Factor of Victory in Sports - Statistics Project Example

memorandum XYZ, Head Coach, ABC School Predicting Revenue & factors that HAVE IMPACT on Win 10/7/06 Hi, Winning is the most important aspect for any sport. In individual sports it depends only on single individual player, however in team sports, it depends on each player of team as well as several other factors. In this memo, I will try to answer factors that influence wins at baseball league. In addition, I will also try to develop a model so that forecast for average team revenue can be made. A sample of 30 teams were taken and data collected for league, surface, size, built, salary, wins, attendance, batting, earned run average (ERA), home runs (HR), errors, and stolen base (SB). In addition, average revenue data from year 1989 to 2006 were also collected. As shown if figure 1, 14 (47%) teams were from National league and 16 (53%) teams were from American league. The average salary of teams was about $77.56 millions (SD = 32.28). The coefficient of variation for salary was about 42%. The range of salary was about $179.70 millions with minimum and maximum salary of team being $15 millions and $194.70 millions, respectively. About one-quarter of the team’s salary was below $60 millions, about half of the team’s salary was below $72 millions, and about one-quarter of the team’s salary was above $92 millions. As mean salary is greater than median salary that suggests distribution of salary is right skewed. The value of skewness coefficient 1.42 confirms that distribution of team’s salary is positively skewed. The team’s salary from one, two, and three standard deviation from mean is 83.3%, 96.7%, and 96.7%, respectively. The average number of wins of teams was about 82 (SD = 10). The coefficient of variation for number of wins was about 12%. The range of number of wins was about 36 with minimum and maximum number of wins of team being 61 and 97, respectively. About one-quarter of the team’s number of wins was below 76, about half of the team’s number of wins was below 81, and about one-quarter of the team’s number of wins was above 88. As mean number of wins is approximately equal to median number of wins that suggests distribution of number of wins is normal. The value of skewness coefficient -0.29 confirms that distribution of team’s number of wins is normally distributed. The team’s number of wins from one, two, and three standard deviation from mean is 66.7%, 93.3%, and 100%, respectively. The average attendance of team was about 2.53 millions (SD = 0.71). The coefficient of variation for attendance was about 28%. The range of attendance was about 3.04 millions with minimum and maximum attendance of team being 1.17 millions and 4.20 millions, respectively. About one-quarter of the team’s attendance was below 2.11 millions, about half of the team’s attendance was below 2.43, and about one-quarter of the team’s attendance was above 3.01 millions. As mean attendance is approximately equal to median attendance that suggests distribution of attendance is normal. The value of skewness coefficient 0.25 confirms that distribution of team’s attendance is normally distributed. The team’s attendance from one, two, and three standard deviation from mean is 73.3%, 96.7%, and 100%, respectively. The average batting of teams was about 0.27 (SD = 0.01). The coefficient of variation for batting was about 3.32%. The range of batting was about 0.03 with minimum and maximum batting of team being 0.26 and 0.29, respectively. About one-quarter of the team’s batting was below 0.26, about half of the team’s batting was below 0.27, and about one-quarter of the team’s batting was above 0.28. As mean batting is equal to median batting that suggests distribution of batting is normal. The value of skewness coefficient 0.24 confirms that distribution of team’s batting is normally distributed. The team’s batting from one, two, and three standard deviation from mean is 63.3%, 100%, and 100%, respectively. The average earned run average (ERA) of teams was about 