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Final

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McMaster University

Commerce

COMMERCE 2QA3

Fouzia Baki

Fall

Description

COMMERCE 2QA3
Professor Fouzia Baki
November 29, 2013
The Relationship Between Game Attendance and Team Performance in the NHL and
NBA
Surname Name Student Number E-mail
Joannou Chris 1206289 [email protected]
Murphy Heather 1206298 [email protected]
Prebianca Connor 1155946 [email protected]
Teymouri Fred
Contents Executive Summary..........................................................................................................1
I. Introduction.....................................................................................................................1
II. Literature Review..........................................................................................................2
III. Project Work.................................................................................................................2
Who.........................................................................................................................3
What........................................................................................................................3
Why.........................................................................................................................3
Where.....................................................................................................................3
When.......................................................................................................................3
How.........................................................................................................................3
Box Plot Method.....................................................................................................4
Figure 1........................................................................................................5
Histogram Method..................................................................................................6
Figure 2........................................................................................................6
Figure 3........................................................................................................6
Linear Regression Model........................................................................................7
Figure 4........................................................................................................7
Figure 5........................................................................................................7
IV. Results/Discussions/Recommendations......................................................................8
V. Conclusion...................................................................................................................10
Appendix A......................................................................................................................11
Appendix B......................................................................................................................12
Appendix C......................................................................................................................13
Appendix D......................................................................................................................14
Appendix E......................................................................................................................15
Notes...............................................................................................................................16
Bibliography.....................................................................................................................19
Secondary Sources..............................................................................................19
2 Executive Summary
***************************************************
I. Introduction
This statistics project will discuss and analyze the correlation, if any, between team
performance and fan attendance of two major professional sports leagues, in particular
the National Hockey League (NHL) and National Basketball League (NBA). The report
will serve the purpose to conclude if there is a correlation, whether it is increased team
performance leading to increased fan attendance, or increased fan attendance leading
to increased team performance, or there is no correlation at all.
Our hypothesis for this research project is that “There is a positive correlation between
team performance and fan attendance in the National Hockey and National Basketball
Leagues. Our group hypothesizes that increased team performance will have a direct
positive impact to increased fan attendance at home games.”
The group decided to address this circumstance because the topic is of much interest to
the group, as we are all sports fanatics, therefore we wanted to ensure that our hobbies
were incorporated in to our work. We also felt that it was prevalent in today’s society, as
it is important for decision makers in the sports industry to know if there is such a
correlation in order to be able to best allocate their finances.
This project is important from a business perspective, as it will allow many insights for
marketers and financial decision makers if there are any changes that they can make in
their strategies. For marketers, it will be important to note if fan attendance increases
team performance, as they should pay special attention in their marketing mix to
aspects affecting ticket sales. For financial decision makers, it will be important to
recognize if team performance increases fan attendance, as they should try to capitalize
on their budgets, maximizing them as much as possible to create the strongest team
possible.
For this project, we specifically considered several sub-topics, as they were important to
note while making conclusions in the project. We had to consider several different
3 topics, including the variation in fan base size (ie. The variation in market share due to
the home city of each team), ________.
The remainder of this report will address previous research that has been done on
