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In celebration of #internationalwomensday, our iclickerqoftheweek highlights a video from the new Marginal Revolution University series on Women in Economics. Check out the newly launched video on Janet Yellen.  "Though she lacked female role models, Janet Yellen remained steadfast in her interest in applying economics to help others--and in the process, became a role model herself of young women all over the world. Chairing the Fed ain't a bad accomplishment, either." These videos feature Test Yourself questions that make great @iclicker questions. Check them out here Janet Yellen Quiz.   Let us know how you use these with your students! 

 

The quiz asks students to 

  • Identify the roles that Yellen had before she was Fed Chair
  • Who she succeeded as Fed Chair, and
  • Commodity bundling

Start your class off with a timely topic with the #iclickerqoftheweek. Ask your students to read Election Infrastructure and the Market for Voting Technology from our friends at Econofact before class (https://econofact.org/election-infrastructure-and-the-market-for-voting-technology via @econofactorg). Kick-off your classroom discussion with these questions from our faculty advisor,Solina Lindahl, who teaches Principles of Economics at Cal Poly, SLO, shares questions related to the State of the Union address.  Let us know how you use these with your students! 

 

*The correct answer is noted in bold.

Topic: Election Infrastructure and the Market for Voting Technology

Economic Concept: Types of Firms, Industrial Organization 

 

  1. What type of market best describes the suppliers of voting equipment? “Dominion Voting Systems, ES&S and Hart InterCivic acquired several of their smaller competitors in the first decade of the 2000s. Together, these three companies provide voting equipment to roughly 92 percent of the voting population in the United States, according to a 2017 report from the Penn Wharton School Public Policy Initiative” (https://econofact.org/election-infrastructure-and-the-market-for-voting-technology)

    1. Perfect Competition

    2. Monopolistic Competition

    3. Oligopoly

    4. Monopoly

 

Topic: Election Infrastructure and the Market for Voting Technology

Economic Concept: Markets

  1. In the “market” for voting technology, who are the demanders and who are the suppliers?

    1. The demanders are the voters, the suppliers are the local governments

    2. The demanders are the local governments, the suppliers are mostly private companies

    3. The demanders are mostly private companies, the suppliers are the local governments

    4. The demanders are the local governments, the suppliers are the voters

Topic: Election Infrastructure and the Market for Voting Technology

Economic Concept: Firms and Profit-Maximization

  1. What type of problem is likely to be created in markets such as those described below?  “Unlike other countries that have a centralized election authority, each individual state in the United States is responsible for setting their own election standards and procedures. In practice, the majority of election management functions are delegated to county and town governments in many states, which means that the potential customers for election technology number in the thousands with varying levels of resources and technical expertise.“(https://econofact.org/election-infrastructure-and-the-market-for-voting-technology

    1. The suppliers will have trouble meeting the exacting requirements of powerful, unified demanders

    2. The suppliers will face low profits since their products “homogeneous” (they are interchangeable with competitors)

    3. The market is so fragmented that suppliers will have trouble developing a consistent, safe and high-quality product

    4. The market is fragmented that buyers will face too many choices of products that fit their specifications, making a decision difficult

Topic: Election Infrastructure and the Market for Voting Technology

Economic Concept: Firms and Profit-Maximization

  1. If you were the CEO of a voting equipment firm who faces a market described by the following, what would be your most likely strategy?

“States and counties often lock themselves into ten- or fifteen-year contracts for voting machines because of how expensive this equipment is and its lack of interoperability with other systems, which requires them to completely replace their equipment if they want to switch to a different vendor.” and “vendors report that acquiring EAC certification, which some states require, can take two years or more and can run above $1 million per voting system” (https://econofact.org/election-infrastructure-and-the-market-for-voting-technology), 

    1. To concentrate on investing in product improvement and safety 

    2. To stick with existing technologies and avoid changes that would require re-certification 

    3. To spend money lobbying and marketing in an effort to gain contracts

    4. To engage in litigation over unsuccessful bids

    5. B, C and D are correct

Engage your students before you launch into your lecture with the #iclickerqoftheweek!  Tyler Cowen and Alex Tabarrok, authors of Modern Principles of Economics, share their favorite question about the market for roses to help you talk about price on #valentinesday.  Have your students watch how the #invisiblehand delivers roses in this short video, and then answer these questions.  (Click here for the video: I, Rose - YouTube )

 

Start your students off with a target question (learn how to use target questions here: iClicker Support) with a world map (search via Google Images for a world map with the countries labeled) and ask your students to Click on the country that the majority of the world's roses are coming from, according to the Chapter Opener in CH 7 The Price System: Signals, Speculation and Prediction (Page 119 in Micro and Econ).  Answer: Kenya. 

