FINAL STATISTICS PROJECT

A Statistical Survey on Attendance the Year Following a World Series Win

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Table of Contents

INTRODUCTION…………………………………………………………………………………………………………………………………………………………… 3

HYPOTHESIS…………………………………………………………………………………………………..………………………………………………………………3

STATISTICAL METHODS……………………………………………………………………………………………………………………………………….…………3

ASSUMPTION…………………………………………………………………………………………………………………………………………………………………4

HYPOTHESIS TEST………………………………………………………………………………………………………………………………..…………………………4

RESULTS…………………………………………………………………………………………………………………………………………………………………………5

SAMPLE CALCULATIONS…………………………………………………………………………………………………………………………………………………7

ANALYSIS AND DISCUSSION……………………………………………………………………………………………………………………………………………8

CONCLUSION………………………………………………………………………………………………………………………………………………………………….9

REFERENCES……………………………………………………………………………………………………………………………………………………….………….10

APPENDIX………………………………………………………………………………………………………………………………………….……………………………11

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I. Introduction

Major League Baseball: More American than apple pie and Chevrolet motors. Baseball is one of the oldest American

sports that are still played today. What was once a game played in small rural dirt lots, baseball has now become one of

the most popular professional American sports. Stadiums were constructed to house the few hundred fans who cheered

on the earliest of teams. Batting helmets weren’t constructed yet, padded gloves were non-existent, and even the left

fielder could pitch. Today, larger and grander stadiums have been implemented to seat upwards of forty thousand

people per game. As TV has emerged, there are more people that watch baseball than ever which translates into more

fans. The more fans a team has, the more likely they are to fill the seats in their home stadium. The most coveted seats

in baseball are to watch the Fall Classic, the World Series. Stadiums pack with fans for the opportunity to see their team

have a chance to win the most coveted prize in Major League Baseball: the World Series Trophy. Teams play hard all

year for a shot at it: to be the best team in baseball for the year.

II. Hypothesis

The objective of this experiment is to compare the attendance of the World Series Champion to the rest of the

teams in that particular division at their respective home fields. We suspected that the attendance would remain the

same because the same number of fans that show up to the other games would be present regardless of who won the

World Series as it is not their team. To do this we analyzed the attendance of the last thirty years of baseball

attendances across six teams per year. Five of which were the divisional teams that didn’t win and the sixth team was

the World Series winner.

III. Statistical Methods

To compare the change in attendance of the World Series winner, we used the other teams in the division to obtain

a comparison for the average teams in the league. The information for the attendance for each team was obtained from

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baseball-reference.com. As the size of stadiums has not changed significantly in the past 30 years, we did not feel the

need to adjust the data to make reasonable comparisons.

The test that is needed for this set of data is a large sample hypothesis test for a population mean. This is a

reasonable test for the given data as the data set is larger than thirty. We will use the average of the other teams in the

division of the World Series winner as the mean. The mean of the World Series winners will then be our large sample

population mean. The standard deviation of the World Series winners will then be obtained from the given data.

The data collected for the sample ranged from the winners of the 1980 World Series up to the winner of the 2013

World Series so that we had the data for both the year that they won and the following year. Of those years, the 1994

season was cancelled so there will be no data for that year. There were games played in 1994 so the data in 1993 will be

affected showing large decreases in attendance. We also have outliers for the years of 1980 and 1981. This was due to

the shortened season in 1981. Since the season was shortened, the attendance numbers for these seasons give us a

large attendance decrease in 1980 and a large spike in 1981. For these reasons those years will not be included in the

calculation of the means or standard deviation. This leaves us with a sample size of 30 which is large enough still that we

can assume a normal distribution.

IV. Assumption

Since we have a sample size larger than 30 we can assume that the sample is normal and can use the Z tables. Also

since the years of 1980 and 1981 were outliers, we did not include them in our analysis of the data, as explained in the

Statistical Methods section.

V. Hypothesis test

We used a two-tailed hypothesis test for the average attendance change of the World Series winner compared to

the average attendance change of the teams in the same division as the World Series winner. The null hypothesis is that

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the percent attendance change for the World Series winner is the same as that of the other teams in the division. The

alternative hypothesis is that the two are not equal.