similar topics, followed by explaining and elaborating on the statistics and work that
were gathered for the project. The methods used for the project will then be explained,
followed by the findings from the project, addressing some discussion points, and points
of recommendation. Lastly, conclusions of the report will be made on our findings, and
our overall learning experiences.
II. Literature Review
In some way, shape, or form, the correlation between the success of a team and the
number of people in attendance to watch their games is a subject of frequent
discussion. For example, it is common for a broadcaster to comment on how difficult or
easy a game might be for a road team on the opponent's home-court. Due to various
reasons, such as curiosity, the potential financial gains, etc. many people have delved
into the data to figure out if this hypothesis, and its variations, are indeed true.
One instance of research into this correlation can be seen in the article "An
investigation of home-advantage and other factors affecting English one-day cricket
1
matches" by Bruce Morley and Dennis Thomas. They discuss the idea behind "home-
field advantage", which means that a team has more than 50% chance of winning a
game on their home-court when there is a balance between the amount of games to be
played at home and on the road. Using this concept, they try to discover if it applies to
situations that do not meet the criteria of "home-field advantage"; one-day cricket
matches were chosen. 3
Their results proved that under a different psychological constraint, the concept
4
continues to hold true.
Moreover, Mahmoud M. Nourayi expands on this correlation by trying to understand if it
can translate to the financial success of a team; his research focuses on the 30 NBA
franchises. He visually shows that attendance and financial success are directly
4 correlated and that the amount of games won is a direct result of the foundation made
by the people within the organization, especially the players. This then leads to the
retention of the "key" athletes that helped won games, which develops a loyal fan
bases, which leads to strong attendance. 7
Looking through several research papers on this subject, there seems to be a lot of
insight to reasoning behind this correlation. With respect to the purpose of this paper,
Dr. Nourayi best describes the connection between attendance and games won as a
process rather than a direct or reciprocal relationship. Along with team success,
attendance records also imply a strong and loyal fan base. One can argue that there is
more emphasis on the latter than the former. One example being the Indiana Pacers
during the 2012 – 2013 NBA season. They were one of the more successful teams in
the league; with a 49-32 record, they became the Central Division Champions. 8
Unfortunately, they were ranked 25 in the league for their attendance record. One of 9
the reasons for this outcome would be because they had put together a team with many
players that were unknown to the general basketball fan base in Indiana after several
10
years in decline due to a team rebuild.
III. Project Work
In order to establish a strong statistical analysis to successfully research and determine
the correlation between attendance at games and overall performance of a team the
“Five W’s” (who, what, when, where and why, along with how) are imperative in creating
a foundation to the project. Answering these questions allow a context for data values to
form, which in turn makes them meaningful to the project. The approach taken with this
project was to rank the “Five W’s” as well as “how” in terms of importance and thus go
about forming the project.
The answers to the first to questions, who and what, were essential to our project as
without them there would be no useful information and as a result of these they were
the first two questions to be addressed. These were then followed by the when, where,
why and finally how.
5 Who
In terms of the “who,” the National Hockey League (NHL) and the National Basketball
Association (NBA) teams will be the core set of data focused on. By defining the “who”
we were able to focus on information specific to the NHL and NBA, which allowed for
our project to be structured upon subset data referring to only the NBA and NHL.
What
The “what” for this project includes that of the number of attendees at games, and
overall league standings from both the NHL and NBA. The purpose of this report is to
determine the correlation between attendance at games, and overall performance of the
team. From these data, game attendance is considered to be a quantitative set of data,
while the rank of each team is categorical variables. These data will provide context as
to what information will be studied and analyzed and along with the “who” creates a
context that the project can be based upon.
Why
The “why” for this project is to determine if there is a relationship between the number of
attendees at games and overall league standings based on information from both the
NHL and NBA. As well as this determining whether one is dependent on the other, or
vise versa was also a component of this project. This was interpreted in a way that
looked at if higher attendance affected team performance either positively or negatively.
Along with if better team performance either positively or negatively affect attendance at
games?
Where
The “where” for this project focuses on where the breadth of information will be
collected from along with the geographic region in which the information studied
resides. In order to gather the required data, we utilized secondary data through various
online sources to gather the data such as ESPN.com and TSN.ca and the geographic
region focused on was North America, particularly Canada and the United States of
America.
6 When
The “when” for this project focuses primarily on the time span of which will be included
in our analysis of data. Following that of a simple random sample the year 2010-2011
was the chosen season to analyze the relationship between the number of attendees at
games and overall league standings based on information from both the NHL and NBA.
However with that being said subsequent information on 2011-2012 and 2012-2013 was
