FINAL STATISTICS PROJECT

A Statistical SurveyonAttendance the YearFollowingaWorldSeriesWin
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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 Americanthanapple pie andChevrolet motors.Baseball is one of the oldestAmerican
sportsthat are still playedtoday. Whatwasonce a game playedinsmall rural dirtlots,baseball hasnow become one of
the most popularprofessional Americansports.Stadiumswere constructedtohouse the few hundredfanswhocheered
on the earliestof teams.Battinghelmetsweren’tconstructedyet,paddedgloveswerenon-existent,andeventhe left
fieldercouldpitch.Today,largerandgranderstadiumshave beenimplementedtoseatupwardsof fortythousand
people pergame.AsTV hasemerged,there are more people thatwatchbaseball thaneverwhichtranslatesintomore
fans.The more fansa team has,the more likelytheyare tofill the seatsintheirhome stadium. The mostcovetedseats
inbaseball are to watchthe Fall Classic,the WorldSeries. Stadiumspackwithfansforthe opportunitytosee theirteam
have a chance to win the mostcovetedprize inMajor League Baseball:the WorldSeriesTrophy.Teamsplayhardall
yearfor a shot at it: to be the bestteamin baseball forthe year.
II. Hypothesis
The objective of thisexperimentistocompare the attendance of the WorldSeriesChampiontothe restof the
teamsinthat particulardivision attheirrespective home fields.We suspected thatthe attendance wouldremainthe
same because the same numberof fans that show up to the othergameswould be presentregardlessof whowonthe
WorldSeriesasit isnot theirteam. To do thiswe analyzedthe attendance of the lastthirty yearsof baseball
attendancesacross six teamsperyear.Five of whichwere the divisional teamsthatdidn’twinandthe sixth teamwas
the World Serieswinner.
III. Statistical Methods
To compare the change inattendance of the WorldSerieswinner,we usedthe otherteamsinthe divisiontoobtain
a comparisonforthe average teamsinthe league.The informationforthe attendance foreachteamwasobtainedfrom

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baseball-reference.com.Asthe size of stadiumshasnotchangedsignificantlyinthe past30 years,we didnot feel the
needtoadjustthe data to make reasonable comparisons.
The test that isneededforthissetof data isa large sample hypothesistestforapopulationmean.Thisisa
reasonable testforthe givendataas the data setis largerthan thirty.We will use the average of the otherteamsinthe
divisionof the WorldSerieswinnerasthe mean.The meanof the World Serieswinnerswillthenbe ourlarge sample
populationmean.The standarddeviationof the WorldSerieswinnerswill thenbe obtainedfromthe givendata.
The data collectedforthe sample rangedfromthe winnersof the 1980 World Seriesuptothe winnerof the 2013
WorldSeriessothat we had the data for boththe year that theywonandthe followingyear.Of those years,the 1994
seasonwascancelledsothere will be nodatafor that year.There were gamesplayedin1994 so the data in1993 will be
affectedshowinglarge decreasesinattendance.We alsohave outliersforthe yearsof 1980 and 1981. This wasdue to
the shortenedseasonin1981. Since the seasonwasshortened,the attendance numbersforthese seasonsgiveusa
large attendance decrease in1980 anda large spike in1981. For these reasonsthose yearswill notbe includedinthe
calculationof the meansor standarddeviation.Thisleavesuswithasample size of 30 whichislarge enoughstill thatwe
can assume a normal distribution.
IV. Assumption
Since we have a sample size largerthan30 we can assume that the sample isnormal andcan use the Z tables.Also
since the yearsof 1980 and1981 were outliers,we didnotinclude theminouranalysisof the data,asexplainedinthe
Statistical Methodssection.
V. Hypothesistest
We useda two-tailedhypothesistestforthe average attendance change of the WorldSerieswinnercomparedto
the average attendance change of the teamsinthe same divisionasthe WorldSerieswinner.The null hypothesisisthat

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the percentattendance change forthe WorldSerieswinneristhe same asthat of the otherteamsinthe division.The
alternative hypothesisisthatthe twoare notequal.
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.
in their Division. Values from Table 1 within the Appendix were used to plot this graph.

