it is a twenty over match, it is often abbreviated as T20 series.

IPL T20 has been selected for collection of data for a various reason. Firstly, IPL, though a domestic tournament organized by BCCI, it offers an amalgamation of players across the globe. It will allow the data set to have more generalized observations rather than specific to any single country. Secondly, IPL T20 is one of the most recently organized tournaments. It will allow the data set to be updated with respect to the current style of playing the game of cricket. Thirdly, IPL is a twenty over game. A twenty over game’s pre-requisite is scoring runs at a smaller number of balls played. As a result, the strike rate of batsman in this tournament will be more than that of any other tournament. Higher observed values offer an ease and perfection to find the correlation than that of smaller observed values.

\(\text{Mean }= \frac{y_1+y_2+...+y_n}n{}\)

\(\text{Arithmetic Mean }= \frac{82.05+92.67+100.96+...+89.47+108.97}{50} = 103.2144\)

\(\text{Standard Deviation }= \frac{\sqrt{(\bar y-y_1)^2+(\bar y-y_2)^2+...+(\bar y-y_n)^2}}{n}\)

\(\\text{Standard Deviation =}\frac{\sqrt{{\overline{(103.2144}-82.05)^2+(103.2144-92.67)^2+...+(\overline{103.2144}-108.97)^2}}}{50} = 14.967\)

The mean strike rate of all the batsman is 103.2144. On the other hand the standard deviation is 14.967. The value of standard deviation, being high, offers a wide range of values of strike rate with respect to the mean. As a result, it can be assumed that the strike rate varies greatly from each player to the other.

The X – Axis of the graph denotes the height of the batsman measured in centimetre (independent variable).

The Y – Axis of the graph denotes the strike rate of the batsman (dependent variable).