4.52 (SD = 0.40). The coefficient of variation for ERA was about 9%. The range of ERA was about 1.81 with minimum and maximum ERA of team being 3.84 and 5.65, respectively. About one-quarter of the team’s ERA was below 4.27, about half of the team’s ERA was below 4.53, and about one-quarter of the team’s ERA was above 4.65. As mean ERA is close to median ERA that suggests distribution of ERA is normal. The value of skewness coefficient 0.67 confirms that distribution of team’s ERA is approximately normally distributed. The team’s ERA from one, two, and three standard deviation from mean is 70.0%, 93.3%, and 100%, respectively. The average home runs (HR) of teams was about 180 (SD = 26). The coefficient of variation for HR was about 15%. The range of HR was about 112 with minimum and maximum HR of team being 124 and 236, respectively. About one-quarter of the team’s HR was below 161, about half of the team’s HR was below 177, and about one-quarter of the team’s HR was above 198. As mean HR is close to median HR that suggests distribution of HR is normal. The value of skewness coefficient 0.16 confirms that distribution of team’s HR is normally distributed. The team’s HR from one, two, and three standard deviation from mean is 70.0%, 93.3%, and 100%, respectively. The average errors of teams was about 102 (SD = 15). The coefficient of variation for errors was about 15%. The range of errors was about 65 with minimum and maximum errors of team being 66 and 131, respectively. About one-quarter of the team’s errors was below 91, about half of the team’s errors was below 103, and about one-quarter of the team’s errors was above 113. As mean errors is close to median errors that suggests distribution of errors is normal. The value of skewness coefficient -0.03 confirms that distribution of team’s errors is normally distributed. The team’s errors from one, two, and three standard deviation from mean is 70.0%, 96.7%, and 100%, respectively. The average stolen base (SB) of teams was about 92 (SD = 32). The coefficient of variation for SB was about 35%. The range of SB was about 97 with minimum and maximum SB of team being 51 and 148, respectively. About one-quarter of the team’s SB was below 62, about half of the team’s SB was below 88, and about one-quarter of the team’s SB was above 122. As mean SB is close to median SB that suggests distribution of SB is normal. The value of skewness coefficient 0.26 confirms that distribution of team’s SB is normally distributed. The team’s SB from one, two, and three standard deviation from mean is 60.0%, 100%, and 100%, respectively. The average revenue of teams for period 1989 to 2006 was about $1.63 millions (SD = 0.75). The coefficient of variation for revenue was about 46%. The range of revenue for this period was about $2.35 millions with minimum and maximum revenue being $0.51 millions and $2.87 millions, respectively. About one-quarter of revenue for period 1989 to 2006 was below $1.09 millions, about half of revenue was below $1.41 millions, and about one-quarter of revenue was above $2.35 millions. The value of skewness coefficient 0.22 suggests that distribution of revenue for period 1989 to 2006 is approximately normally distributed. The team’s revenue from one, two, and three standard deviation from mean is 61.1%, 100%, and 100%, respectively. As shown in figure 2, there appears a linear relationship between year and average team revenue. The value of correlation coefficient 0.98 suggests there is a perfect positive linear relationship between year and average team revenue. The value of coefficient of determination (R2) is 0.96 that suggests that about 96% of variation in average team revenue is explained by year. Only, about 4% variation in average team revenue remains unexplained. The regression model for predicting average team revenue is given by Average Team Revenue = – 272347762 + 137160.51(Year) As shown in figure 3, there appears a linear relationship between team’s salary and wins. The value of correlation coefficient 0.59 suggests there