 

Why did flower production move out of the United States in the 1970s?
a) Flower blight in the United States.
b) Disco
c) An increase in the price of oil raised heating costs relative to transportation costs.
d) A change in preferences increased the demand for flowers grown elsewhere.
Correct answer: c
Suppose that imports of flowers were taxed (a tariff) what would happen to the US production and consumption of flowers?
a) US production would increase, US consumption would decrease
b) US production would decrease, US consumption would increase
c) US production would decrease, US consumption would decrease
d) US production would increase, US consumption would increase
Correct answer: a
Suppose that imports of flowers were taxed (a tariff) what would happen to chocolate consumption around Valentine's Day?
a) No expected change
b) Chocolate consumption would increase
c) Chocolate consumption would decrease
Correct answer: b (chocolate is a substitute for flowers)

 

 

Additional questions for discussion

  1. Why are so many countries involved with getting roses into the United States for Valentine's Day?
  2. If the price of airline fuel goes up, trace out the mechanism by which the number of roses given on Valentine's Day is likely to decline. 
  3. If you are trying to predict which countries might supply roses for Valentine's Day, which factors might be likely to play a role?

 

 

 

 

Engage your students before you launch into your lecture with the #iclickerqoftheweek.  Our faculty advisor, Solina Lindahl (@SolinaLindahl), who teaches Principles of Economics at Cal Poly, SLO, shares questions related to the State of the Union address.  Let us know how you use these with your students! 

*The correct answer is noted in bold.

Topic: State of the Union Address

Economic Concept: Unemployment

 

 

  1. As the President reminded us in the State of the Union Address, U.S. unemployment is at record lows. Which type of unemployment is lowest (nonexistent)?

    1. Structural unemployment

    2. Frictional unemployment 

    3. Cyclical unemployment

    4. Seasonal unemployment

Topic: State of the Union Address

Economic Concept: Fiscal Policy and Deficit

  1. In the State of the Union address, the President mentioned NASA’s Artemis Project, aimed at getting “the next man and the first woman” U.S. astronauts on the moon by 2024.  The effect of increased government spending on projects like this alongside tax cuts like the 2017 Tax Cuts and Jobs Act (TCJA) will have which of the following effects (other things equal) in the U.S. in the near future?

    1. To expand the economy and shrink the deficit

    2. To expand the economy and the deficit

    3. To slow the economy and shrink the deficit

    4. To slow the economy and expand the deficit

Topic: State of the Union Address

Economic Concept: Trade 

  1. In the State of the Union address, the President spoke about the trade war with China and his ongoing efforts to combat its “massive of theft of America’s jobs” and argued that the strategy has worked.  If the trade barriers are targeted toward saving U.S. manufacturing jobs, what are the likely effects according to economists?
    1. Manufactured goods prices in the U.S. will fall but will rise in China
    2. Manufactured goods prices in the U.S. will rise but U.S. manufacturing workers will lose their jobs
    3. U.S. consumers face lower prices but U.S. manufacturing workers will lose their jobs
    4. U.S. consumers face higher prices but U.S. manufacturing workers are helped

For all of you who #teachecon, our authors share an #iclickerqoftheweek with timely topics for Econ101. Eric Chiang, (@ProfessorChiang) author of Economics: Principles for A Changing World, Fifth Edition, starts us off with three questions on the #coronavirus 

*The correct answer is noted with an asterisk. 

 

Topic Coronavirus Epidemic

Economic Concept: Production Possibilities Frontier (Chapter 2 in Economics: Principles for A Changing World)

Question: To contain the spread of the coronavirus from its epicenter in Wuhan, authorities have temporarily closed all public transportation including airports, train and bus stations. This has caused some factories to halt production as workers stay home. How does this affect Wuhan’s PPF?

a) Wuhan’s production would temporarily move to a point farther to the right of its PPF

*b) Wuhan’s production would temporarily move to a point farther inside of its PP

c) Wuhan’s PPF would shift to the right

d) Wuhan’s production would stay on its PPF but at a different point

 

Topic: Coronavirus Epidemic

Economic Concept: Supply and Demand (Chapter 3 Economics: Principles for A Changing World)

Question: To accommodate the increase in demand for health care services in Wuhan due to the coronavirus epidemic, the government is building a temporary hospital with 1,000 beds. If the increase in supply is smaller than the increase in demand, what happens to the market price for health care, all else equal?


