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Chapter 5

- The standard deviation of win percentage for the 32 teams in the NBA in 2005–2006 was 0.134. The NBA plays an 82 game season. The standard deviation of win percentage for the 20 teams in the English Premier League in 2005–2006 was 0.158. The EPL plays a 38 game season. The idealized win percentages for the NBA and EPL are

(a) 0.055 (NBA) and 0.081 (EPL)

(b) 0.078 (NBA) and 0.115 (EPL)

(c) 1.672 (NBA) and 1.580 (EPL)

(d) 2.427 (NBA) and 1.948 (EPL)

**Answer: (a) **The “ideal” standard deviation for a league in which all teams are equally likely to win is given by the equation

where *G *is the number of games played. Under an 82 game season, the ideal standard deviation is

Under a 38 game season, the ideal standard deviation is

- Based on the information in Question 1, which league exhibits more competitive balance?

(a) The NBA exhibits more within-season competitive balance, but between-season competitive balance cannot be determined from the information given.

(b) The EPL exhibits more within-season competitive balance, but between-season competitive balance cannot be determined from the information given.

(c) The NBA exhibits more between-season competitive balance, but within-season competitive balance cannot be determined from the information given.

(d) The EPL exhibits more between-season competitive balance, but within-season competitive balance cannot be determined from the information given.

(e) Because the leagues have a different number of teams and/or play a different number of games each season, neither between-season nor within-season competitive balance can be determined from the information given.

**Answer: (b) **One can compare the within-season competitive balances of multiple leagues by calculating the ratio of the standard deviation of win percentage by the idealized win percentage. For the EPL the ratio is 0.158/0.081 = 1.948. For the NBA the ratio is 0.134/0.055 = 2.437. Since the EPL has a lower ratio, it has the better within-season balance. This ratio, however, tells nothing about between-season competitive balance.

- Over the past 12 years in Patriot League Women’s Volleyball, American has won five titles, Colgate has won three league titles, Bucknell has won two titles, and Lehigh and Army have each won one title. In the NBA over the past 12 years, the L.A. Lakers, San Antonio Spurs, and Chicago Bulls have each won three titles, the Houston Rockets, Detroit Pistons, and Miami Heat have each won one title. The HHI for championships in Patriot League Volleyball and the NBA are

(a) 2.5 (NBA) and 3.3 (PL)

(b) 12.0 (NBA) and 12.0 (PL)

(c) 30 (NBA) and 40 (PL)

(d) 7.0 (NBA) and 4.0 (PL)

**Answer: (a) **The HHI index is given by the equation

where *f *is the number of first-place finishes, and *T* is the number of seasons. Here, for Patriot League Volleyball, *f _{i} *is five for American, three for Colgatge, two for Bucknell, and one each for Army and Lehigh, so the HHI = (5

12 = 40/12 = 3.33. For the NBA, volleyball

1

- Based on the information in Question 3, which league exhibits more competitive balance?

(a) The NBA exhibits more intra-season competitive balance, but inter-season competitive balance cannot be determined from the information given.

(b) The PL exhibits more intra-season competitive balance, but inter-season competitive balance cannot be determined from the information given.

(c) The NBA exhibits more inter-season competitive balance, but intra-season competitive balance cannot be determined from the information given.

(d) The PL exhibits more inter-season competitive balance, but intra-season competitive balance cannot be determined from the information given.

(e) Because the leagues have a different number of teams and/or play a different number of games each season, neither inter-season nor intra-season competitive balance can be determined from the information given.

**Answer: (e) **While the Patriot League has a slightly higher HHI, which indicates that fewer teams generally win the championships in the league, since the Patriot League has only eight teams versus 32 in the NBA, one would naturally expect championships to be more concentrated in the Patriot League. It is generally not possible to compare the between-season competitive balance for leagues with a different number of teams using the HHI.

- What is a shortcoming of the HHI measure?

**Answer:** One flaw with the HHI measure is that as *N* (the number of teams increases) the value of HHI decreases even if the league has not become more competitive. Therefore, the HHI cannot generally be used to compare between-season competitive balance between two leagues of different sizes.

- Is free agency without a salary cap good or bad for competitive balance?

**Answer:** If all teams have equal resources to pursue free agents then a salary cap is not needed. However if some large market teams (like the Yankees) have superior resources then free agency without a hard cap allows these teams to hoard the best talent in the league. This talent presumably will generate a higher winning percentage for the rich team, which in turn will bring in more revenues.

- What is the uncertainty of outcome hypothesis?

