1. Do Revenues Effect Success Among Professional Sports Teams?
Kenny Jacobson, Thomas Brewster, Grace McVey, and Peter McAuliffe
Department of Economics, Colby College
Introduction
In the United States, professional sports accounts for a tremendous amount in revenue every year. The wealthiest franchises in the big four of professional sports: Major League Baseball, National Football League, National Basketball Association, and National Hockey League bring in roughly $500 million each year. A popularly held belief is that franchises with more revenue win more games. We are testing this belief and examining the extent revenue has on a team’s success across the four major leagues.  
Our hypothesis is that the sports teams with more revenue will have a relatively higher win percentage in a given season. We are checking how this hypothesis differs across different sports including professional football, baseball, hockey, and basketball. We have tested our hypothesis by comparing team revenues to team wins for each team in the NFL, MLB, NHL, and NBA for the seasons. Our goal is to determine which sports are more reliant on team revenue to to generate wins.  We also are looking to determine how that reliance has changed over the years.  
The findings of this paper will be relevant for understanding the effects team revenue has on sports franchises win percentages and how the elasticity between revenue and wins differs between the four major sports.  
Regression Model
WinPercentage = β0 + β1(Revenue) + β2(NHL) + β3(NBA) + β4(MLB) +
β5(CityPopulation) + β6(Attendance) + e
Conclusions
In order to interpret each variable, we must look at the coefficients, standard error, and t-statistic for each. For Revenue, which is expressed in millions of dollars, our results indicate that a $1 million dollar increase in a team’s revenue relates to a predicted percentage point increase in a team’s win percentage, while holding all other variables in the model constant. The standard error for this variable is .011, which gives a t-statistic of This tells us that we reject the null hypothesis that the variable is statistically insignificant
The city population variable is interesting. The coefficient of can be interpreted as a 1 million person increase in population relates to an expected .643 percentage point decrease in win percentage. This variable is statistically significant at the 5% level but not the 1% level. A 1 million person increase in population is a very significant increase from an economic standpoint, but it only relates to a .643 percentage point decrease in win percentage. We do not think is very telling in predicting win percentage, so it could potentially be omitted from our model.
The fan attendance variable is more important than it seems at first glance. The coefficient of .138 indicates an expected increase in win percentage of .138 percentage points from a 1% increase in fan attendance/Stadium capacity. This varies between leagues, but in some leagues, like the MLB, there is sometimes only 50% of the stadium filled at a game as opposed to another team’s 100% of the seats filled. This can be related to how popular a team is, which can be directly related to how much a team wins. If a team’s stadium has a season average of 70% of the seats filled and another team has a season average of 100% of the seats filled, a 30 percentage point difference relates to a predicted 4.14 percentage point increase in a team’s win percentage. .
Regression Results
Data
The data for city population was calculated for each team based on the city in which the team’s stadium is located. The majority of the teams are the namesake of the major city they play in, however, there are some teams that are the namesake of the state. For example, the Arizona Diamondbacks of the MLB play their home games in Phoenix, Arizona, so the population data was based on statistics from Phoenix. This variable helps measure the magnitude of revenue that a team brings in each year. A city with a larger population value will have a higher expected revenue.
The other variable we included was fan attendance, which measures the amount of people willing to pay to watch a team play. For the purposes of this study, attendance is measured as a percentage of the team’s stadium that is filled on average this year. This is done to try and combat the size differences of stadiums or arenas across  different leagues. For example, an NHL arena is much small than a football stadium, so a less popular NFL team could have more fans in the seats than a more popular NHL team. This variable can also have an effect on a team’s revenue, as the teams with larger percentages of attendance will likely have higher expected revenues. Both city population and fan attendance have an impact on the correlation between a team’s revenue and its win percentage, which is why we included them in the regression equation.
Histogram of all team’s revenue in NBA, NHL, NFL, MLB