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Chapter 5

Chapter 5. Competitive Balance. Competitive balance is about the degree of parity in a league .

baeddan-williams
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Chapter 5

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  1. Chapter 5 Competitive Balance

  2. Competitive balance is about the degree of parity in a league. • Over the last 10 years or so I have asked people I know what they think about the idea of forcing our pro sports leagues to increase the number of teams in their leagues. The answers I get have 3 common themes: • -You can’t force a league to have more teams, • -The level of play will fall – the absolute quality of play will fall, and • -The balance of competition will fall. • The authors of the book point out that historically leagues that have one or a few teams dominate (not much parity or balance) have lower ticket sales!!!! • The uncertainty of outcome hypothesis (UOH) is an idea that while fans do not want their team to lose, they are most interested when the home team has a 60 to 70% chance of winning. Table 5.1 of the book has information about the 1950’s when the New York Yankees were dominant. Note AL and Yankee attendance falls! • Is baseball unbalanced today with the Yankees? Was the NBA unbalanced when Michael Jordan was winning with the Bulls?

  3. Certainly at the pro level, highly matched teams tend to generate the most interest and that is what can generate the most money. So, I want to mention something I should have before. The demand for the networks to televise games is a derived demand. It is derived from their desire to sell advertising. Analogy: Why do firms demand labor? So the labor can help the firm make stuff and supply to the market. This is similar to TV networks and sports. Sports are like labor and the real supply is advertising. If leagues are highly competitive, there will be more interest, the TV networks will offer to pay more for putting games on TV and can sell ads for more money.

  4. Do teams in larger population cities that have a higher population fan base and thus a higher revenue base have an unfair advantage in the league? If so, then you would expect the balance in the league to become imbalanced as the richer teams buy up all the best talent. This could make the fan interest decline and thus league as a whole gets less revenue. In this light the league has an incentive to find competitive balance. We will look at measures that help us see if a league is balanced or unbalanced. But first let’ see how the idea of diminishing returns may mean league imbalance may not occur as suggested above. The basic idea of diminishing returns is that as you add some input like labor to a fixed input, the amount of output rises, but the increments to output slow down or diminish as more labor is added. In sports, with only so many spots on a field, does adding a superstar to the team help? Adding the 1st superstar is likely a good thing.

  5. Is adding the 2nd superstar a good thing? The 3rd? The 4th?... Even large population cities probably won’t buy all the best talent because eventually the contribution of the additional players, while positive, will likely not be as much as before and at some point will not be worth the additional cost of getting the superstar. Having said this, teams in larger cities probably have an incentive to buy more superstars than teams in smaller cities because at the margin the large market teams have greater range of revenue to spread out over the superstars. Next, let’s turn to measures of competitive balance as indicators of how balanced a sports league might be. (Remember folks say if you force leagues to expand balance will go down!) One method that is quick to calculate is just to take the range of the wins of the most winning team minus the wins of the fewest winning team.

  6. Measures of competitive balance • Quick story – have you ever been to a little league game? Many times the teams are evenly matched so that there is a high degree of competition. We could say the relative quality of play is high. But certainly the little league game is at an absolute level way below the high school and up levels. • Within-season variation - formula - you take the square root of the following: [Σ(wpct - .5)^2]/[N]. This is a standard deviation calculation. Here is what the formula is wanting you to do: • -For each of N teams take the winning percentage and subtract the average winning percentage of .500, • -Square the result of the subtraction problem for each team • -Add across all teams • -Divide the result of the addition by N (teams) • -Take the square root. • Example of two team league. Team A has 60% winning percentage and team B has 40% • (.6 - .5) and (.4 - .5) then (.6 - .5)^2 = .01 and (.4 - .5)^2 = .01 • .01 + .01 = .02 and .02/2 = .01 • Sqrt(.01) = .1

  7. Here is the calculation for the 2011-2012 NSIC Women’s Basketball Conference. Note the value for the within-season variation is .218. This may be hard to understand. Place in context of comparison with other years. What would be the within-season variation if everyone had the same 11-11 record? It would be 0! So, the larger the number the more imbalance there is in the conference.

  8. In general we say the larger the standard deviation here the more unbalanced the league is. The authors mention that different leagues have a different number of games and this makes comparisons across leagues difficult. But if you take the result above and divide by .5/sqrt(games per team) you will get a value that is comparable across leagues. • So, in baseball with 162 games per team the adjustment is to divide by 5/sqrt(162) = .039. • For the NSIC example .5/22 = .023 and the adjusted value is .218/.023 = 9.48 • Table 5.3 has information that suggests in 2008 the NBA was the most imbalanced based on this measure (3.07). • Between-season variation – This measure is for 1 team but across T years. The more the winning percentage for a team is different from year to year the greater this measure will be and thus the greater the balance. If a team has the same record every year this measure will be 0, suggesting imbalance. Here is the measure: you take the square root of the following: [Σ(wpct - avgwpct)^2]/[T], where T is the number of years in the calculation. Also note there is no adjustment made here when comparing to other leagues.