**Answer:** The uncertainty of outcome hypothesis loosely states that fans are more excited about a game (and therefore more likely to attend) if the outcome of the game is uncertain. It is not the case that one team is very likely to win. Recent research shows that fans are most interested in games when the home team has a 60 to 70 percent chance of winning.

- What does the standard deviation statistic tell you?

**Answer:** The standard deviation describes the average distance that observations lie from the mean of the observations of the dataset.

- Why is standard deviation useful in studying competitive balance?

**Answer:** A league that has a smaller standard deviation (than one with a large standard deviation) of winning percentages has teams that win more or less the same percentage of their games. In other words this is a balanced league where on any given occasion any given team can beat another team.

- What is a shortcoming of using the standard deviation of winning percentage (within a season) to study competitive balance?

**Answer:** Standard deviation of winning percentage just measures the spread of winning percentages around the average winning percentage. It does not account for who is doing the winning. If a league has similar standard deviations in two different seasons this tells you nothing about the order in which teams finished. The order of finishing a season (by winning percentage) could have been reversed from one year to the next with first team finishing last but as long as the winning percentages are more or less the same the standard deviation statistic will have the same value. This shortcoming can be overcome by using a variety of between-season competitive balance measures.

- Given the following winning percentages of the teams in a league (for a single year) compute the within-season standard deviation for the league.

Team |
Season Winning Percentage |

1 | 0.750 |

2 | 0.750 |

3 | 0.200 |

4 | 0.600 |

5 | 0.200 |

**Answer: **

- Given the winning percentages of the teams from Problem 11 in a league (for a single year) compute the within-season ratio
*R*for the league if the league plays 20 games per season.

**Answer:**

- All of the major sports leagues in the United States use a reverse order draft to promote competitive balance. The NBA is unique in that it utilizes a “draft lottery” such that the worst team in the league is not guaranteed the top pick in the draft but instead only receives the highest probability in the lottery to receive the top pick. Why does the NBA use a draft lottery? Why might it be the case that only the NBA uses a lottery while the other leagues use a straight reverse order draft?

**Answer: **The NBA uses a draft lottery in order to prevent teams from losing on purpose (sometimes known as “tanking”) in order to secure the top pick in the draft. This problem may be particularly severe when the draft is likely to contain one or two very highly touted players. This system preserves uncertainty of outcome and the game’s integrity within the league. There are several possible reasons why the NBA might have a draft lottery while other leagues utilize a straight reverse-order draft. First, the draft may be a better predictor of talent in the NBA than in other sports, and therefore a higher draft position may be more valuable in the NBA, giving teams more incentive to tank. Next, in a sport with only five players on the court, the value of getting one particular player may be higher in the NBA than other teams. The variability of skill may be higher in basketball so that the difference between a #1 and #2 pick is more significant in the NBA than other sports. NBA fans may also be more responsive to the quality of the opponent than fans in other leagues so that having a team tanking is particularly bad for league revenues. Teams in other leagues may also have fewer historical examples of teams actually tanking. Finally the NBA may have better alternative methods of achieving competitive balance than other leagues, so they can afford to have a less effective draft.

- Which move would be more effective for increasing the level of competitive balance in baseball, a hard salary cap or a 50-50 gate revenue-sharing plan?

**Answer: **First of all, gate revenues are only a small portion of total revenues collected in professional sports, so even complete sharing of gate revenues will leave some teams with significantly higher revenues. Even if all revenues are shared equally, however, players still flow to the same teams they would have gone to if there were no revenue- sharing. When teams evenly split revenue they effectively put all their revenue in a pile in the middle of the room and then divide the pile equally among themselves. If teams maximize profits, they want to make the pile as large as possible. If a star player is more valuable in Los Angeles than in Cleveland, then the pile in the middle of the room is larger—and the revenue for Los Angeles *and *Cleveland—will be greater if the player moves to Los Angeles. Thus, even a 50-50 revenue split may have little impact on the distribution of talent or competitive balance. A hard salary cap limits what a team can pay its players. Even if a player is worth more in Los Angeles then in Cleveland, Los Angeles may not be able to lure him away if it is already spending close to its limit on its other players. This limit evens out what teams can spend for players and has the potential for evening out the distribution of talent.

- Just before the 2007 Daytona 500, NASCAR heavily fined several racing teams for using fuel additives that make cars go slightly faster. Why would NASCAR want to take steps to lower the speed of their race cars?

(a) Like MLB with steroids, NASCAR fears that if they don’t act to prevent the use of illegal substances, the federal government will step in instead to regulate their league.

(b) NASCAR fans prefer relative quality over absolute quality.

(c) Slower cars provide for significantly better track safety.