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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.
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 samedivision as the World Series winners experienc ed
a .649% increase the following season.
VII. Sample Calculations
Average PercentDifference from1982-2013: WorldSeriesWinner/DivisionPercentDifference
Note:The year 1993 wasexcluded,reasoning being stated in section III statistical methods.
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 =
𝑆𝑢𝑚 𝑜𝑓 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑓𝑜𝑟 𝑊𝑜𝑟𝑙𝑑 𝑆𝑒𝑟𝑖𝑒𝑠 𝑊𝑖𝑛𝑛𝑒𝑟 (1982 − 2013)
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑌𝑒𝑎𝑟𝑠 (2013 − 1982)
𝑋 100
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 =
−38.20+51.55+9.75…5.43−.24+4.33
30
𝑋 100 = 7.58%
Z-score:
𝑧 =
𝛸−µ0
𝜎/√ 𝑛
→ 𝑧 =
7.58−0.649
13.95/√30
= 2.72

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Example of PercentDifference:1982 WorldSeriesWinner
𝐺𝑎𝑚𝑒 𝐴𝑡𝑡𝑒𝑛𝑑𝑎𝑛𝑐𝑒 𝑦𝑒𝑎𝑟 𝑎𝑓𝑡𝑒𝑟 𝑤𝑜𝑟𝑙𝑑 𝑠𝑒𝑟𝑖𝑒𝑠 𝑤𝑖𝑛−𝐺𝑎𝑚𝑒 𝐴𝑡𝑡𝑒𝑛𝑑𝑎𝑛𝑐𝑒 𝑦𝑒𝑎𝑟 𝑜𝑓 𝑊𝑜𝑟𝑙𝑑 𝑆𝑒𝑟𝑖𝑒𝑠 𝑊𝑖𝑛
𝐺𝑎𝑚𝑒 𝐴𝑡𝑡𝑒𝑛𝑑𝑎𝑛𝑐𝑒 𝑦𝑒𝑎𝑟 𝑜𝑓 𝑊𝑜𝑟𝑙𝑑 𝑆𝑒𝑟𝑖𝑒𝑠 𝑊𝑖𝑛
𝑋 100 = % Difference
Ex.
% Difference =
2,317,914 − 2,111,906
2,111,906
𝑋 100 = 9.75%
Example of Average PercentDifference:1982 League Average
The Individual PercentDifference of eachDivisionteamcanbe foundby applyingthe same equationshownabove for
Percentdifference toeachindividual team’sattendancestatsfoundinthe spreadsheet.
𝑆𝑢𝑚 𝑜𝑓 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑜𝑓 𝐷𝑖𝑣𝑖𝑠𝑖𝑜𝑛 𝑇𝑒𝑎𝑚𝑠
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑇𝑒𝑎𝑚𝑠 𝑖𝑛 𝑎 𝐷𝑖𝑣𝑖𝑠𝑖𝑜𝑛
𝑋 100 =
(−10.44 + 19.71 + 18.45 − 15.89)
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𝑋 100 = 2.96%
VIII. Analysis& Discussion
The resultsof the hypothesistestyieldedaZ-score of 2.72 as showninthe sample calculations.The corresponding
percentile forthisZ-score is99.67%.Using thisas a two-tailedtestthe probabilitythatthe average attendance change
of the WorldSerieswinneris.0066. Thisis certainlyasignificantresultasitis a verylow probability.Asisseen inFigure
5, while the otherteamsinthe divisionmaintainedasteadyattendance withaverage attendance increase beingless
than 1%, the average increase thatisseeninthe attendance of the WorldSerieswinner isgreaterthan7%.In fact on
onlythree occasionsisitseenthat the winnerof the WorldSerieshasa significantdecrease inattendance whichis
showninFigure 1. In 1993 the decrease isdue to the shortenedseason.1984 and1997 can certainlybe considered
anomaliesasthe otherteamsintheirdivisioninthose yearssaw increasesinthe average attendance.Alsoseenin
Figure 1 is while the WorldSerieswinneralmostalwayssaw anincrease,the otherteamsinthe divisionvariedtoa

