Correlation between Height and Weight in Relation to the Ability of the Basketball Players - Assignment Example

of Learning: Internal Assessment, Portfolio, International Bacculaureate Correlation is measure of two or more variables comparing the variables in an effort to infer how the variables are relate to each other. This can be explained in form of a graph with the variables plotted against each other. The more the selected variables are to each other, the more the graph when will appear to be a straight perfect line with a positive number representing a positive relation between the variables while a negative number will represent a negative relationship as one variable reduces, the other one increases. This correlation can be used in our case in an effort to analyze the relationship between weight and height and the role the two play in the performance of NBA players and how good they are in scoring. To achieve this, data from the NBA association will be used to try relating the two. When weight is plotted in a graph with any completion percentage, the outcome will be a straight line that rises to the right and the correlation will be 1. In case the straight line tends to the left, then the correlation with the selected variable will be a negative one. When weight and height of basket ball players are plotted against one another and the correlation comes out as positive, this implies that heavier or taller players have better statistics compared to the lighter and short players. There exists a small positive correlation when it comes to weight and most of the stats in basket ball a part from yards per attempt (Belloti, 2002, p. 89). In each case when the weight of the players is correlated with the stats, the selected stat rises accordingly unless there is an interception. The largest correlation that can be achieved when height is being used as a variable against any passing statistics has been observed to be interesting between the completion percentage and height, however, the correlation in this case is negligible (Belloti 36) It has also been observed that very little correlation exists between rushing statistics and measurable with rushing touchdowns and weight being exempted. Players with heavier running backs have been observed to share the largest percentage of the touchdown scores as expected. Wideouts can also be used in determining the correlation between weight and height of the basket ball players. There exists a strong correlation between yards per catch and weight with the correlation being placed at -0.653 (BodBendieck and Reheuser 74). Such a correlation implies that counter-intuitive characteristic of shorter wide receivers tend to have more yards per catch as compared to those with taller receivers. To get the winning percentage with regards to defensive and offensive efficiency, we use the model; PE=FGA +0.45*FTA +TO-REBO And PA=DFGM+0.45*DETM+REBD+DTO+REBTM ……………………. (Dey 87). Where Offensive Efficiency will be given by; Points Scored divided by the Possessions Employed (PE) while Defensive Efficiency will be given by; Points Surrendered divided by Possession Acquired (PA). In such a case, the dependent variable will be the wining percentage while the Independent variables coefficient will be as shown in the table bellow. Independent Variable Coefficient t-statistic Offensive Efficiency 3.152 82.110 Defensive Efficiency -3.134 -73.348 Constant term 0.481 8.702 The table bellow provides the meaning of the symbols used in the formula above. FGA = Field Goal Attempts FTA = Free Throw Attempts TO = Turnovers REBO = Offensive Rebounds DFGM = Opponent’s Field Goals Made DFTM = Opponent’s Free Throws Made REBD = Defensive Rebounds DTO = Opponent’s Turnovers REBTM = Team Rebounds The correlation will be observed to be more staggering in case the difference in weight remains unique. In such a case, the correlation will rise to -0.819 considering the average yards for every catch at the selected unique weights (BodBendieck and Reheuser 108). A correlation with few unique heights or weights will have coefficients that are not able to bring out the relationship between on-field productions and the variables. In order to come up with a better correlation, then the receivers performance with regards to weight and height has to be considered together and the statistics be examined from the total receivers performance (BodBendieck and Reheuser 90). Looking at the quarter backs with the heights considered in inches while the weights in pounds, the performance of quarter backs are highest when the passer has a height of approximately 74 inches tall. A good example of such cases includes names like Kurt Warner, Steve Young, Brett Favre and Joe Montana all were 74 inches. Doing away with a particular height, quarterbacks rating tend to rise at every height increment. In addition, the completion percentage of the quarter backs that are shortest will be lower than the rest of the heights which reflects to a full point that is lower than the tallest completion percentage. In such a situation, there will be no correlation between completion percentage and height after this mark. Touchdowns for every attempt reduce every time weight is increased as the season intensifies. In addition, the probability of having player’s throw for 12 or less interceptions increases as the weight of the players increases. NBA official records have it that the difference between a 77-inch quarterback’s player and a 73-inch quarterback basketball player passer rating equals 2.74 quarterbacks rating points thus favoring the smaller players as the height’s coefficient remain negative. Weight has been observed to affect the ratings of passers thus the heavier players having the upper advantage over the lighter ones. Another example is that the smaller QBs players show an 8.82 fantasy-point advantage over their taller QBs counterparts in relation to the 450 pass course attempts. However, weight showed a lesser effect with regards to the fantasy points (Dey 85). To calculate the value of the performance of players and their scoring ability, this can be achieved through multiplying the statistics of a given player with the corresponding performance value as shown bellow; PROD=3FGM*0.064+2FGM*0.032+FTM*0.017+FGMS*-0.034+FTMS*-0.015+REBO*0.034+REBD*0.034 +TO*-0.034+STL*0.033+FTM(opp)*-0.017+BLK*0.020 (Dey 87). This can be demonstrated by applying the formula in calculating the performance of Derrick Rose which will