VI. Results

Figure 1. Graph shows the Percent Difference in Attendance between 1982 and 2013 for the World Series Winners and Other teams in their Division. Values from Table 1 and Table 2 within the Appendix were used to plot this graph.

Figure 2. Graph shows the Percent Difference in Attendance between 1982 and 1991 for the World Series Winners and Other teams in their Division. Values from Table 1 within the Appendix were used to plot this graph.

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Figure 3. Graph shows the Percent Difference in Attendance between 1992 and 2001 for the World Series Winners and Other teams in their Division. Values from Table 1 and Table 2 within the Appendix were used to plot this graph. There was no World Series in

1994.

Figure 4. Graph shows the Percent Difference in Attendance between 2002 and 2013 for the World Series Winners and Other teams in their Division. Values from Table 2 within the Appendix were used to plot this graph.

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Figure 5. Graph shows the Average Percent Difference in Attendance between 1982 and 1991 for the World Series Winners and Other teams in their Division. Values from Table 1 and Table 2 within the Appendix were used to plot this graph. The average

Percent Difference in Attendance experienced in the year after a World Series win between 1982 and 2013 for the World Series winners was 7.58% increase in attendance. The other teams who were in the same division as the World Series winners experienced

a .649% increase the following season.

VII. Sample Calculations

Average Percent Difference from 1982-2013: World Series Winner/Division Percent Difference

Note: The year 1993 was excluded, reasoning being stated in section III statistical methods.

Average Percent Difference=∑ of Percent Difference forWorld SeriesWinner (1982−2013)Number of Years(2013−1982)

X 100

%

Z-score:

z=Χ−µ0σ /√n

→ z=7.58−0.64913.95 /√30

=2.72

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Example of Percent Difference: 1982 World Series Winner

Game Attendance year after world serieswin−Game Attendance year of World SeriesWinGame Attendance year of World SeriesWin

X 100= % Difference

Ex.

%Difference=2,317,914−2,111,9062,111,906

X 100=9.75%

Example of Average Percent Difference: 1982 League Average

The Individual Percent Difference of each Division team can be found by applying the same equation shown above for Percent difference to each individual team’s attendance stats found in the spreadsheet.

∑ of Percent Difference of DivisionTeamsNumber of Teams∈a Division

X 100=(−10.44+19.71+18.45−15.89)

4X 100=2.96%

VIII. Analysis & Discussion

The results of the hypothesis test yielded a Z-score of 2.72 as shown in the sample calculations. The corresponding

percentile for this Z-score is 99.67%. Using this as a two-tailed test the probability that the average attendance change of

the World Series winner is .0066. This is certainly a significant result as it is a very low probability. As is seen in Figure 5,

while the other teams in the division maintained a steady attendance with average attendance increase being less than

1%, the average increase that is seen in the attendance of the World Series winner is greater than 7%. In fact on only

three occasions is it seen that the winner of the World Series has a significant decrease in attendance which is shown in

Figure 1. In 1993 the decrease is due to the shortened season. 1984 and 1997 can certainly be considered anomalies as

the other teams in their division in those years saw increases in the average attendance. Also seen in Figure 1 is while

the World Series winner almost always saw an increase, the other teams in the division varied to a much greater extent.

Gains many years are only marginal while a significant number of years the other teams saw an average loss.

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In analyzing the data in Figures 1 through 4 and both tables one and two, we see that attendance gains are generally

in favor of the World Series winners as compared with the other teams in their division. In figures 3 and 4 it is evident

that the World Series winner in the 90’s and 00’s has had a significant gain in their attendance the year after a World

Series win.

IX. Conclusion

With a Z-score as high as 2.72 which resulted in a two-tailed test result of .0066 we can safely reject the null

hypothesis that the attendance change of the World Series winner is the same as the attendance change of the other

teams in their division. Since we see that the attendance gain is much larger for the World Series winner we can

conclude that winning is certainly beneficial for a positive gain in attendance for the most successful team.

X. References

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"Complete Baseball Team and Baseball Team Encyclopedias." Baseball-Reference.com. N.p., n.d. Web. 05 Dec. 2014.

Navidi, William Cyrus. Statistics for Engineers and Scientists. Boston: McGraw-Hill Higher Education, 2008. Print.

Picture on Front Cover is a picture taken during the 2014 World Series and was found using Google Images.