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much greaterextent.Gainsmanyyearsare onlymarginal while asignificantnumberof yearsthe otherteamssawan
average loss.
In analyzingthe datainFigures1 through4 and bothtablesone andtwo, we see thatattendance gainsare generally
infavor of the World Serieswinnersascomparedwiththe otherteamsintheirdivision.Infigures3and4 it is evident
that the WorldSerieswinnerinthe 90’s and00’s has hada significantgainintheirattendance the yearafteraWorld
Serieswin.
IX. Conclusion
Witha Z-score as highas 2.72 whichresultedina two-tailedtestresultof .0066 we can safelyrejectthe null
hypothesisthatthe attendance change of the WorldSerieswinneristhe same asthe attendance change of the other
teamsintheirdivision.Sincewe see thatthe attendance gainismuchlargerfor the WorldSerieswinnerwe can
conclude thatwinningiscertainlybeneficialforapositive gaininattendance forthe mostsuccessful team.

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X. References
"Complete Baseball TeamandBaseball TeamEncyclopedias." Baseball-Reference.com.N.p.,n.d. Web.05Dec. 2014.
Navidi,WilliamCyrus. StatisticsforEngineersand Scientists.Boston:McGraw-Hill HigherEducation,2008. Print.
Picture onFront Coverisa picture takenduringthe 2014 World SeriesandwasfoundusingGoogle Images.

