Chapter 8

1. The Economics of Sports FIFTH EDITION Chapter 8 An Introduction to Labor Markets in Professional Sports Michael A. Leeds | Peter von Allmen

2. Incentives and Labor Supply • Joe Louis and Oscar de la Hoya are two of the greatest boxers ever • Both fought longer than they should have • Louis fought because he had so little money • De la Hoya fought because he was offered so much • Both Louis’s and de la Hoya’s actions can be linked to labor supply

3. Learning Objectives • Understand the basic model of wage determination in labor markets • Be able to describe why the salaries of superstars are much higher than the salaries of average players • Analyze the labor markets for individual sports, such as golf and tennis • Explain why players use performance-enhancing drugs despite knowing their harmful effects

4. 8.1 Labor Supply and Demand • Figure 8.1 shows that in the last 20 years alone, the average salary of a Major League Baseball player has almost quadrupled • From about $850,000 to over $3.3 million • To put this in perspective, the average MLB salary was approximately • 36 times per capita GDP in 1991 • 65 times per capital GDP in 2011 • Salaries have risen similarly in other professional sports, both in the US and abroad

5. Figure 8.1

6. Labor Supply • The supply curve has a slightly different character from the typical supply curve • We usually see the price of a product on the vertical axis and the quantity of a product on the horizontal axis • In labor markets, the price is the wage rate and the quantity is the number of hours a worker chooses to work • The upward-sloping labor supply curve thus indicates that a worker responds to higher wages by offering more work time to employers • See Figure 8.2a

7. Figure 8.2a

8. Sports Application • One can analyze team sports markets in several ways • To analyze career length • Players have no say over work hours • The axes become salary per season and the number of seasons • To analyze the number of players hired in a season • The axes become salary per season and the number of players willing to work at a given salary • See Figure 8.2b

9. Figure 8.2b

10. Boxing Application • Fighters can choose how many fights they engage in • The axes become reward per fight and number of fights • The boxing example in Figure 8.2b shows that a boxer is induced to take on more fights as his pay increases • The player moves from point A to point B • This was the case for Oscar de la Hoya • The supply for Joe Louis shifted because his savings/wealth was lower due to tax problems • He moved from point A to point A’

11. Labor Supply Analysis • The work decision is a trade-off between income and leisure • Wage is the opportunity cost of leisure • As wages rise, leisure becomes more expensive • The substitution effect is away from leisure: As wages rise, workers work more • But income rises with wages: with higher income, workers can afford more of everything • The income effect is positive for leisure and negative for work: Workers buy more leisure & work less • Typically, the substitution effect is stronger than the income effect, so the supply curve slopes up

12. Labor Supply Curve • De la Hoya made huge sums • His substitution effect exceeded his income effect • He fought more bouts • His labor supply curve slopes up • Joe Louis made much less • Why didn’t he fight less? Prize money S Bouts

13. Moving the Labor Supply Curve • Louis’s supply curve also sloped up • But he had financial trouble • His income was misappropriated He owed back taxes • His wealth was very low • He could afford less of everything, including leisure • Less leisure means more labor • His labor supply shifted right Wage S S’ L; H

14. Labor Demand • To analyze labor demand, we consider the following simple scenario for firms • They produce a single output using two inputs, capital (K) • They operate in the short run (so capital is fixed) • They can alter output (Q) only by changing the labor input (L) • We assume that all markets are perfectly competitive • Firms cannot affect the market price of their output. • Firms maximize profit by choosing L to maximize profit • Profit is the difference between revenue and cost: profit • It is maximized when marginal revenue (MR) from employing one more worker equals the marginal cost of employing that worker (MC)

15. Marginal Revenue Product • Marginal benefit of a unit of labor is a new concept • The extra worker produces extra output: DQ/DL = MPL • The output can be sold for additional revenue: MR • Marginal Revenue Product (MRP)=MR*MPL • In competitive markets, MR = P, the market price • MRP = P x DQ/DL • Marginal cost • Wage or salary (w) • The firm maximizes profits when w=MR*MPL • The MRP is the firm’s demand for labor: Figure 8.3

16. Labor Demand Curve • Labor demand slopes down • MPL falls as L rises • So MRP also falls • Measuring MRP can be complicated • What do players produce? • How do individual statistics relate to the team’s output? • What is the market value of that output?