*a) market price and quantity both increase

b) market price and quantity both decrease

c) market price increases but market price decreases

d) market price decreases but market price increases

 

Topic: Coronavirus Epidemic

Economic Concept: Supply and Demand (Chapter 3 Economics: Principles for A Changing World)

Question: To contain the spread of the coronavirus from its epicenter in Wuhan, authorities have temporarily closed all public transportation including airports, train and bus stations during the Lunar New Year holiday. What is the likely impact of this policy on auto travel, all else equal?

 

a) A decrease in demand in auto travel, a complement to public transportation

b) A decrease in demand in auto travel, a substitute to public transportation

c) An increase in demand in auto travel, a complement to public transportation

*d) An increase in demand in auto travel, a substitute to public transportation

Monica Abbott led all pitchers of the the National Pro Fastpitch (NPF) league with 17 wins during the 2017 season. Since Abbott's team -- the Scrap Yard Dawgs -- only won 31 games that year, Abbott was apparently worth 55% of her team's wins.

Of course, that can't be right.  Although people in softball (and baseball) routinely assign team wins to individual pitchers, it is incorrect to think a pitcher is the sole reason why a team wins (or loses). So that leaves us with a question.

How many wins do pitchers in softball really produce? Similar to what has been done for hitters in softball, this question can be answered by looking at the box score statistics.

The process for pitchers begins with the concept of Fielding Independent Pitching Earned Run Average (FIP ERA).  As detailed in Sports Economics, Earned Run Average (ERA) is not the best measure of a pitcher's performance. Because earned runs depend on the fielders around the pitcher, a pitcher's ERA is not simply about the pitcher's performance.  The better (or worse) the fielders around the pitcher perform the better (or worse) will be a pitcher's ERA.

The problem with ERA was originally noted by Voros  McCracken.  And McCracken also devised a better approach.  This approach -- as detailed in Chapter Eight of Sports Economics -- was adapted to data from the NPF.  The specific model involves regressing a pitcher's ERA on defensive independent statistics -- specifically strike outs, walks, hit-by-pitch, and home runs -- and one defensive dependent measure.  This last measure was Hits per Ball in Play (HperBIP), which is calculated as follows:

HperBIP = [Hits – Home Runs]/[Outs + Hits – Strike Outs – Home Runs]

The data employed to estimate this model included every pitcher in the NPF from 2004 to 2018 who had at least 50 innings pitched in a single season. In all, there were 221 pitcher observations. The results -- reported in the table below -- indicate that 89% of the variation in pitcher's ERA is explained by these factors.

To construct the FIP ERA, we simply multiply each pitcher's defensive independent statistic by the corresponding coefficient. We then use the average value for HperBIP in the aforementioned player sample to construct each player's FIP ERA.

 

The following example for Monica Abbot's 2017 season illustrates the process. In column (2) we have the value of each statistics for Monica Abbott in 2017 and in the third column are the coefficients from the aforementioned model.  Multiplying these two columns -- and then summing these values -- gives us Abbott's FIP ERA. As one can see, Abbott's FIP ERA was 1.47; or a bit worse than her actual ERA of 1.17.

 

 

Of course, the objective is to measure Abbott's production of wins.  To do this we follow the following steps:

  1. For each pitcher we determine the number of earned runs the pitcher surrendered that can be attributed to each pitcher's FIP stats (i.e. strike outs, walks, hit-by-pitch, and home runs).  For Abbott in 2017, her FIP stats for the season were worth -3.95 runs for the season.
  2. Abbott pitched 144 innings in 2017.  The next step is to determine how many runs an average pitcher would have surrendered with her FIP stats in that many innings. From 2004 to 2018, NPF pitchers recorded 24,908.67 innings pitched and surrendered in these innings 3,998.4 FIP earned runs. This means that per inning, an average pitcher surrendered 0.16 runs.  So, in 144 innings an average pitcher's FIP stats would have led to 23.1 earned runs. In other words, Abbott surrendered 27.1 fewer runs than an average NFP pitcher.
  3. A regression of team winning percentage on runs scored per game and runs surrendered per game indicates that each additional run scored is worth 0.085 additional wins in the NPF. This means that Abbott produced 2.30 wins more than an average NFP pitcher (i.e. 0.085*27.1).
  4. From 2004 to 2018, NPF teams won 1950 games.  Let's assume hitters produce half a team's wins and pitching and defense produce the remaining half.  So, pitchers and the defensive players are credited with 975 wins. To split the credit for pitchers and the defenders around the pitchers we will look at total runs surrendered and FIP earned runs.  From 2004 to 2018, teams surrendered 12,038 total runs. But again, the FIP earned runs were only 3,998.41. Therefore, pitchers were only responsible for 33% of the runs allowed by NPF teams. And therefore, we can argue that pitchers are only responsible for 33% of the wins attributed to the pitchers and defense.  That means, pitchers are credited with 323.8 wins. Given the number of innings pitched, this means an average pitcher produced 0.013 wins per inning.
  5. Again, Abbott pitched 144 innings.  If she was average, she would have produced 1.87 wins.  Given that she produced 2.30 wins above average, we can now see that all these calculations indicate Abbott was worth 4.17 wins in 2017.