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XI. Appendix
Year
World Series
Winner
Game Attendance
year of World Series
win
Game Attendance
year after world
series win
Difference
Percent
Difference
(%)
League
Other Divisional
Teams
Game Attendance
win
Game Attendance
year after world
series win
Difference
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 19.71
Chicago Cubs 1,249,278 1,479,717 230,439 18.45
New York Mets 1,323,036 1,112,774 210,262 -15.89
Boston Red Sox 1,782,285 1,661,615 120,670 -6.77
Detroit Tigers 1,829,636 2,704,794 875,158 47.83
New York Yankees 2,257,976 1,821,815 436,161 -19.32
Toronoto Blue Jays 1,930,415 2,110,009 179,594 9.30
New York Yankees 1,821,815 2,214,587 392,772 21.56
Boston Red Sox 1,661,618 1,786,633 125,015 7.52
Baltimore Orioles 2,045,784 2,132,387 86,603 4.23
California Angels 2,567,427 2,655,872 88,445 3.44
Detroit Tigers 2,286,609 1,899,437 387,172 -16.93
Chicago White Sox 1,669,888 1,424,313 245,575 -14.71
Minnesota Twins 1,651,814 1,255,453 396,361 -24.00
San Fransisco 1,528,748 1,917,168 388,420 25.41
Cincinati Reds 1,692,432 2,185,205 492,773 29.12
San Diego Padres 1,805,716 1,454,061 351,655 -19.47
Los Angeles 3,023,208 2,797,409 225,799 -7.47
Kansas City Royals 2,392,471 2,350,184 42,287 -1.77
Oakland A's 1,678,921 1,570,035 108,886 -6.49
Los Angeles Angels 2,696,299 2,340,925 355,374 -13.18
San Diego Padres 1,506,896 2,009,031 502,135 33.32
Cincinati Reds 2,072,528 1,979,320 93,208 -4.50
San Fransisco 1,785,297 2,059,701 274,404 15.37
New York Mets 3,055,445 2,918,710 136,735 -4.48
California Angels 2,647,291 2,555,688 91,603 -3.46
Minnesota Twins 2,277,438 1,751,584 525,854 -23.09
Seattle Mariners 1,298,443 1,509,727 211,284 16.27
Los Angeles 3,002,396 3,348,170 345,774 11.52
San Fransisco 1,975,528 1,737,478 238,050 -12.05
Houston Astros 1,310,927 1,196,152 114,775 -8.76
San Diego Padres 1,856,396 1,804,289 52,107 -2.81
Texas Rangers 2,297,720 2,198,231 99,489 -4.33
Oakland A's 2,713,493 2,494,160 219,333 -8.08
Detroit Tigers 1,423,963 1,971,431 547,468 38.45
New York Yankees 1,748,737 2,416,942 668,205 38.21
Boston Red Sox 2,468,570 2,422,021 46,549 -1.89
Detroit Tigers 1,971,431 1,184,783 786,648 -39.90
New York Yankees 2,416,942 1,675,556 741,386 -30.67
Baltimore 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 24.75
Phillidelphia 2,043,598 1,801,677 241,921 -11.84
Florida Marlins 1,700,466 1,746,767 46,301 2.72
Montreal Expos 1,309,618 1,616,709 307,091 23.45
Detroit Tigers 1,168,610 1,365,157 196,547 16.82
Boston Red Sox 2,315,231 2,226,136 89,095 -3.85
AL 3.9729567881996
New York
Yankees
2,250,877 2,580,325 329,448.00 14.64
X
1995 Atlanta Braves 2,561,831 2,901,242 339,411.00 13.25 NL 9.771471021
X X X X X X1994
NO WORLD
SERIES
X X X X
AL 19.23352808
1993
Toronto Blue
Jays
4,057,947 2,907,933 1,150,014.00 -28.34 AL -31.92485301
1992
Toronto Blue
Jays
4,028,318 4,057,947 29,629.00 0.74
NL -3.02387156
1991
Minnesota
Twins
2,293,842 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
1989
Oakland
Athletics
2,667,225 2,900,217 232,992.00 8.74 AL -4.917854467
1988
Los Angeles
Dodgers
2,980,262 2,944,653 35,609.00 -1.19
NL 6.895146105
1987
Minnesota
Twins
2,081,976 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
1985
Kansas City
Royals
2,162,717 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
1983
Baltimore
Orioles
2,042,071 2,045,784 3,713.00 0.18 AL 7.762190778
1982
St. Louis
Cardinals
2,111,906 2,317,914 206,008.00 9.75
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)