also analyzed to compare and assess the validity of our findings and to see if any
consistent trends were present. With that being said the focus and main source of
information for this project was on data pertaining to the seasons from 2010-2011.
How
The “how” for this project focuses on two aspects, how the information for this study will
be acquired and what types of analyses will be used to find if there is a relationship
between the two variables. In order to gather the required data we decided against
using primary research for this report, as it is too difficult to gather for our needs, but
rather we utilized secondary research through various online sources to gather the data
such as ESPN.com and TSN.ca.
Three forms of analyses will be used in this report in order to find and represent if there
is a relationship between the two variables. Each method with its description is given
below:
Box Plot Method
Figure 1
Note: for every given value in Figure 1, please refer to Appendix A
In Figure 1, we analyzed data from the NHL and NBA from the 2010-11 season
separately in order to show if they were comparable or contrasting. On the y-axis of this
graph is the quantitative measure for the data being analyzed. Specifically, this is the
absolute values of the difference between a team’s standings rank and their attendance
7 rank. The x-axis is the qualitative measure, in this case, the NHL and the NBA. The
entire top to bottom of each individual box plot is referred to as the range. The formula
for the range is Range=Max –Min . For the NHL, the range is 20−0=20 , and for
the NBA the range is 26−0=26 . The green and purple boxes together in this graph
represent the interquartile range (IQR), or, the data that makes up the central 25% to
75% of the quantitative data. The formula for the IQR is IQR=Q3−Q1 . For the
12−4.25=7.75 9.75−3.25=6.5
NHL, the IQR is , for the NBA, the IQR is . The lines
separating the green and purple boxes represent the median for that specific set of
15
data. The median is the qualitative value that is exactly in the middle of the set of data
16
for that specific box plot. For the NHL, the median is 7.5, and for the NBA is 6.5. Lastly,
17
the lines extending from each box plot represent the outliers of each data set. Outliers
are values that are uncharacteristically higher or lower than the rest of the data set. A8
value is determined to be an outlier if it is outside of the IQR.9
Histogram Method
Figure 2
Note: for every given value in Figure 2, please refer to Appendix B
Figure 3
Note: for every given value in Figure 3, please refer to Appendix C
Figure 2 and Figure 3 are based on data from the 2010-11 season for their respective
sports. On the y-axis of Figure 2 and Figure 3 is the quantitative measure, which is the
frequency that each absolute difference between the standings rank and attendance
rank occurs. On the x-axis is also quantitative data, which are the absolute differences
between the standings rank and attendance rank. Figure 2 is multimodal and Figure 3 is
8 bimodal; this means that for Figure 2, three or more of the “bars” are noticeably higher
than the others, and for Figure 3, two of the “bars” are noticeably higher than the
others. It can also be seen that the frequencies in Figure 2 are equally distributed; this
means that there is not one side of the graph (left or right) that has consistently lower
frequencies. Figure 3 has consistently lower values on the right side of the graph,
making this graph right-skewed. 22
Figure 4 Figure 5
Note: for every value given in Figure 4 and Figure 5, please refer to Appendix D
Linear Regression Model
Figure 4 and Figure 5 are based on data from the 2010-11 season for their respective
sports where Figure 4 represents data from the NHL and Figure represents data from
the NBA. In Figure 4 and Figure 5, both y-axes, “Rank (Based on Attendance),” and x-
axes, “Rank (Based on points),” are quantitative data measures. The original data for
this model is arranged as a scatter plot, in which one variable, “Rank (Based on
Attendance),” is plotted against the other, “Rank (Based on points),”and represented by
a dot on the graph. Then, a line of best fit is run through the scatter plot; this shows the
23
relationship of the two variables in a linear method. The line of best fit is represented
by the formula in the top right hand corner of the graph. This is the basic formula for a
line, y=mx+b , that’s calculated by using the average position of all the points on the
scatter plot, essentially. For the NHL, the formula is y=0.3743x+9.7863 ; for the
9 y=0.4572x+8.4591
NBA, the formula is . From this model, we can also see a
statistical model that is known as regression. Regression shows the relationship
between two variables to see if they are correlated or not. It is typically represented by
2 26 2
a R value. R -values use a percentage to show the extent to which the independent
2
variables accurately predict the dependent variables; as R approaches 100%, the
greater the correlation between independent variables and the dependent variables
exist on the line of best fit (opposite is held true).
The formula for the R value is:
R2=1− ∑ of squarederrors(SSE)/total∑ of squares(SST)
Specifically, SSE=( y−y)̂ 2 and SST=(y−y) ́ 2. For the NHL, the R value is
2
0.14371, and for the NBA, the R value is 0.2099. This means that the Rank (based on
attendance) and the rank (based on points) for the NHL for the 2010-11 season is
14.371% related, and that the rank (based on attendance) and the rank (based on
points) for the NBA for the 2010-11 season is 20.999% related.
IV. Results/Discussion/Recommendations
After completing a statistical analysis of the data collected for both leagues, our suggested
hypothesis was answered with mixed results.
Without delving into various factors the histogram and box-plot proved the compliment
of the hypothesis to be true, as seen by the absolute values of rank differences between number
of wins/points to attendance records in the 2010 – 2011 season for each league. The NHL
showed the greatest emphasis on the compliment as there existed 16 different outcomes in
differences with only one team correlating attendance with wins. Moreover, t

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