(d) All of the above

**Answer: d. **NASCAR wants all drivers’ equipment (and fuel) to be identical in order to promote close races even if this means that the cars need to go slightly slower. One difference between MLB and NASCAR is that the NASCAR drivers were only breaking league rules and not local, state, or national laws by using fuel additives. Note: NASCAR’s rules had a positive impact on the race as driver Kevin Harvick won the 2007 Daytona 500 by less than 1 second over runner-up Mark Martin.

- Go to the official MLB website (http://www.mlb.com) and check the order of finish in the American League East for the 1998–2003 seasons. What is the between-season variation for this league over this time span?

**Answer: **The order of finish was unchanged between 1998 and 2003. This indicates a complete lack of inter-season competitive balance.

- What is competitive balance?

**Answer: **Competitive balance is loosely defined as two teams having a roughly equal chance of winning a game that they play against each other.

- Why do leagues care about competitive balance?

**Answer:** Leagues are concerned about competitive balance because of the connection between competitive balance and attendance. If the results of contests are forgone conclusions then fans will not be drawn to witness their outcomes.

- The minimum possible value of the “Frequency of Championships” Herfindahl-Hirschman Index Index is:
- 0
- 1
- 1/n (where n = number of teams in the league).
- Number of championships won by the “winningest team” times n.

**Answer: c. **1/n would represent a perfectly-balanced league in which each team has an equal probability of winning the championship.

- Which of the following is/are ways in which sports leagues have attempted to promote competitive balance?

- The reverse-order draft.
- Revenue sharing.
- Salary caps.
- All of the above.

**Answer: d. **All of the strategies listed above represent efforts by sports leagues to enhance (or maintain) competitive balance.

- True or false: A larger HH Index indicates greater competitive balance within a league.

- True.
- False.

**Answer: b (false). **The Herfindahl-Hirschman Index (HHI) is a measure of concentration of power (measured by the sum of squared market shares), with a larger HHI representing greater concentration of power in an industry or a sports league. In industrial organization, the largest possible HHI is 10,000, which occurs when one firm has a monopoly (100^{2}). In sports leagues, the largest possible HHI is 1 (representing a situation where 1 team wins all the championships within the relative time frame).

- The invariance principle breaks down when:

- Those in the market have significant monopoly power.
- Property rights belong to the government.
- Property rights belong to citizens (the people).
- There are significant transactions costs.

**Answer: d. **Significant transaction costs increase the costs of dealing for buyers and/or sellers in a market and thus can mitigate the likelihood that resources flow to their most highly-valued use.

- An actual-to-ideal ratio of standard deviations of winning percentages of 5 in a league means:

- The standard deviation of winning percentages is 1/5 (20%) more than it would be in a world with absolutely balanced teams.
- The standard deviation of winning percentages is 5 times more than it would be in a world with absolutely balanced teams.
- The standard deviation of winning percentages in this league represents perfect competitive balance.
- There is not enough information to determine.

**Answer: b. **The higher the actual-to-ideal ratio of standard deviations of winning percentages, the greater the degree of competitive *imbalance* in a league.

- The marginal benefit of winning:

- Is greatest for teams in small markets.
- Is greatest for teams in medium-sized markets.
- Is greatest for teams in large markets.
- Does not vary based on market size.

**Answer: c. **Teams in larger cities enjoy greater increases in fan support (and therefore revenue) for an additional win than teams in small cities

- True or false: Perennial losers are the only group within “the baseball fraternity” who you would expect to support competitive balance.

- True.
- False.

**Answer (b). False. **As noted in the very first sports economics article (Rottenberg, 1956), a successful sports leagues relies on relatively even competition. Thus, even perennial winners, such as the New York Yankees, rely on viable competition from other teams in the league to create and maintain fans’ interest in the game.

- What does “The Moneyball Hypothesis” imply about the traditional ways scouting has been done in major league baseball and the efficiency of markets to process all available information in the decision-making process?

**Answer: **“The Moneyball Hypothesis” demonstrated that there were imperfections in the market in terms of traditional scouting methods in Major League Baseball (which have traditionally emphasized slugging percentage, a player’s “look” and the “gut feelings” of scouts regarding a player’s probability of success in the Major Leagues). By demonstrating that increasing players’ on-base percentage contributed more to wins than increasing slugging percentage, those employing “The Moneyball Hypothesis” were able to gain a first-mover advantage over teams still stuck in an outmoded model of evaluating player productivity. However, in an efficient market such as Major League Baseball, this first-mover advantage was short-lived as other team in the league applied the “Moneyball” approach.

Category: Economics

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