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Year
World Series
Winner
Game Attendance
win
Game Attendance
year after world
series win
Difference
Percent
Difference
(%)
League
Other Divisional
Teams
Game Attendance
win
Game Attendance
year after world
series win
Difference
Percent
Difference
(%)
Average
Percent
Difference (%)
Atlanta Braves 3,464,488 3,360,860 103,628 -2.99
New York Mets 1,766,174 2,287,948 521,774 29.54
Montreal Expos 1,497,609 914,909 582,700 -38.91
Phillidelphia 1,490,638 1,715,722 225,084 15.10
Tampa Bay Rays 2,506,293 1,562,827 943,466 -37.64
Toronoto Blue Jays 2,454,303 2,163,464 290,839 -11.85
Baltimore Orioles 3,684,650 3,433,150 251,500 -6.83
Boston Red Sox 2,314,704 2,446,162 131,458 5.68
Tampa Bay Rays 1,562,827 1,449,673 113,154 -7.24
Boston Red Sox 2,446,162 2,585,895 139,733 5.71
Tampa Bay Rays 1,449,673 1,298,365 151,308 -10.44
Boston Red Sox 2,585,895 2,625,333 39,438 1.53
San Diego Padres 2,378,128 2,220,601 157,527 -6.62
Colorado Rockies 3,166,821 2,737,838 428,983 -13.55
Los Angeles 3,017,143 3,131,255 114,112 3.78
Arizona D-Backs 2,736,451 3,198,977 462,526 16.90
Oakland A's 2,169,811 2,216,596 46,785 2.16
Seattle 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 -3.06
Phillidelphia 2,259,948 3,250,092 990,144 43.81
Montreal Expos 1,025,639 749,550 276,089 -26.92
New York Mets 2,140,599 2,318,951 178,352 8.33
Tampa Bay Rays 1,274,911 1,141,669 133,242 -10.45
New York Yankees 3,775,292 4,090,696 315,404 8.35
Cleveland Indians 2,013,763 1,997,995 15,768 -0.78
Minnesota Twins 2,034,243 2,285,018 250,775 12.33
Detroit Tigers 2,024,431 2,595,937 571,506 28.23
Kansas City Royals 1,371,181 1,372,638 1,457 0.11
Houston Astros 3,022,763 3,020,405 2,358 -0.08
Cincinati Reds 2,134,607 2,058,593 76,014 -3.56
Milwaukee Brewers 2,335,643 2,869,144 533,501 22.84
Pittsburgh Pirates 1,861,549 1,749,142 112,407 -6.04
Tampa Bay Rays 1,387,603 1,811,986 424,383 30.58
New York Yankees 4,271,083 4,298,655 27,572 0.65
New York Mets 4,042,045 3,168,571 873,474 -21.61
Florida Marlins 1,335,076 1,464,109 129,033 9.66
Atlanta Braves 2,532,834 2,373,631 159,203 -6.29
Washington 2,320,400 1,817,226 503,174 -21.68
Tampa Bay Rays 1,874,962 1,864,999 9,963 -0.53
Boston Red Sox 3,062,699 3,046,445 16,254 -0.53
San Diego Padres 2,131,774 2,143,018 11,244 0.53
Colorado Rockies 2,875,245 2,909,777 34,532 1.20
Los Angeles 3,562,320 2,935,139 627,181 -17.61
Arizona D-Backs 2,056,697 2,105,432 48,735 2.37
Milwaukee Brewers 3,071,373 2,831,385 239,988 -7.81
Cincinati Reds 2,213,588 2,347,251 133,663 6.04
Pittsburgh Pirates 1,940,429 2,091,918 151,489 7.81
Chicago Cubs 3,017,966 2,882,756 135,210 -4.48
San Diego Padres 2,123,721 2,166,691 42,970 2.02
Colorado Rockies 2,630,458 2,793,828 163,370 6.21
Los Angeles 3,324,246 3,743,527 419,281 12.61
Arizona D-Backs 2,177,617 2,134,895 42,722 -1.96
Tampa Bay Rays 1,510,300 1,446,464 63,836 -4.23
New 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
2012
San Francisco
Giants
3,377,371 3,369,106 8,265.00 -0.24
NL -3.376983866
2011
St. Louis
Cardinals
3,093,954 3,262,109 168,155.00 5.43 NL 0.387851806
2010
San Francisco
Giants
3,037,443 3,387,303 349,860.00 11.52
NL -9.978806382
2009
New York
Yankees
3,719,358 3,765,807 46,449.00 1.25 AL -7.620521361
2008
Philadelphia
Phillies
3,422,583 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
2006
St. Louis
Cardinals
3,407,104 3,552,180 145,076.00 4.26
AL -0.098353312
2005
Chicago White
Sox
2,342,833 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
2002
Anaheim
Angels
2,305,547 3,061,094 755,547.00 32.77
AL -0.687311207
2001
Arizona
Diamonds
2,736,451 3,198,977 462,526.00 16.90 NL 0.128590472
2000
New York
Yankees
3,055,435 3,264,907 209,472.00 6.86
AL -12.66010164
1999
New York
Yankees
3,292,736 3,055,435 237,301.00 -7.21 AL -6.662784453
1998
New York
Yankees
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
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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