 

Each of those steps were applied to all pitchers in the NPF from 2004 to 2018. What follows are the top 20 pitchers -- in Wins Produced -- from 2004 to 2018.  

As one can see, Monica Abbott's 2017 performance ranks 3rd all-time in NPF history.  She is also listed five more times in the list of top 20 pitchers. She never did quite as well as Christa Williams in 2005 and Amanda Scott in 2004.  But Wins Produced suggests Abbott is likely the greatest pitcher in NPF history.

When a game ends we know which team won. What we don't know is how each player contributed to the outcome we observed.

Coaches -- and perhaps some fans -- might want to think that teams win and lose entirely as a team.  But that is not exactly right. Some players clearly seem to matter more than others.

In basketball -- as Sports Economics details -- we can convert the box score statistics into a measure of Win Produced. We can also do something similar -- as the discussion of Reggie Jackson in Sports Economics explains -- for hitters in baseball. And now we can do the same thing for hitters in softball.

According to Softball America, the top returning hitter in college softball is Amanda Lorenz of the University of Florida. Lorenz's stats are impressive in 2018.  As Softball America notes, Lorenz posted the following numbers last year:

  • Batting Average: 0.416
  • On-Base-Percentage: 0.582
  • Slugging Average: 0.753
  • Home Runs: 11

Those stats are impressive. But as noted in Sports Economics, we can do more than just look at the some numbers. Once again, the numbers tracked for players can be translated into a measure of how many wins each player produced.

The process begins with measuring how many runs each player creates.  Following the methodology laid forth by Asher Blass in the Review of Economics and Statistics in 1992, we begin by regressing how many runs a team scores per game on a collection of per-game team statistics.  This was applied to college softball with data from 2012 to 2018. The results -- reported below --indicate that 94.49% of the variation in team runs is explained by the thirteen box score statistics listed.

 

Independent Variable

Coefficient

t-stat

p-value

Constant Term

1.25

8.37

0.00

Single

0.55

48.33

0.00

Double

0.88

30.44

0.00

Triple

1.39

17.65

0.00

Home Runs

1.46

57.79

0.00

Walks

0.41

35.57

0.00

Hit-by-Pitch

0.40

14.88

0.00

Stolen Bases

0.21

11.93

0.00

Caught Stealing

-0.48

-7.49

0.00

Sacrifice Flies

0.81

9.34

0.00

Strike-outs

-0.19

-19.05

0.00

Double-Plays

-0.46

-7.10

0.00

Ground outs

-0.14

-14.58

0.00

Fly outs

-0.22

-23.64

0.00

R-squared

0.9449

 

As both the t-statistic and p-values indicate, the estimated coefficients are all significant at the 99% level.  These coefficients can also be used to measure how many runs Lorenz created in 2018. This involves multiplying Lorenz's production of each statistic by the corresponding coefficient.  For example, Lorenz had 40 singles and the above analysis says each single is worth 0.55 runs. Therefore, Lorenz is worth 21.8 runs (or 40 * 0.55). If we do this for every statistic (as one sees in the following table) Lorenz's stats were worth 72.4 runs in 2018.

 

Variable

Amanda Lorenz

production

Coefficient

Runs

Created

(production * coefficient)

Single

40

0.55

21.8

Double

19

0.88

16.7

Triple

4

1.39

5.5

Home Runs

11

1.46

16.1

Walks

70

0.41

28.4

Hit-by-Pitch

2

0.40

0.8

Stolen Bases

6

0.21

1.2

Caught Stealing

1

-0.48

-0.5

Sacrifice Flies

1

0.81

0.8

Strike-outs

16

-0.19

-3.0

Double-Plays

2

-0.46

-0.9

Ground outs

40

-0.14

-5.6

Fly outs

42

-0.22

-9.1

Total Runs Created

72.4

 

To convert these 72.4 Runs Created into a measure of Wins Created, we follow these steps (also detailed for Major League Baseball players in Sports Economics):

  1. From 2012 to 2018, all softball hitters created 349,157.22 runs (following the methodology outlined above). These hitters also had 2,796,591 plate appearances. So, per plate appearance, an average hitter created 0.125 runs. Lorenz had 250 plate appearances in 2018. If she was average, she would have created 31.2 runs. In other words, Lorenz created 41.2 runs beyond average.
  2. A regression of team winning percentage on runs scored per game and runs surrendered per game indicates that each additional run scored is worth 0.076 additional wins. That means that Lorenz produced 3.114 wins beyond what an average hitter would have created (i.e. 0.076 * 41.2).
  3. If we assume hitters produced half of a team's wins (pitching and defense produce the remaining half), the average hitter from 2012 to 2018 produced 0.0096 wins per plate appearance. This means that an average player in Lorenz's plate appearances would have produced 2.409 wins (i.e. 0.0096*250).
  4. Putting steps #2 and #3 together, we see that Lorenz's hitting was worth 5.523 wins for the Florida Gators (i.e. 3.114 + 2.409).