17. One Way to Measure Labor Demand in the NBA • David Berri, Stacey Brook and Martin Schmidt (2006) claim: MRPij = MRwin*Dwinsij • MRPij = MRP of player i on team j • MRwin = Revenue from 1 more win (~$1.67 M) • Dwinsij = Added wins team j gets from player i • They also claim Dwinsij = points + rebounds + steals + .5(blocks+ assists) – field goal attempts – turnovers – .5(free throws + personal fouls)

18. Do Teams Reward Performance? • Berri found that LeBron James produced 17.3 wins in 2011-12 • Most in the NBA (in a 62-game season) • Made him worth $28.9 Million to the Miami Heat • He was actually paid ~$17.5 Million • The third most valuable player was Tyson Chandler • He scored only 11.3 points per game • But he produced 13.3 wins – worth ~$22.2 million • He was paid “only” $13.6 million • Berri asserts that teams reward points more than performance

19. Imperfect Competition • If we assume imperfection in the product market, then MR no longer equals the market price • Recall that to sell another unit of output, the monopolist must sell all previous units at a lower price, so his MR curve is always below his demand curve • This is illustrated in Figure 8.4 • A monopolist hires fewer workers and pays lower wages than it would if the industry were competitive • This is consistent with the fact that monopolists restrict output as part of their strategy to maximize profits

20. Figure 8.3

21. Figure 8.4

22. Labor Market Equilibrium • The market demand curve is the summation of all individual demand curves • This is a summation over all teams in a league • The market supply curves is the summation of all individual supply curves • This is a sum across all players • See Figure 8.5

23. Figure 8.5

24. Impact of Growing Popularity • Equilibrium is where demand and supply meet • As the NBA became more popular in the 1970s • The value of players’ output rose • MR rose as ticket prices did • Marginal product was unchanged • Demand shifted right • Salaries rose and rosters increased w D’ S e’ D e L

25. The 2008 Recession • The recession reduced revenues • Fans could not afford tickets • Sponsors cut back on marketing • This reduced the value of output • Demand shifted left • Salaries fell w D’ D” S e’ D e” e L

26. Effect on Rosters • The standard analysis does not seem to apply to quantity • Figures 8.5 and 8.6 imply that roster size rises in good times and falls in bad times • This does not happen • Roster limits impose a vertical line at the set size • Salaries adjust as demand fluctuates • The quantity of players stays fixed • See Figure 8.7

27. Figure 8.6

28. Figure 8.7

29. Human Capital and Player Compensation • Investment is a sacrifice that brings future gains • Investment is an increase in capital • Firms invest in physical capital (plant & equipment) • Gary Becker introduced the theory of human capital • People invest in human capital (embodied knowledge or skills) • Attending college is one such investment • On-the-job training is another • As human capital rises, so do MPL and wage • Athletes acquire human capital like other workers

30. General Human Capital • General skills of workers are useful to all employers • In sports, these skill are basic footwork, fielding, and shooting • Workers can benefit from the general skills with any employer • Workers can easily leave after receiving training • If a worker leaves, the firm cannot recoup its investment in the worker’s general skills • Thus, workers typically pay to acquire general skills • They pay in the form of lower salaries • This is one reason why minor leagues pay so little

31. Specific Human Capital • Specific skills are useful to only one firm • Sports: How to play within a specific system or team? • A worker with specific human capital cannot earn as much elsewhere • He is less likely to leave • The firm can recoup its investment as the worker is more productive and does not leave • The firm pays for much of investment in specific skills

32. A Simple Example • Assume a player’s career lasts two seasons • He brings benefits MRP1 in period 1 and MRP2 in period 2 • The team sets w1 = MRP1 and w2 = MRP2 • If the team provides general skills to the player at cost T • The team’s costs in period 1 rise • The team cannot recoup cost T in period 2 or the player leaves • The team sets w1+ w2/(1+r) + T = MRP1 + MRP2/(1+r) • r is the discount rate • The fir reduces w1 – so the player “pays” for training • If the skills are specific to the team, the firm reduces w2 • It has no problem

33. 8.2 Tournaments and Superstars • In 2009, Roger Federer barely beat Andy Roddick at Wimbledon • Gentlemen’s final: 5-7, 7-6, 7-6, 3-6, 16-14 • If both players received their marginal product, the two should have received almost identical prizes • In fact Federer received twice as much (£750,000 v. £375,000) • The winner of a tournament typically gets a huge prize regardless of the margin of victory • The runner up gets half as much • Players eliminated early get virtually nothing