be; 128*0.064 + 583*0.032 + 476*0.017 + 886*-0.034 + 79*-0.015 + 81*0.034 + 249*0.034 + 278*-0.034 + 85*0.033 + 119.5*-0.017 + 51*0.020 Giving us 7.47 Completion percentage remains unaffected by the changes in either weight or height. Touchdowns, Passing yards as well as interceptions all remained in favor of the smaller quarterbacks yet interceptions and touchdowns on the other hand favor the heavier QBs players. Most of the stats are in favor of the small but height wise as well as heavy quarterbacks. Considering the body mass index of the players in the examination of the players who are either obese, underweight and normal, the players who are heavy but stature had an advantage than the obese and underweight players. Quarterbacks tend to favor passers who are beefier with an edge of approximately 3.16 on the ratings of quarterback, fantasy points of approximately 8.39, a minimal completion percentage change of a ratio of o.5 to 1, yards of about 13.89, less interceptions of about 1.91 and 1.09 touchdowns (Dey 87). Good examples of such cases are David Garrard and Eli Manning with regards to the difference between the two in relation to BMI, that is Garrard’s MBI being at 32.2 and Manning’s BMI being at 26.5 resulting to a remarkable 12 fantasy points within 450 trials. Taking another look at the running backs, the average stats for each weight and height groups show a strong correlation between the yards for every carry and height. There is a downward trend in the yards for every carry as the height rises. The only exemption in this case being the 74 to 75 inches tall jumps (Dey 90) While referring to both weight and height with regards basket players who play the role of receivers; it is seen that for approximately 60 receptions by players in three back to back years in a selected team, the height only impacts a minimal of 7.86 yards in every 70 receptions and this implies an advantage to the smaller wide outs. This also affects the fantasy points by players in relation to the touchdowns and this remains beneficial to the taller receivers. Looking at weight, it has been observed that approximately 180 pound receivers have a 6.55 fantasy point and this is 37 more compared to 230 pound receivers who are shorter in weight and this does not put into consideration the 0.45 touchdown benefit the heavier receivers have as an advantage (Dey 85). NBA official statistics have it that height doubled as well as weight increased with the consideration that both the measurable variables are more preferred indicators than other variables like BMI. The correlation between rushing downs and weight is regarded as small but still apparent in the performance of the players especially in the scoring of the players. This follows the fact that the touchdown percentage increases as the weight of the players increases. (BodBendieck and Reheuser 89). Considering the pattern existing between the relationship between fantasy points and weights, the trend is a down ward one which shows less chances of a team finishing in the top quarters with the weight of players increasing. Following the subjective weight of the fantasy points placed at 10 yards for every point; six points for every touchdown, the average of the running backs is almost 70 percent of the fantasy points of the total yard of players thus benefiting the players assuming the small backs role covering more yards but gain fewer scores. While trying to predict the weight and height value, the running back difference between 6’3” and 5’8” is 5.9 fantasy points from 250 attempts by the players and this is an advantage to the players who play as small backs. This means that the coefficient of the percentage of running down is negative but this is small enough to be neglected. Considering the weight variable, lighter backs tend to have a fantasy point placed at 2.39 as well as an edge of about 18 yard compared to their heavier counterparts. The heavier rushers on the hand have a touchdown difference of about 0.55. This means that in this case, the lighter backs will be better scorers than the heavier rushers. (BodBendieck and Reheuser 61). To include the defensive factor in scoring in while putting height and weight constant, we have to calculate the Team Defense Adjustment given by; [(3FGM(opp)*-0.064+(2FG(opp)*-0.031+TO(opp)*0.033+TOTM*-0.034+REBTM*0.033-BLKTM*0.033-BLKTM*0.200)/Minutes Played]*48 Taking an example of the Defensive Adjustment of the Bulls; [(427*-0.064+2378*-0.032+567*0.033+57*-0.034+415.0*0.033-468*0.200)/19, 830]*48=-0.195 (Belloti 122). The comparison between weight and height indicates that the smaller in weight and shorter in size players who assume the backs position perform better in both their scoring and defending. When BMI is applied in this situation, it divides weight on the basis of height while at the same time neutralization the relationship between weight and height. This is evident with the fact that when MBI is applied, the difference between lowest and highest backs remains less than a single fantasy points, one touchdown and five rushing yards. From the above analysis, it is evident that the correlation between height and weight in relation to the ability of the players to score depend on other several factors such the position of the players. Despite such factors, the two go hand in hand as the performance of a player depends on the two; a player has to be of a given height as well as be of some given weight. Taller players are better scores in general and they still have to put in some weight in order to maintain a mass index fit for a player. This implies that there is a positive correlation between height and weight and the two contribute positively to the scoring ability of players. Some of the other factors that switch the correlation coefficient include touchdowns and wideouts, interception percentage, yards per catch, completion percentage and the position played by each player as shown in the table bellow as each position has a varying average adjustment (Belloti 122). . Position Average Adj. P48 Point Guards 0.191 Shooting Guards 0.158 Small Forwards 0.186 Power Forwards 0.256 Centers 0.296  Works Cited Belloti, Reagan. The Points Created Basketball Book. New Jersey: New Brunswick, 2002. Print BodBendieck Reheuser. Official NBA Register, New York: The Sporting News Publishing Company, 2006.Print Dey, Megan. Racial and Size Difference in National Basketball Association, American Economists, 41, 84-90 Read More