The Gators won 56 games in 2018.  The numbers indicate that Lorenz's hitting was worth nearly 10% of this total.

We can repeat this exercise for every hitter in softball from 2012 to 2018. Here are the top 10 hitters from the Power 5 Conferences (ACC, Big 12, Big 10, Pac 12, and SEC):

  1. Lauren Chamberlain (Oklahoma, 2013): 8.395
  2. Sierra Romero (Michigan, 2015): 7.485
  3. Kasey Cooper (Auburn, 2016): 7.460
  4. Sierra Romero (Michigan, 2014): 7.080
  5. Maddie O'Brien (Florida State, 2014): 7.023
  6. Katelyn Boyd (Arizona State, 2012): 7.022
  7. Emily Carosone (Auburn, 2015): 6.830
  8. Lauren Chamberlain (Oklahoma, 2015): 6.788
  9. Valerie Arioto (California, 2012): 6.628
  10. Sierre Romero (Michigan, 2016): 6.587

Sierra Romero shows up three times on this list and Lauren Chamberlain appears twice.  Today this duo is starring for the USSSA Pride of the National Pro Fastpitch league (NPF). In 2018, USSSA Pride won the Cowles Cup and Romero and Chamberlain were a big part of that title team. Of course, they also had quite a bit of help (the Pride have many stars).

Part of that help came from the Pride's pitchers. In a future post we will discuss how to measure wins for pitchers in softball. And yes, it involves more than just observing who won the game.

The NFC and AFC championship games are this weekend. The quarterbacks in these games -- Tom Brady, Patrick Mahomes, Drew Brees, and Jared Goff -- are the last signal callers playing and clearly must be the best quarterbacks in the game. Right?

 

Although these quarterbacks are the only quarterbacks with something to play for anymore, the NFL marketplace did not rank them among the best before the season started. According to Spotrac, here were the top quarterbacks in average salary in 2018.

  1. Aaron Rodgers (Green Bay Packers): $33,500,000
  2. Matt Ryan (Atlanta Falcons): $30,000,000
  3. Kirk Cousins (Minnesota Vikings): $28,000,000
  4. Jimmy Garoppolo (San Francisco 49ers): $27,500,000
  5. Matthew Stafford (Detroit Lions): $27,000,000
  6. Derek Carr (Oakland Raiders): $25,000,000

 

Not only are these quarterbacks not playing this weekend, none of these quarterbacks even made the playoffs. How can the quarterbacks the market decided were the best fail so miserably on the field?

 

The appendix to Sports Economics provides one answer. NFL Quarterbacks are -- relative to basketball players and hitters in baseball -- remarkably inconsistent. Only 31.1% of a quarterback's current completion percentage is explained by what that same NFL quarterback did the previous season. For passing yards per attempt, only 22.1% of
current performance is explained by last year. And for touchdowns per attempt, only 10.1% of a quarterback's current mark is linked to last year's performance.

 

When we turn to interceptions we see predicting the future is almost impossible. Only 0.6% (i.e. less than 1%) of a quarterback's current interceptions per attempt are explained by what the quarterback did last year. This means that you can't know how many interceptions a quarterback will throw before the season starts.

 

Salaries are a statement about a player's future performance. The salary paid to Aaron Rodgers in 2018 was determined before the 2018 season started. This salary was set so high because the Packers believed he would perform well. But as the data indicates, the performance of quarterbacks is immensely difficult to predict. In sum, it simply isn't possible for teams to know with certainty which quarterbacks will perform well.

 

Why is a quarterback's performance so difficult to predict? A quarterback's passes depend on his offensive line, his receivers, the quality of his running game, the plays that are called by his coaches, and the quality of the opposing defense. In sum, quarterbacks do not act by themselves and the quality of everyone else on the field -- and the coaches off the field -- dramatically impact the outcomes we assign to quarterbacks.

 

Given all this, as chapter two notes, payroll in the NFL explains less than 3% of wins in the NFL. Yes, predicting outcomes in the NFL is very difficult.