  9. Frequency of Championships • To consider this idea, think of a time period such as a decade. Then compile a list of all the champions in the time period. Let T be the number of years in the time period and Z be the number of teams on the list of champions. If Z < T then there has been at least 1 team being champ more than once during the period. The greater the “gap” between Z and T the more imbalance there is in the league. • The Herfindahl-Hirschman Index – HHI • From above we had Z teams on the list of champions over T periods. Let C be the number of championships a team has during the T periods. C = 0 for a team that is not on the list (like the Bungels in the NFL). The HHI = Σ (C/T)^2. This means take C/T for each team and square the result. Then add across all the teams. • Examples • a) 1 team wins in all T years and thus C = T – HHI = (C/T)^2 = (T/T)2 = 1 and this is as big as the number can be and this mean imbalance. • b) 2 teams each win half the time and thus C = .5T – HHI = (.5T/T)^2 + (.5T/T) ^2 = (.5)^2 + (.5)^2 = .25 + .25 = .5 • c) Lets expand T = N and have each team win 1 championship and thus C = 1 – HHI = (1/N)^2 + (1/N)^2 + … + (1/N)^2 N times = 1/(N^2) N times = N/N^2 = 1/N. This is as small as the measure can be. Remember the bigger the value the more imbalance.

  10. Lorenz curve • The Lorenz curve is a very general process where you look at a group and something about each member of the group. A common example in economics is to look at households as making up the group and also look at each household’s income. • The process of constructing a Lorenz curve would have you arrange the members of the group from the lowest value of the variable (like income) to the highest. Then you think about if equal increments of households (in % terms) yield the same increment in the variable. If so, you have perfect equality. But typically the increment in the variable is slower than the increment in the group. • Perhaps it would be best to consider an example. Let’s look at the NSIC 2011-2012 Women’s Bball again. Note that I sorted the data and have the team with the fewest wins first and then move up. Plus I have a column with the % of wins by the team. When there are 14 teams playing a 22 game schedule the total number of wins will be .5(14)(22) = 154. So, Upper Iowa, with 3 wins had 3/154 = .0194805 or about 1.9% of all wins.

  11. The 3 worst teams (or the worst 21.4% of teams(3/14 times 100)) won 9.09% of the games. The Lorenz curve plots the accumulation of both the % of teams and the % of wins. A graph of the Lorenz curve is seen on the next slide.

  12. The solid line here is a 45 degree line and would show what would happen if we had perfect balance – all teams winning the same number of games. We would have complete equality of teams. The dashed line is the Lorenz curve for the NSIC data. The more imbalanced the league the more the dashed line curves away from solid equality line. Think about the case where the three worst teams only won against each other once and so each had 3 wins each. The cumulative % would be just below 6% instead of the just over 9% we have.

  13. Here are a few slides to show you about the Lorenz curve for income in the US. In the United States, as in other countries, each family does not have the same income level. Here we want to consider the measurement of the inequality. One measurement that is looked at is the percentage of income each quintile of families has. Let’s consider how the measure is constructed. Imagine in a room we could put all the families in the country. Plus we would line the families up in a certain way. On the left side of the room we would start with the poorest family and the next family would have the next highest income, and so on. This would continue on until we had the richest family on the right. All of this is based on family income for the year. Next we would take the total number of families (not total income) and group them into 5 groups called quintiles. Each quintile would have the same number of families.

  14. Quintile % of income cumulative % Bottom 20% 4 4 Second 20% 10 14 Middle 20% 16 30 Fourth 20% 23 53 Fifth 20% 47 100 Here we have a table of income as distributed across the economy for a given year. Remember each group has the same number of families. The bottom 20% of families had only 4% of the income generated in a recent year. The highest 20% had 47% of the income. What would the table look like if every family had the same income?

  15. Cumulative % of income Lorenz curve A B Cumulative % of households

  16. The Lorenz curve is a graph of the cumulative percent of income by quintiles, starting with the bottom 20% on the horizontal axis.. The degree to which the curve is bowed out is an indication of the income inequality in the economy, with a larger bow meaning more inequality. The Gini coefficient is the ratio of area A to area A + B. The Gini has a coefficient value between 0 and 1, with 0 meaning perfect equality of income. What would the Lorenz curve look like and what would be the Gini coefficient if every family had the same income? Let’s get back to the sports econ stuff, okay?

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