XI. Appendix

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Year World Series Winner

Game Attendance year of World Series

win

Game Attendance year after world

series winDifference

Percent Difference

(%)League Other Divisional

Teams


win



Percent Difference

(%)

Average Percent

Difference (%)Phillidelphia 2,376,394 2,128,339 248,055 -10.44

Pittsburgh Pirates 1,024,106 1,225,916 201,810 19.71Chicago Cubs 1,249,278 1,479,717 230,439 18.45

New York Mets 1,323,036 1,112,774 210,262 -15.89Boston Red Sox 1,782,285 1,661,615 120,670 -6.77Detroit Tigers 1,829,636 2,704,794 875,158 47.83

New York Yankees 2,257,976 1,821,815 436,161 -19.32Toronoto Blue Jays 1,930,415 2,110,009 179,594 9.30Toronoto Blue Jays 2,110,009 2,468,925 358,916 17.01New York Yankees 1,821,815 2,214,587 392,772 21.56

Boston Red Sox 1,661,618 1,786,633 125,015 7.52Baltimore Orioles 2,045,784 2,132,387 86,603 4.23California Angels 2,567,427 2,655,872 88,445 3.44

Detroit Tigers 2,286,609 1,899,437 387,172 -16.93Chicago White Sox 1,669,888 1,424,313 245,575 -14.71Minnesota Twins 1,651,814 1,255,453 396,361 -24.00

San Fransisco 1,528,748 1,917,168 388,420 25.41Cincinati Reds 1,692,432 2,185,205 492,773 29.12

San Diego Padres 1,805,716 1,454,061 351,655 -19.47Los Angeles 3,023,208 2,797,409 225,799 -7.47

Chicago White Sox 1,208,060 1,115,749 92,311 -7.64Kansas City Royals 2,392,471 2,350,184 42,287 -1.77

Oakland A's 1,678,921 1,570,035 108,886 -6.49Los Angeles Angels 2,696,299 2,340,925 355,374 -13.18San Diego Padres 1,506,896 2,009,031 502,135 33.32

Cincinati Reds 2,072,528 1,979,320 93,208 -4.50San Fransisco 1,785,297 2,059,701 274,404 15.37

New York Mets 3,055,445 2,918,710 136,735 -4.48Kansas City Royals 2,477,700 2,244,956 232,744 -9.39California Angels 2,647,291 2,555,688 91,603 -3.46Minnesota Twins 2,277,438 1,751,584 525,854 -23.09Seattle Mariners 1,298,443 1,509,727 211,284 16.27

Los Angeles 3,002,396 3,348,170 345,774 11.52San Fransisco 1,975,528 1,737,478 238,050 -12.05

Houston Astros 1,310,927 1,196,152 114,775 -8.76San Diego Padres 1,856,396 1,804,289 52,107 -2.81

Chicago White Sox 2,934,154 2,681,156 252,998 -8.62Texas Rangers 2,297,720 2,198,231 99,489 -4.33

Oakland A's 2,713,493 2,494,160 219,333 -8.08Kansas City Royals 2,161,537 1,867,689 293,848 -13.59

Detroit Tigers 1,423,963 1,971,431 547,468 38.45New York Yankees 1,748,737 2,416,942 668,205 38.21Baltimore Orioles 3,567,819 3,644,965 77,146 2.16

Boston Red Sox 2,468,570 2,422,021 46,549 -1.89Detroit Tigers 1,971,431 1,184,783 786,648 -39.90

New York Yankees 2,416,942 1,675,556 741,386 -30.67Baltimore Orioles 3,644,965 2,535,359 1,109,606 -30.44

Boston Red Sox 2,422,021 1,775,818 646,203 -26.68

New York Mets 1,273,183 1,588,323 315,140 24.75Phillidelphia 2,043,598 1,801,677 241,921 -11.84

Florida Marlins 1,700,466 1,746,767 46,301 2.72Montreal Expos 1,309,618 1,616,709 307,091 23.45

Toronoto Blue Jays 2,559,573 2,589,297 29,724 1.16Detroit Tigers 1,168,610 1,365,157 196,547 16.82

Baltimore Orioles 3,646,950 3,711,132 64,182 1.76Boston Red Sox 2,315,231 2,226,136 89,095 -3.85