 

So, maybe it isn't surprising the highest paid quarterbacks are watching the playoffs this weekend. When it comes to player pay in football, teams definitely do not have a crystal ball. And the inability to predict the future will mean we will see cases where the market tells one story while the outcomes on the field tell a very different tale.

The NFC and AFC championship games are this weekend.  The quarterbacks in these games -- Tom Brady, Patrick Mahomes, Drew Brees, and Jared Goff -- are the last signal callers playing and clearly must be the best quarterbacks in the game. Right?

Although these quarterbacks are the only quarterbacks with something to play for anymore, the NFL marketplace did not rank them among the best before the season started.  According to Spotrac, here were the top quarterbacks in average salary in 2018.

  1. Aaron Rodgers (Green Bay Packers): $33,500,000
  2. Matt Ryan (Atlanta Falcons): $30,000,000
  3. Kirk Cousins (Minnesota Vikings): $28,000,000
  4. Jimmy Garoppolo (San Francisco 49ers): $27,500,000
  5. Matthew Stafford (Detroit Lions): $27,000,000
  6. Derek Carr (Oakland Raiders): $25,000,000

Not only are these quarterbacks not playing this weekend, none of these quarterbacks even made the playoffs.  How can the quarterbacks the market decided were the best fail so miserably on the field?

The appendix to Sports Economics provides one answer. NFL Quarterbacks are -- relative to basketball players and hitters in baseball -- remarkably inconsistent.  Only 31.1% of a quarterback's current completion percentage is explained by what that same NFL quarterback did the previous season. For passing yards per attempt, only 22.1% of current performance is explained by last year. And for touchdowns per attempt, only 10.1% of a quarterback's current mark is linked to last year's performance.

When we turn to interceptions we see predicting the future is almost impossible. Only 0.6% (i.e. less than 1%) of a quarterback's current interceptions per attempt are explained by what the quarterback did last year. This means that you can't know how many interceptions a quarterback will throw before the season starts.  

Salaries are a statement about a player's future performance.  The salary paid to Aaron Rodgers in 2018 was determined before the 2018 season started.  This salary was set so high because the Packers believed he would perform well. But as the data indicates, the performance of quarterbacks is immensely difficult to predict. In sum, it simply isn't possible for teams to know with certainty which quarterbacks will perform well.

Why is a quarterback's performance so difficult to predict? A quarterback's passes depend on his offensive line, his receivers, the quality of his running game, the plays that are called by his coaches, and the quality of the opposing defense. In sum, quarterbacks do not act by themselves and the quality of everyone else on the field -- and the coaches off the field -- dramatically impact the outcomes we assign to quarterbacks.

Given all this, as chapter two notes, payroll in the NFL explains less than 3% of wins in the NFL.  Yes, predicting outcomes in the NFL is very difficult.

So, maybe it isn't surprising the highest paid quarterbacks are watching the playoffs this weekend.  When it comes to player pay in football, teams definitely do not have a crystal ball. And the inability to predict the future will mean we will see cases where the market tells one story while the outcomes on the field tell a very different tale.

The NBA season begins this week. In most sports, the start of a new season is time for optimism.  But in the NBA -- as I detail in my latest for Forbes -- for most teams, there isn't much reason to be optimistic. At least, if by optimism we mean "there is hope your favorite team can win a championship in 2019" then for most teams there is no real hope.

This conclusion is based on the story told in Chapter Five of Sports Economics. Basketball suffers from a "short supply of tall people." As detailed in the book, the average height of an NBA player (which is about 6-7) is somewhat rare in the world.  And 7-foot tall players - who are somewhat common in the NBA -- are immensely hard to find.

Because the NBA is drawing on a very small population, the supply of tremendously gifted basketball players -- like LeBron James, Kevin Durant, Ben Simmons, etc... -- is quite limited. This means that most NBA teams must fill out their rosters with less gifted players. And the teams with less gifted players really don't have a chance. Or in other words, the NBA lacks competitive balance.

Of course -- again, as detailed in Chapter Five -- the NBA has adopted quite a few institutions to address the lack of competitive balance. The NBA has a reverse-order draft, a cap on payrolls, a cap on individual salaries, and a luxury tax.  All of these institutions are designed to improve competitive balance. But because balance appears to be about the underlying population of talent --which the NBA can't change -- these institutions do not have much impact on the NBA's competitive balance problem.

Fortunately for the NBA -- again, as detailed in Chapter Five -- it doesn't appear a lack of competitive balance really has much impact on demand.  So although the NBA season lacks the drama we see in other sports, we can still expect fans to enjoy watching the games and the NBA to do quite well.  But we can also expect that if you are not a fan of the few teams that are truly going to contend, the ending for your team is likely a foregone conclusion. 