Such a correlation implies that counter-intuitive characteristic of shorter wide receivers tend to have more yards per catch as compared to those with taller receivers. To get the winning percentage with regards to defensive and offensive efficiency, we use the model; PE=FGA +0.45*FTA +TO-REBO And PA=DFGM+0.45*DETM+REBD+DTO+REBTM ……………………. (Dey 87). Where Offensive Efficiency will be given by; Points Scored divided by the Possessions Employed (PE) while Defensive Efficiency will be given by; Points Surrendered divided by Possession Acquired (PA).

In such a case, the dependent variable will be the wining percentage while the Independent variables coefficient will be as shown in the table bellow. Independent Variable Coefficient t-statistic Offensive Efficiency 3.152 82.110 Defensive Efficiency -3.134 -73.348 Constant term 0.481 8.702 The table bellow provides the meaning of the symbols used in the formula above. FGA = Field Goal Attempts FTA = Free Throw Attempts TO = Turnovers REBO = Offensive Rebounds DFGM = Opponent’s Field Goals Made DFTM = Opponent’s Free Throws Made REBD = Defensive Rebounds DTO = Opponent’s Turnovers REBTM = Team Rebounds The correlation will be observed to be more staggering in case the difference in weight remains unique.

In such a case, the correlation will rise to -0.819 considering the average yards for every catch at the selected unique weights (BodBendieck and Reheuser 108). A correlation with few unique heights or weights will have coefficients that are not able to bring out the relationship between on-field productions and the variables. In order to come up with a better correlation, then the receivers performance with regards to weight and height has to be considered together and the statistics be examined from the total receivers performance (BodBendieck and Reheuser 90).

Looking at the quarter backs with the heights considered in inches while the weights in pounds, the performance of quarter backs are highest when the passer has a height of approximately 74 inches tall. A good example of such cases includes names like Kurt Warner, Steve Young, Brett Favre and Joe Montana all were 74 inches. Doing away with a particular height, quarterbacks rating tend to rise at every height increment. In addition, the completion percentage of the quarter backs that are shortest will be lower than the rest of the heights which reflects to a full point that is lower than the tallest completion percentage.

In such a situation, there will be no correlation between completion percentage and height after this mark. Touchdowns for every attempt reduce every time weight is increased as the season intensifies. In addition, the probability of having player’s throw for 12 or less interceptions increases as the weight of the players increases. NBA official records have it that the difference between a 77-inch quarterback’s player and a 73-inch quarterback basketball player passer rating equals 2.74 quarterbacks rating points thus favoring the smaller players as the height’s coefficient remain negative.

Weight has been observed to affect the ratings of passers thus the heavier players having the upper advantage over the lighter ones. Another example is that the smaller QBs players show an 8.82 fantasy-point advantage over their taller QBs counterparts in relation to the 450 pass course attempts. However, weight showed a lesser effect with regards to the fantasy points (Dey 85). To calculate the value of the performance of players and their scoring ability, this can be achieved through multiplying the statistics of a given player with the corresponding performance value as shown bellow; PROD=3FGM*0.

064+2FGM*0.032+FTM*0.017+FGMS*-0.034+FTMS*-0.015+REBO*0.034+REBD*0.034 +TO*-0.034+STL*0.033+FTM(opp)*-0.017+BLK*0.020 (Dey 87). This can be demonstrated by applying the formula in calculating the performance of Derrick Rose which will be; 128*0.064 + 583*0.032 + 476*0.017 + 886*-0.

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