AL 3.9729567881996New York Yankees

2,250,877 2,580,325 329,448.00 14.64

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1995 Atlanta Braves 2,561,831 2,901,242 339,411.00 13.25 NL 9.771471021

X X X X X X1994NO WORLD

SERIESX X X X

AL 19.23352808

1993Toronto Blue

Jays4,057,947 2,907,933 1,150,014.00 -28.34 AL -31.92485301

1992Toronto Blue

Jays4,028,318 4,057,947 29,629.00 0.74

NL -3.02387156

1991Minnesota

Twins2,293,842 2,482,428 188,586.00 8.22 AL -8.657467805

1990 Cincinnati Reds 2,400,892 2,372,377 28,515.00 -1.19

NL 9.930063187

1989Oakland Athletics

2,667,225 2,900,217 232,992.00 8.74 AL -4.917854467

1988Los Angeles

Dodgers2,980,262 2,944,653 35,609.00 -1.19

NL 6.895146105

1987Minnesota

Twins2,081,976 3,030,672 948,696.00 45.57 AL -7.268576007

1986 New York Mets 2,767,601 3,034,129 266,528.00 9.63

AL 12.58161919

1985Kansas City

Royals2,162,717 2,320,794 158,077.00 7.31 AL -13.04720823

1984 Detroit Tigers 2,704,794 2,286,609 418,185.00 -15.46

NL 2.955265247

1983Baltimore

Orioles2,042,071 2,045,784 3,713.00 0.18 AL 7.762190778

1982St. Louis Cardinals

2,111,906 2,317,914 206,008.00 9.75

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Table 1. Table displays the Attendance each year for both the World Series winner and the teams in their division. Attendance is shown for the year the World Series was won and also the attendance the following year. The Percent Difference in attendance was

calculated for both the World Series winner and the other Teams in the division. (Displays years 1982-1996)


Year World Series Winner


win



Percent Difference

(%)League Other Divisional

Teams


win



Percent Difference

(%)

Average Percent

Difference (%)Atlanta Braves 3,464,488 3,360,860 103,628 -2.99New York Mets 1,766,174 2,287,948 521,774 29.54Montreal Expos 1,497,609 914,909 582,700 -38.91

Phillidelphia 1,490,638 1,715,722 225,084 15.10Tampa Bay Rays 2,506,293 1,562,827 943,466 -37.64

Toronoto Blue Jays 2,454,303 2,163,464 290,839 -11.85Baltimore Orioles 3,684,650 3,433,150 251,500 -6.83

Boston Red Sox 2,314,704 2,446,162 131,458 5.68Tampa Bay Rays 1,562,827 1,449,673 113,154 -7.24


Boston Red Sox 2,446,162 2,585,895 139,733 5.71Tampa Bay Rays 1,449,673 1,298,365 151,308 -10.44

Toronoto Blue Jays 1,705,712 1,915,438 209,726 12.30Baltimore Orioles 3,297,031 3,094,841 202,190 -6.13

Boston Red Sox 2,585,895 2,625,333 39,438 1.53San Diego Padres 2,378,128 2,220,601 157,527 -6.62Colorado Rockies 3,166,821 2,737,838 428,983 -13.55

Los Angeles 3,017,143 3,131,255 114,112 3.78Arizona D-Backs 2,736,451 3,198,977 462,526 16.90

Oakland A's 2,169,811 2,216,596 46,785 2.16Seattle Mariners 3,542,938 3,268,509 274,429 -7.75

Texas Rangers 2,352,397 2,094,394 258,003 -10.97

Atlanta Braves 2,401,084 2,327,565 73,519 -3.06Phillidelphia 2,259,948 3,250,092 990,144 43.81

Montreal Expos 1,025,639 749,550 276,089 -26.92New York Mets 2,140,599 2,318,951 178,352 8.33Tampa Bay Rays 1,274,911 1,141,669 133,242 -10.45

Toronoto Blue Jays 1,900,041 2,014,995 114,954 6.05Baltimore Orioles 2,744,018 2,624,740 119,278 -4.35New York Yankees 3,775,292 4,090,696 315,404 8.35Cleveland Indians 2,013,763 1,997,995 15,768 -0.78Minnesota Twins 2,034,243 2,285,018 250,775 12.33