A few more thoughts on my latest for Forbes:

Few Would Take The Nobel Prize Selection Process Seriously If Applied To Sports

In sports -- as noted in Chapter Six -- we have a number of metrics to answer that question. But this class isn't just about sports. It's also about economics.

When people ask the question "who is the best?" in economics, often they turn to Svergiges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel (i.e. the Nobel Prize in Economics). Economists who receive this prize are often thought of as "the best". But as detailed in my latest for Forbes, the methodology used to determine this award seems a bit suspect. Specifically, it appears the Nobel Prize is determined by less than ten people primarily from Sweden.

To put that in perspective, imagine if the NFL's Hall of Fame -- located in Canton, Ohio -- was entirely determined by six people from Canton, Ohio. Or members to baseball's Hall of Fame-- located in Cooperstown, New York -- was selected by six people from Cooperstown. One suspects that many people might wonder if each Hall of Fame was really selecting "the best" with this approach.

Perhaps the issues with the Nobel Prize selection played a role in the interesting story told in Chapter Four.  As the book notes, Ronald Coase received a Nobel Prize (in 1991) for the Coase Theorem. But as the book notes, what Coase said was

  • originally said about sports by Simon Rottenberg in 1956 (well, sort of -- Rodney Fort stated more clearly what Rottenberg was saying).
  • and as Paul Samuelson notes, the Coase Theorem wasn't really said by Coase. It was originally said by George Stigler (who also was given a Nobel Prize in 1982 -- but not for this).

Yes, it is a bit confusing. But one could argue that Coase's Nobel Prize could have gone to Rottenberg. Or maybe Rod Fort!

Regardless, the story of the Nobel Prize in Economics does give us an opportunity to think about how we measure performance. This is a crucial topic in economics (not just sports economics) because by being able to measure performance we can discuss a host of issues including the existence of discrimination (race, gender, nationality, etc...), whether or not workers are exploited, how managers impact performance, and many more.

Exploitation was defined by Joan Robinson as a worker being paid a wage less than their marginal revenue product. As noted in Sports Economics, we expect this to happen if the worker's bargaining power is limited by an employer with monopsonistic power. A good example was Major League Baseball prior to the enactment of free agency in the mid-1970s.  Another good example is college sports in the United States. The NCAA limits a college athlete's compensation to the cost of attendance. The existence of such a limit suggests a college athlete would be exploited. In fact, if that wasn't the case then we would wonder why the limit was even necessary.

Although exploitation happens outside the world of sports, the world of sports gives us an opportunity to measure the size of the effect.  The first approach to measuring exploitation in sports came from Gerald Scully. In 1974, Gerald Scully empirically examined how the reserve clause -- which forced Major League Baseball players to only negotiate with one team -- led to the exploitation of professional baseball players.

The Scully approach involves estimating two relationships.

First, one looks at the link between team revenue, team wins, and a collection of control variables.  From this model, we derive the dollar value of a team win.

One then examines the link between team wins and player statistics.  This model is used to measure how many wins a player creates.

The Scully model has been used in a number of academic articles. Despite its repeated use, though, it has some serious flaws.  For example, there is no value in the Scully model for participating in practice. A player is only given credit for producing wins in the actual games. But practice is a large part of what any athlete does and those players who don't produce wins do provide economic value to a team.  In other words, contrary to the words of Allen Iverson, it is likely practice matters.

There is also an issue with the revenue model.  As detailed in Sports Economics (and a working paper I wrote with Anthony Krautmann), the value of a win in baseball changes dramatically over time.  Specifically, if we look back to the original sample Scully considered from the late 1960s, the value of a win is so large that the amount of revenue Scully attributes to the players exceeds all the revenue in the league.  In more recent years -- as noted in a paper I wrote with Michael Leeds and Peter von Allmen (and also noted in Sports Economics) -- the impact of fixed revenues (i.e. revenues that are not impacted by wins such as broadcasting revenues), causes the estimated value of a wins to be so low that it appears most (if not all) players are now dramatically overpaid.

Given the problems with the Scully model, an alternative approach is needed.  In the Marquette Sports Law Review -- and yes, in Sports Economics  -- the following method for college basketball was briefly described.

We begin by looking at how pay is allocated in the National Basketball Association. As Larry Coon's NBA Salary Cap FAQ details, the NBA pays about 50% of league revenue to its players.  In addition, the average minimum pay in the first year of a contract is currently $1.71 million (minimum pay varies by years of experience). Since average pay -- or total revenue shared with players divided by the number of players in the league -- was $4.24 million in 2017-18, the NBA currently sets its minimum pay at about 35% of its average pay.  

