Introduction

Workers in many occupations and industries have felt the need to band together in unions so that they could bargain collectively with management. In this way, the workers sought to level the playing field in negotiating wages, hours, benefits, and working conditions with large, powerful employers. Much the same has been true in professional sports: the players have formed unions to offset the collective monopsony power of the team owners. These players’ unions, however, are somewhat different from the traditional craft unions or industrial unions. We explore some of the differences here.

We begin this chapter by introducing the players’ unions in the four major sports leagues. We then turn our attention to the economics of unions. Successful unions are labor cartels, which would ordinarily be illegal under the antitrust laws. There is, however, an explicit antitrust exemption for organized labor, which we outline briefly. When the union meets the league management negotiators, we have a market structure known as bilateral monopoly. We develop a simple model of bilateral monopoly and relate it to professional sports. We then examine minimum salaries in the major professional sports leagues, salary caps and luxury taxes, revenue sharing, and free agency. All of these issues are subject to collective bargaining and are largely protected from antitrust scrutiny.

Introduction

Following the University of Florida's (UF's) 2006 National Collegiate Athletic Association (NCAA) Championship in men's basketball, Gator fans held their collective breath. Four of UF's starters could have declared for the National Basketball Association (NBA) draft even though they had college eligibility remaining. To the great relief of the Gator Nation, they all decided to return for another season. Whether this was a wise decision ex post, only time will tell, but the relevant issue is whether it was wise ex ante; after all, we all have 20-20 hindsight.

Every year, there are hundreds of athletes with college eligibility remaining who must decide whether to stay in school – or even to go to school in the first place. Star athletes – and even some who are not stars – agonize over whether they should take a shot at fame and fortune in professional sports before they have exhausted their college eligibility. No doubt, this is a difficult decision with many risks whether the athlete stays or leaves. There are some prominent examples of those who made the wrong choice.

Introduction

Drug use has long been a serious problem in the sports world. For many years, the central concern was over the use of illegal “street” drugs such as marijuana, cocaine, and heroin. More recently, however, attention has shifted to performance-enhancing drugs: anabolic steroids, human growth hormone, stimulants, and erythropoietin (EPO). There are almost daily allegations and revelations regarding the use of performance-enhancing drugs across all sports – amateur as well as professional. These reports appear so often we are hardly surprised to find that one of our heroes – Marion Jones, Justin Gatlin, Shawne Merriman, Alex Rodriguez – has feet of clay. Some athletes have been temporarily suspended, and others have been banned for life. Suppliers have gone to prison, paid heavy fines, or both. Surveillance is increasing, and sanctions are becoming more severe. In this chapter, we examine the health risks associated with using performance-enhancing drugs. We also review the policies of several sports leagues and organizations and the sanctions they impose for using banned substances. We then employ the expected utility model to identify the potential for deterrence.

Prevalence of Abuse

No one can be quite sure just how prevalent the use of steroids has become in the sports world. Athletes do not want to admit to steroid use. In fact, several prominent athletes have lied about it. Some have persistently and vehemently denied using steroids when, in fact, they did use them.

Talent: A Risky Asset

Player talent is a valuable asset that is put at risk every time athletes play or practice. Some injuries – even if relatively severe – can be overcome. There are numerous examples of football players who have overcome serious knee and shoulder injuries. Willis McGahee, for example, suffered a devastating knee injury during the 2003 Fiesta Bowl game while playing for the University of Miami. The Buffalo Bills took a huge chance by drafting him in the first round of that year's National Football League (NFL) draft. McGahee sat out his entire rookie year rehabbing his knee, while earning $1.8 million. He recovered from the injury and rushed for 1,128 yards and 13 touchdowns in 2004. Dan Marino, the great Miami Dolphins quarterback, played for years after having torn his Achilles tendon. Tommy John was an ace of the Los Angeles Dodgers pitching staff for years after elbow surgery. Sometimes, however, injuries can end a career. In some sports – golf, tennis, cycling, track, and professional football – the athlete is out of luck if he or she suffers a career-ending injury because incomes are not guaranteed. In other sports, notably baseball and basketball, professional contracts are guaranteed, which means that the athlete gets paid even if he or she cannot perform. A career-ending injury does not void the contract or lead to a financial disaster for the player, but the financial loss does fall on the team, which must pay both the athlete who can no longer play and his replacement.

The value of athletic talent is a risky asset. Who bears that risk depends on the contract. For example, Carl Pavano signed a four-year contract with the New York Yankees in 2005. The contract was reported to be worth $39.95 million. Pavano developed shoulder problems in his first year (2005) and could not pitch after June 27. Pavano worked to rehab his shoulder but developed back, buttocks, and elbow problems. To make matters worse, he was in a car accident and cracked some ribs. He did not pitch at all for the Yankees in 2006 but remained optimistic about his health in 2007. In 2007, Pavano developed further problems. After just two starts, he went on the disabled list and was scheduled for Tommy John surgery. This ended 2007 for him as well as most of 2008 because of the prolonged rehab that such surgery requires. Before his injury in 2005, Pavano won four games while pitching 100 innings. The Yankees paid him some $17 million for the 2005 and 2006 seasons, which works out to $4.3 million per win or $170,000 per inning. If Pavano had not regained his physical abilities, the Yankees would still have had to pay for the remaining two years on his contract. That is, the risk of a career-ending injury falls squarely on the team in Major League Baseball (MLB). When contracts are not guaranteed, as is generally the case in the NFL, the risk of a career-ending injury falls on the player's shoulders. This, of course, is true for all amateur athletes as well. If a college player is injured, the expected value of his future professional compensation is lost.