is a moderate positive linear relationship between team’s salary and wins. The value of coefficient of determination (R2) is 0.35 that suggests that about 35% of variation in wins is explained by salary. As shown in figure 4, there appears a linear relationship between team’s attendance and wins. The value of correlation coefficient 0.65 suggests there is a strong positive linear relationship between team’s salary and wins. The value of coefficient of determination (R2) is 0.42 that suggests that about 42% of variation in wins is explained by attendance. As shown in figure 5, there appears a linear relationship between team’s earned run average and wins. The value of correlation coefficient -0.74 suggests there is a strong negative linear relationship between team’s earned run average and wins. The value of coefficient of determination (R2) is 0.55 that suggests that about 55% of variation in wins is explained by attendance. Therefore, team’s attendance, earned run average, and salary have a strong impact on team’s number of wins. In conclusion, there is a perfect positive linear relationship between year and average team revenue and hence year can be used for prediction of average revenue of teams for any year. The team’s number of wins shows strong or moderate linear relationship with team’s attendance, earned run average, and salary. Therefore, team’s attendance, earned run average, and salary have a strong impact on team’s number of wins. I hope above analysis regarding forecasting of team average revenue for any year and factors that have impact on team’s number of wins will help you to coach better your team. Yours truly, Your Name Attachments Table 1 – Descriptive Statistics   Salary Wins Attendance Batting ERA HR Errors SB Revenue Count 30 30 30 30 30 30 30 30 18 Mean 77.56 81.63 2,533,254 0.27 4.52 179.53 102.23 92.23 1,630,354 Standard Deviation 32.28 9.71 706,601 0.01 0.40 26.19 15.14 32.11 747,366 Minimum 15 61 1,165,120 0.26 3.84 124 66 51 512,930 Maximum 194.70 97 4,200,518 0.29 5.65 236 131 148 2,866,544 Range 179.70 36 3,035,398 0.03 1.81 112 65 97 2,353,614 Skewness 1.419 -0.29 0.25 0.24 0.67 0.16 -0.03 0.26 0.22 Kurtosis 5.094 -0.35 0.02 -0.73 1.17 -0.30 0.00 -1.42 -1.32 COV 41.62% 11.90% 27.89% 3.32% 8.95% 14.59% 14.81% 34.81% 45.84% Q1 60.00 76.00 2,113,114 0.26 4.27 161.50 91.25 62.00 1,093,370 Q2 72.25 81.00 2,434,737 0.27 4.53 177.50 103.00 88.50 1,412,492 Q3 92.00 88.00 3,006,426 0.28 4.65 198.25 112.75 122.50 2,353,527 IQR 32.00 12.00 893,312 0.01 0.39 36.75 21.50 60.50 1,260,158 Mode #N/A 78.00 #N/A 0.27 4.60 164.00 104.00 121.00 #N/A Empirical Rule Mean - 1s 45.28 71.92 1,826,653 0.26 4.12 153.35 87.09 60.12 882,988 Mean + 1s 109.84 91.35 3,239,855 0.28 4.93 205.72 117.38 124.34 2,377,721 % In Interval (68.26%) 83.3% 66.7% 73.3% 63.3% 70.0% 70.0% 70.0% 60.0% 61.1% Mean - 2s 12.99 62.20 1,120,052 0.25 3.71 127.16 71.95 28.01 135,621 Mean + 2s 142.12 101.06 3,946,456 0.29 5.33 231.91 132.52 156.45 3,125,087 % In Interval (95.44%) 96.7% 93.3% 96.7% 100.0% 93.3% 93.3% 96.7% 100.0% 100.0% Mean - 3s -19.29 52.49 413,452 0.24 3.31 100.98 56.81 -4.09 -611,745 Mean + 3s 174.40 110.78 4,653,056 0.30 5.74 258.09 147.66 188.56 3,872,453 % In Interval (99.73%) 96.7% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% Table 2 – Correlation Matrix Salary Wins Attendance Batting ERA HR Errors Salary 1.000             Wins .593 1.000           Attendance .884 .648 1.000         Batting .362 .403 .259 1.000       ERA -.189 -.742 -.370 -.105 1.000     HR .357 .362 .231 .080 -.160 1.000   Errors -.268 -.255 -.183 -.144 .078 .066 1.000 SB .205 .160 .247 -.030 -.108 -.036 .450 30 sample size ± .361 critical value .05 (two-tail) ± .463 critical value .01 (two-tail) Figure 1 – League Figure 2 – Year vs. Average Revenue Figure 3– Salary vs. Wins Figure 4– Attendance vs. Wins Figure 5– Earned Run Average vs. Wins Table 3 – Correlation Matrix Year Revenue Year 1.000   Revenue .980 1.000 18 sample size ± .468 critical value .05 (two-tail) ± .590 critical value .01 (two-tail) Read More

