Free Essay About Basketball Statistical Analysis

Introduction

Basketball is attractive because of its entertainment, an abundance of various technical and tactical methods, emotion, lightness, dynamism, both collectivism and individualism. In my opinion, it is also the most effective way for a comprehensive physical development.
The popularity of basketball and its wide application in the system of physical education are due economic accessibility of the game, high emotion, great visual effects, complex effects on the body and the education of youth. Basketball is a non-standard situational exercise sharply varying intensity. During the game, the intensity of the movements may be the maximum, moderate, and in some moments of the game an intensive muscle activity may be stopped. Similar changes occur continuously intensity, as determined by the changing environment, the conditions of the game. As a result, basketball helps to develop a special kind of dynamic stereotype of the nervous processes, providing a rapid transition, switching functions with the same level of activity to another, from high to low and vice versa.
Unlike other sports, basketball players are very high – 190 centimeters and above. Also their weight is significant. To a certain extent it affects the nature of the sport. In the course of sports perfection, the abilities to control their movements, increased reaction rate, the function of the analyzers are being improved. Basketball players have good indicators of the field of view, depth of view, allowing them to focus on the well site. High level of development reaches the motor analyzer. High-class athletes appreciate good effort, the execution time of movement, precision gears and throws. The activity basketball game is very intensive. The evidence of this, in particular, is a high rate of functional changes during the game. The heart rate of basketball player can reach up to 180-230 beats per minute. During the game, the level of oxygen consumption is within 72,3-96,6% of the maximum. In this case, the respiratory rate is 50-60 breaths per minute, and respiratory volume reaches 120-150 liters per minute.
Thus, participation in games makes high demands on physical abilities of basketball players. Energy consumption per game in basketball is 900-1200 kcal. In other words, modern basketball makes high demands on the level of physical fitness of the players.
Thus, it is logical to assume that the success of the basketball players is closely linked to their physical data. In this paper we will explore the data set of basketball players and investigate whether the physical performance of the players is associated with their effectiveness in games.

Data Introduction and Measurement

In this research we are given with the data of 54 professional basketball players. This data is taken from the official NBA basketball Encyclopedia (Villard Books). For each player in the data set, there are 5 measures (variables) are given:

Height – the height of a player (in feet)

Weight – the weight of a player (in pounds)
Field_goals_success – the percent of goals in field, the ratio out of 100 attempts.
Free_throw_success – the percent of goals in free throws, the ratio out of 100 attempts.
Points_per_game – the average points earned during a game.
Descriptive Statistics
The first section of mathematical statistics is a descriptive statistics. It is intended to represent the data in a convenient form and a description of the information in terms of mathematical statistics and probability theory. To do this, there are invented such descriptive statistics as minimum, maximum, mean, variance, standard deviation, median, quartiles, mode, etc.
I use SPSS 22 statistical software to retrieve all necessary information of descriptive statistics.
This data can be visualized by histograms. Frequency histograms help to summarize and show the distribution of variables in easy and convenient form. Also, in such form it is possible to make a conclusion about the type of the distribution (at first glance).
It seems that the “Height” distribution is close to a Gaussian (normal) distribution. The distributions of other variables are not so close to the normal distribution. However, we can check if these distributions are significantly different from normal by using a non-parametric test.
I can test the variables for normality using Kolmogorov-Smirnov and Shapiro-Wilk tests. We know that Shapiro-Wilk tests is useful for the samples with n<2000. Thus, I use Shapiro-Wilk test:
Since p-value of Height and Field_goals_success is higher than 0.05, I can conclude that the data comes from normal distribution (at 5% level of significance). The distribution of other variables is not normal.

Analysis

As a first step of this section I would like to check the bivariate associations between the variables. I want to understand which pairs of variables are related to each other. To do this I run a correlation matrix between all 5 variables:
It seems that there is no significant association between Points per game and Height and Weight. There is a weak association between Points per game and success ratios.
Height variable is strongly associated with Weight (and this is natural), moderately associated with Field Goals Success and weakly associated with Free Throws Success.

Weight is moderately associated with Field Goal Success and weakly associated with Free Throws Success.

Free Throw Success and Field Goals Success are not associated.
Since my goal is to understand which factors affect the overall success in games, I look for association with Points Per Game. I see that Points per Game is associated with Success ratios. And Field Goals Success associated with Height and Weight. That’s why in regression model development I can omit Height and Weight to avoid autocorrelation.
Perform regression analysis using Points_per_game as a dependent variable and Free_throw_success and Field_goals_success as independent variables:
According to the ANOVA results, F=5.516 with p=0.007. Since p-value is lesser than 0.05, I can conclude that the overall model is significant and may be used in forecasts. Since p-value of coefficients are 0.009 and 0.053 respectively, I can conclude, that the variables included in the model are significant at 10% level of significance.
The coefficient of determination R-square is 0.422. This means that the variance of Points_per_game variable is explained by this model for 42.2%. This is a moderate value for goodness-of-fit coefficient. I assume that there are some factors which affect the overall success of the game, which are not included in this study.

However, the obtained regression equation has the following form:

PointsPerGame=-15.277+35.825*FieldGoalsSuccess+14.799*FreeThrowsSuccess

Conclusion and Validity

In this research I have investigated which factors affect the effectiveness of basketball players, measured as average points earned per game. I have found out that there is no direct association between the effectiveness and physical characteristics of basketball players, such as height and weight. However, I noted that these characteristics are correlated with the percent of goals in field and the percent of goals in free throws, and the last two variables are associated with effectiveness. To avoid autocorrelation between the independent factors, I have included only two factors in regression equation. The percent of goals in field and the percent of goals in free throws are not correlated to each other and that’s why I could consider them as independent variables.
The obtained regression equation can be used to make a prediction about effectiveness of basketball players based on the given values of percent of goals in field and the percent of goals in free throws to some extent. The model is not very effective because of significance of the coefficients of the equation, the moderate value of coefficient of determination and ANOVA result. Another factor which affects the validity of the study is that the percent of goals in free throws is not normally distributed. This can bias the results of regression analysis.

Works Cited

Draper, Norman Richard, and Harry Smith. Applied Regression Analysis. 3rd ed. New York: Wiley, 1998. Print.
Sachare, Alex. The Official NBA Basketball Encyclopedia. 2nd ed. New York: Villard, 1994. Print.