Introduction

When star players are free agents, several teams may bid for their services in a kind of auction. Barry Zito is a good example of this. Several Major League Baseball (MLB) teams were interested in signing Zito when he became a free agent after the 2006 season. In the end, the San Francisco Giants and the New York Mets battled down to the wire over Zito. The Giants ultimately won the battle and Zito's services by outbidding everyone else. Zito, of course, was the real winner: $126 million over seven years. In this instance, Zito's salary was determined through competitive bidding. In other cases, however, salaries are determined through bilateral bargaining between one team and one player (or his agent). Top NFL draft choices for example, bargain over the terms of their initial contracts with the teams that selected them in the draft. Some players who are currently under contract bargain over multiyear contract extensions. At the end of the 2010 season, for example, Derek Jeter and the New York Yankees engaged in a very public bargaining struggle. Jeter wanted more than his market value, and the Yankees wanted to pay less than his market value. In the end, they settled on a three-year contract for $51 million. Some National Football League (NFL) players bargain over restructuring their current contract because of salary cap constraints.

In this chapter, we develop the simple economics of bidding at auctions and how it applies to professional sports. We also develop the basics of bargaining. Several examples illustrate the applicability of bargaining theory. Finally, we examine the posting system that applies to players under contract with professional baseball teams in Japan. As it applies in the United States, the posting system combines bidding at one stage with bargaining at the next stage.

Introduction

Advertising is part of the landscape in both professional and amateur sports. It comes in all shapes and sizes. In 2006, Anheuser-Busch spent more than a quarter of a billion dollars on sports advertising. American Express was a corporate sponsor of the 2006 National Basketball Association (NBA) draft. Sony sponsored the Hawaiian Open golf tournament on the Professional Golf Association (PGA) Tour. The Pittsburgh Steelers play their home games at Heinz Field. We now have “Bears football presented by Bank One,” and the White Sox start their home games at 7:11pm because of 7-Eleven's support. Phil Mickelson and Annika Sorenstam tout Callaway Golf, and Tiger Woods is a Nike man. Gatorade is the “official” sports drink of the National Football League (NFL). All of these are examples of advertising in sports, which is a multibillion dollar business.

The reason for all this activity is simple: profit. Advertising (and other forms of promotion) is designed to increase demand for the advertiser's product. Some advertising does this by being informative, whereas other forms do this by being persuasive. In either event, the idea is to increase the quantity demanded at the same price or, viewed differently, to increase the price at the same quantity. Teams advertise their games to increase attendance, whereas leagues and organizations advertise the athletic competition that their members produce. Of course, producers of a wide array of goods and services advertise to sports fans on television and radio as well as at the venue. All of the billions of dollars that are spent on advertising are geared toward improving the advertiser's profit. To be successful, the ads must increase the advertiser's total revenue by more than they increase its total cost.

This textbook grew out of my dissatisfaction with other textbooks on sports economics that were available. As my own course evolved over time, these books became increasingly unsuitable for my class in part because of coverage and in part because of level and organization. This book reflects my interests and those of my students at the University of Florida. Unlike other books on this subject, this one includes extensive use of present values, choice under uncertainty, pricing models, and numerical examples. The content includes multiyear contracts, insurance, sports gambling, misconduct (and its discipline), the steroid scandal, and many other topics that are not standard fare in the existing sports economics textbooks.

An important pedagogical feature of this book is the involvement of students in the learning process through problem solving. At the end of each chapter, there are Problems and Questions that are intended to help students learn the concepts in the text. There are also some Research Questions that will help students learn how to find information and present it.

Introduction

Many cities have an unmet demand for a professional sports franchise in their midst. Whenever an existing franchise expresses an interest in relocating to greener pastures, there is no apparent shortage of willing hosts. The same is true when one of the major sports leagues contemplates expansion. For strategic reasons, the major sports leagues make sure that there are a few viable locations that go unserved. In this way, they ensure the presence of excess demand and thereby improve the credibility of threats by existing franchises to move. This excess demand also provides leverage when either a new or existing franchise is bargaining with a city for benefits.

Cities also compete for major sports events. Major cities around the world compete with one another to host the Olympics or the World Cup. On a somewhat smaller scale, Omaha pursued the College World Series. Some U.S. cities compete to host the NFL player draft, which has turned into a media event. Cities compete in the only way they can by providing benefits to the organizers. Usually these are legitimate, but there have been instances of corruption.