Detroit Tigers 2,024,431 2,595,937 571,506 28.23Kansas City Royals 1,371,181 1,372,638 1,457 0.11

Houston Astros 3,022,763 3,020,405 2,358 -0.08Cincinati Reds 2,134,607 2,058,593 76,014 -3.56

Milwaukee Brewers 2,335,643 2,869,144 533,501 22.84Pittsburgh Pirates 1,861,549 1,749,142 112,407 -6.04

Tampa Bay Rays 1,387,603 1,811,986 424,383 30.58Toronoto Blue Jays 2,360,644 2,399,786 39,142 1.66Baltimore Orioles 2,164,822 1,950,075 214,747 -9.92New York Yankees 4,271,083 4,298,655 27,572 0.65

New York Mets 4,042,045 3,168,571 873,474 -21.61Florida Marlins 1,335,076 1,464,109 129,033 9.66Atlanta Braves 2,532,834 2,373,631 159,203 -6.29

Washington 2,320,400 1,817,226 503,174 -21.68Tampa Bay Rays 1,874,962 1,864,999 9,963 -0.53


Boston Red Sox 3,062,699 3,046,445 16,254 -0.53San Diego Padres 2,131,774 2,143,018 11,244 0.53Colorado Rockies 2,875,245 2,909,777 34,532 1.20

Los Angeles 3,562,320 2,935,139 627,181 -17.61Arizona D-Backs 2,056,697 2,105,432 48,735 2.37

Milwaukee Brewers 3,071,373 2,831,385 239,988 -7.81Cincinati Reds 2,213,588 2,347,251 133,663 6.04

Pittsburgh Pirates 1,940,429 2,091,918 151,489 7.81Chicago Cubs 3,017,966 2,882,756 135,210 -4.48

San Diego Padres 2,123,721 2,166,691 42,970 2.02Colorado Rockies 2,630,458 2,793,828 163,370 6.21

Los Angeles 3,324,246 3,743,527 419,281 12.61Arizona D-Backs 2,177,617 2,134,895 42,722 -1.96Tampa Bay Rays 1,510,300 1,446,464 63,836 -4.23

Toronoto Blue Jays 2,536,562 2,375,525 161,037 -6.35Baltimore Orioles 2,357,561 2,464,473 106,912 4.53New York Yankees 3,279,589 3,401,624 122,035 3.72

NL 4.721246674

2013 Boston Red Sox 2,833,333 2,956,089 122,756.00 4.33 AL -0.57986019

2012San Francisco

Giants3,377,371 3,369,106 8,265.00 -0.24

NL -3.376983866


3,093,954 3,262,109 168,155.00 5.43 NL 0.387851806

2010San Francisco

Giants3,037,443 3,387,303 349,860.00 11.52

NL -9.978806382

2009New York Yankees

3,719,358 3,765,807 46,449.00 1.25 AL -7.620521361

2008Philadelphia

Phillies3,422,583 3,600,693 178,110.00 5.20

NL 3.291080463

2007 Boston Red Sox 2,970,755 3,048,250 77,495.00 2.61 AL 5.741925899


3,407,104 3,552,180 145,076.00 4.26

AL -0.098353312

2005Chicago White

Sox2,342,833 2,957,414 614,581.00 26.23 AL 9.970344897

2004 Boston Red Sox 2,837,294 2,847,888 10,594.00 0.37

AL -5.519096175

2003 Florida Marlins 1,303,215 1,723,105 419,890.00 32.22 NL 5.540980897

2002Anaheim

Angels2,305,547 3,061,094 755,547.00 32.77

AL -0.687311207

2001Arizona

Diamonds2,736,451 3,198,977 462,526.00 16.90 NL 0.128590472


3,055,435 3,264,907 209,472.00 6.86

AL -12.66010164


3,292,736 3,055,435 237,301.00 -7.21 AL -6.662784453


2,955,193 3,292,736 337,543.00 11.42

1997 Florida Marlins 2,364,387 1,730,384 634,003.00 -26.81 NL 0.685655709

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Table 2. Table displays the Attendance each year for both the World Series winner and the teams in their division. Attendance is shown for the year the World Series was won and also the attendance the following year. The Percent Difference in attendance was

calculated for both the World Series winner and the other Teams in the division. (Displays years 1997-2013)

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FINAL STATISTICS PROJECT