34. Rank Order Tournaments • Tournaments are settings in which rewards are based on “rank order” • The rank order is a measure of relative performance • Rewards are independent of the absolute level of performance • This system of award is very common in settings in which absolute performance is hard to determine • The outcome depends on other factors, such as playing surface and weather

35. Rationale for Rewarding Rank • We assume that participants maximize utility and that their utility increases with income and leisure and decreases with effort • Marginal curve in Figure 8.8 shows that marginal cost of effort is positive rises at an increasing rate • Marginal reward in Figure 8.9 must rise disproportionately to get effort to rise from E1 to E0 • Note that the tangent is a result of the same starting point

36. Why Use Rank Order? • Paying workers their MRP is the best incentive • Pay improves with performance • Firms usually do not pay workers their MRP • They pay workers by the hour, month, or year • It is often hard to measure MRP • It is costly or impossible to monitor workers perfectly • It is usually much easier to tell whose MRP is bigger • Tournaments set up distinct rewards • The winner receives much more than the loser • Increasing spread increases the incentive to win

37. Studies of Tournament Theory • Ehrenberg and Bognanno applied it to golf • They showed that scores in the last round improved with • The total prize money available • The reward to improving • Moving from 2nd to 1st is more rewarding than going from 22n to 21st • Do men and women respond differently? • Gneezy and Rustichini tested Israeli 4th graders • Had them run alone and then in pairs • The girls ran slower in pairs than alone – the boys ran faster in pairs • Gilsdorf and Sukhatme find no gender difference in tennis • Leeds and Leeds find female figure skaters respond more to incentives than male skaters

38. Payment to Celebrities • Superstars get most of the reward --see Table 8.1 • The effect of success lingers • Michael Jordan was among the highest earners long after he retired • Athletes earn relatively little • Tiger Woods – the highest-ranked athlete—was 14th • The highest-paid female athlete, Maria Sharapova, was 72nd • Executives are paid like celebrities • The salary of a top executive in a large corporation is likely to be at least twice that of his or her nearest rival • Output of executives is hard to measure

39. Table 8.1

40. 8.3 Tournaments and Cheating • Is trying hard the only way to win? • Teamwork can be harmed • Players can try to harm others’ performance • Shoot first, pass second • Competitors might try to sabotage the performance of others

41. The Case of NASCAR • NASCAR doesn’t want drivers to be too aggressive • It fears the negative externalities of dangerous driving • Too many accidents can reduce viewership and harm the sport • Peter von Allmen notes a much flatter reward structure • Figure 8.10 • Frick and Humphreys confirm that NASCAR times improve as the prize spread increases

42. Figure 8.8

43. Figure 8.9

44. Figure 8.10

45. Too Much of a Good Thing • High rewards put pressure on athletes and their coaches to succeed • Children leave their families to train and may be abused • Children are prohibited from working but not training • Many young female athletes have very delayed puberty • They eat too little and work out too much • They endanger their bone structure later in life • In some cases, the effort to lose weight has proven fatal

46. Performance-Enhancing Drugs (PEDs) • We celebrate the athletes who use innovations • Experimental surgery that extends a career • New strokes and new suits that make them swim faster • New techniques that allow them to clear a higher high bar • PEDs seem different from the above • Many PEDs are dangerous, controlled substances • We do not know who is taking them • First known PED fatality was a bicyclist in 1879 • In 1980s East German girls were given “vitamins” • They were actually steroids and male hormones • Birth defects and medical & sexual side-effects resulted

47. A Study of PEDs • Humphreys and Ruseski find that 5.4% of high school boys used PEDs in 1991-2005 • This was roughly twice the rate of usage by girls • Humphreys and Ruseski found distinct patterns to usage • Greater for multisport athletes • Less for youths with better-educated, wealthier parents • Greater for those using other, non-enhancing drugs

48. Doping is the dominant strategy Doping leads to a suboptimal outcome Consider the outcome payoff matrix below Doping as a Prisoner’s Dilemma

49. PEDs Have Tarnished Entire Sports • Baseball has been particularly affected • The following news items have stood out • Barry Bonds’ tainted home run title in 2007 • Ryan Braun’s tainted MVP award in 2011 • Melky Cabrera’s tainted batting title in 2012 • Track and Field has seen regular forfeits of gold medals • Marion Jones went from the podium to prison

50. PEDs and the Tour de France • Cycling has been more affected than most sports • Since 1998 doping has been linked to • 37% of all top 10 finishers • 80% of all winners • Lance Armstrong has been stripped of his 7 titles