Introduction

Professional teams, university athletic departments, event sponsors, and sports facility owners all provide something of value to sports fans and participants. Through their pricing decisions, they extract some of that value for themselves. The more that they extract, the more profit they earn at the expense of the fans and participants. As a result, pricing decisions are critical to their financial success. These pricing decisions also have important welfare consequences because they may result in allocative inefficiency. In this chapter, we examine various pricing models that have been used to extract value from the consumer. We begin with competitive pricing to provide a benchmark for comparison. We then examine various ways to exploit monopoly power: simple monopoly pricing, price discrimination, peak load pricing, bundling, two-part pricing, and pricing complements. Finally, we examine ticket scalping, which is the practice of reselling tickets at prices above the face value.

Competitive Pricing

We begin by examining the results of competitive pricing. Suppose that the demand for tickets to a basketball game is represented by D in Figure 5.1. The marginal cost of each additional spectator is low and we assume that it is constant. When marginal cost is constant, average cost is also constant and equal to marginal cost. The constant marginal and average cost are shown as MC = AC in Figure 5.1. Now, in competitive markets, price is driven to marginal cost by competing sellers. If the organizer of the basketball game were to price at the competitive level, price would be P 1, which is equal to MC, and the number of spectators would be Q 1.

Introduction

Major sports events undeniably bring with them large crowds of fans and media. The Super Bowl, Major League Baseball's (MLB's) All-Star Game, the Masters Golf Tournament, and big home football games in College Station, Auburn, Tallahassee, and Clemson all attract hordes of people and an apparent burst of economic activity. Thousands of people flock to these events, and they spend plenty of money in the local area. In addition to their spending at the event (tickets, concessions, and souvenirs), these fans spend substantial sums at local hotels and motels, car rental agencies, bars and restaurants, gas stations, T-shirt shops, and so on. This first round of spending provides income to residents in the local community, which results in subsequent rounds of spending. There is a multiplied effect of the initial spending, which is the economic impact of the sports event. Sports leagues and organizations often grossly exaggerate this economic impact for their own purposes. The National Football League (NFL), for example, claims that the impact of the Super Bowl is hundreds of millions of dollars. As we will see, however, such claims are dubious.

In this chapter, we examine the fundamentals of economic impact analysis. We begin with a simple multiplier model and explain why the impact of an event is not as large as some leagues and organizations would have us believe. We also review and evaluate some empirical studies that have been conducted to test the reliability of some claimed impacts.

This chapter is primarily concerned with algorithms for efficient computation of the Discrete Fourier Transform (DFT). This is an important topic because the DFT plays an important role in the analysis, design, and implementation of many digital signal processing systems. Direct computation of the N-point DFT requires computational cost proportional to N2. The most important class of efficient DFT algorithms, known collectively as Fast Fourier Transform (FFT) algorithms, compute all DFT coefficients as a “block” with computational cost proportional to Nlog2N. However, when we only need a few DFT coefficients, a few samples of DTFT, or a few values of z-transform, it may be more efficient to use algorithms based on linear filtering operations, like the Goertzel algorithm or the chirp z-transform algorithm.

Although many computational environments provide FFT algorithms as built-in functions, the user should understand the fundamental principles of FFT algorithms to make effective use of these functions. The details of FFT algorithms are important to designers of real-time DSP systems in either software or hardware.

Study objectives

After studying this chapter you should be able to:

• Understand the derivation, operation, programming, and use of decimation-in-time and decimation-in-frequency radix-2 FFT algorithms.

• Understand the general principles underlying the development of FFT algorithms and use them to make effective use of existing functions, evaluate competing algorithms, or guide the selection of algorithms for a particular application or computer architecture.

In theory, all signal samples, filter coefficients, twiddle factors, other quantities, and the results of any computations, can assume any value, that is, they can be represented with infinite accuracy. However, in practice, any number must be represented in a digital computer or other digital hardware using a finite number of binary digits (bits), that is, with finite accuracy. In most applications, where we use personal computers or workstations with floating point arithmetic processing units, numerical precision is not an issue. However, in analog-to-digital converters, digital-to-analog converters, and digital signal processors that use fixed-point number representations, use of finite wordlength may introduce unacceptable errors. Finite wordlength effects are caused by nonlinear operations and are very complicated, if not impossible, to understand and analyze. Thus, the most effective approach to analyze finite wordlength effects is to simulate a specific filter and evaluate its performance. Another approach is to use statistical techniques to derive approximate results which can be used to make educated decisions in the design of A/D converters, D/A converters, and digital filters. In this chapter we discuss several topics related to the effects of finite wordlength in digital signal processing systems.

Study objectives

After studying this chapter you should be able to:

• Understand the implications of binary fixed-point and floating-point representation of numbers for signal representation and DSP arithmetic operations.

• Understand how to use a statistical quantization model to analyze the operation of A/D and D/A converters incorporating oversampling and noise shaping.

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