The average batting of teams was about 0.27 (SD = 0.01). The coefficient of variation for batting was about 3.32%. The range of batting was about 0.03 with minimum and maximum batting of the team being 0.26 and 0.29, respectively. About one-quarter of the team’s batting was below 0.26, about half of the team’s batting was below 0.27, and about one-quarter of the team’s batting was above 0.28. As mean batting is equal to median batting that suggests the distribution of batting is normal. The value of skewness coefficient 0.24 confirms that the distribution of the team’s batting is normally distributed. The team’s batting from one, two, and three standard deviations from mean is 63.3%, 100%, and 100%, respectively.

The average earned run average (ERA) of teams was about 4.52 (SD = 0.40). The coefficient of variation for ERA was about 9%. The range of ERA was about 1.81 with the minimum and the maximum ERA of the team being 3.84 and 5.65, respectively. About one-quarter of the team’s ERA was below 4.27, about half of the team’s ERA was below 4.53, and about one-quarter of the team’s ERA was above 4.65. As mean ERA is close to median ERA that suggests the distribution of ERA is normal. The value of the skewness coefficient 0.67 confirms that the distribution of the team’s ERA is approximately normally distributed. The team’s ERA from one, two, and three standard deviations from mean is 70.0%, 93.3%, and 100%, respectively.

The average home runs (HR) of teams was about 180 (SD = 26). The coefficient of variation for HR was about 15%. The range of HR was about 112 with the minimum and maximum HR of the team being 124 and 236, respectively. About one-quarter of the team’s HR was below 161, about half of the team’s HR was below 177, and about one-quarter of the team’s HR was above 198. As mean HR is close to median HR that suggests the distribution of HR is normal. The value of skewness coefficient 0.16 confirms that the distribution of the team’s HR is normally distributed. The team’s HR from one, two, and three standard deviations from mean is 70.0%, 93.3%, and 100%, respectively.

The average errors of teams were about 102 (SD = 15). The coefficient of variation for errors was about 15%. The range of errors was about 65 with minimum and maximum errors of the team being 66 and 131, respectively. About one-quarter of the team’s errors were below 91, about half of the team’s errors were below 103, and about one-quarter of the team’s errors were above 113. As mean errors are close to median errors that suggest the distribution of errors is normal. The value of skewness coefficient -0.03 confirms that the distribution of team’s errors is normally distributed. The team’s errors from one, two, and three standard deviations from the mean are 70.0%, 96.7%, and 100%, respectively.

The average stolen base (SB) of teams was about 92 (SD = 32). The coefficient of variation for SB was about 35%. The range of SB was about 97 with the minimum and maximum SB of the team being 51 and 148, respectively. About one-quarter of the team’s SB was below 62, about half of the team’s SB was below 88, and about one-quarter of the team’s SB was above 122. As mean SB is close to median SB that suggests the distribution of SB is normal. The value of skewness coefficient 0.26 confirms that the distribution of the team’s SB is normally distributed. The team’s SB from one, two, and three standard deviations from mean is 60.0%, 100%, and 100%, respectively.

The average revenue of teams for the period 1989 to 2006 was about $1.63 million (SD = 0.75). The coefficient of variation for revenue was about 46%. The range of revenue for this period was about $2.35 million with minimum and maximum revenue is $0.51 million and $2.87 million, respectively. About one-quarter of revenue for the period 1989 to 2006 was below $1.09 million, about half of revenue was below $1.41 million, and about one-quarter of revenue was above $2.35 million. The value of skewness coefficient 0.22 suggests that the distribution of revenue for the period 1989 to 2006 is approximately normally distributed. The team’s revenue from one, two, and three standard deviations from mean is 61.1%, 100%, and 100%, respectively.

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