One can think of minimum pay as what a player gets for practice.  Again, practice matter. So, everyone's pay should begin with this payment.

Of course, some players also produce wins and those players should be paid more. Here are the specific steps one follows to allocate revenue in terms of how many wins each player produces. For illustrative purposes, the 2017-18 women's basketball team at South Carolina University is examined.

  1. Determine how much revenue should be paid to the players: According to the Department of Education, the South Carolina's women's basketball team reported $2,046,234 in revenue in 2016-17 (this is the last year data was available). If we assume revenue was the same in 2017-18 (likely it was higher -- as revenues grow over time), and the South Carolina Gamecocks gave 50% of its revenue to its players, then the players in 2017-18 would be splitting $1,023,117.
  2. Determine average and minimum pay:  In 2017-18, there were 10 players who logged minutes for the Gamecocks. So, if the players received $1,023,117 then the average player would be paid $102,312.  In addition, if players are guaranteed 35% of the average, then minimum pay would be $35,809.
  3. Determine how much revenue will be allocated by a player's production of wins: If each player is paid at least $35,809, then the summation of minimum pay across all players is $358,091. This number is subtracted from $1,023,117 (i.e. the total allocation to players) to determine how much revenue will be allocated by wins produced.  The result of this subtraction is $665,026.
  4. Address players who produce negative wins: A player's production of wins can be measured in basketball (again, this is detailed in Sports Economics and in other places for the NBA and WNBA). Some players, though, have an estimated negative impact. If we believe all players should be guaranteed a minimum wage, we need to address this issue.  The approach taken is to sum the wins production of all players who produced a positive quantity of wins. For the Gamecocks in 2017-18, the summation of wins for all players who produced a positive quantity of wins is 28.92.  The value of each of these wins is then $22,997 (i.e. $665,026 divided by 28.92).
  5. Determine how much revenue should be paid to each player: A'Ja Wilson -- the number one pick in the 2018 WNBA draft -- produced 7.71 wins for the Gamecocks in 2017-18.  Wilson's estimated value would then be as follows:

Wilson's Economic Value: 7.71 * $22,997 + $35,809 = $213,049

In words… a player's value is simply the value of their wins production (or wins produced time the value of a win) plus the value of the minimum wage.  If a player didn't produce wins, or their wins production was negative, then that player is simply worth the minimum wage.

Here are the results for all players who logged minutes for South Carolina in 2017-18.

Player

Wins Produced

Economic Value

A'Ja Wilson

7.71

$213,049

Tyasha Harris

6.61

$187,880

Alexis Jennings

4.82

$146,765

Bianca Jackson

3.13

$107,871

Doniyah Cliney

2.64

$96,602

Mikiah Herbert Harrigan

1.59

$72,390

Lele Grissett

1.21

$63,733

Lindsey Spann

0.97

$58,150

Ladazhia Williams

0.22

$40,867

Victoria Patrick

-0.28

$35,809

TOTALS

28.63

$1,023,117

 

South Carolina won 29 games in 2017-18.  So, the estimated wins are quite close to the actual total.  In addition, the summation of economic values exactly matches the 50% split of revenue determined in step one above.

The cost of attending South Carolina for out-of-state students is $47,587. This cost is the sticker price, which generally is not paid by many students.  Nevertheless, if this value was taken as an estimate of what South Carolina is paying players, then we can see that eight of these ten players are -- by definition -- exploited.

So, does this analysis suggest that Ladazhia Williams and Victoria Williams are not exploited? Well, maybe not.  There is an important impact of sports that are not captured in the revenue numbers submitted to the Department of Education. A universities' sports teams provide an immense amount of advertising for the school. This is especially true when we consider "the Flutie Effect"; or the impact athletic success has on a school's admissions. The analysis reported above ignore this effect, so what we are seeing above likely underestimates a player's value. In sum, it is likely all the players listed above are paid a wage that is less than their marginal revenue product.

Of course, is the measure listed above really a player's marginal revenue product? The approach taken above assumes that players should be paid 50% of league revenues.  But that is based solely on current bargaining in the NBA. In the past, the NBA gave a higher percentage of revenue to its players. Furthermore, in European soccer in the past as much as 76% of its revenue went to its players.

So, what is the "right" revenue split? It doesn't appear this can be determined. What we can do is say what a player would be paid if

  • revenues were split in a certain fashion
  • players were guaranteed a minimum wage
  • players were generally paid for wins

When we take that approach, it appears the basketball players for the women's basketball team at South Carolina in 2017-18 were generally underpaid.  In other words, exploitation was the norm.

This is not an unusual story in college sports. Exploitation is not simply something that happens in men's basketball and football.  We can find players that would likely be paid more than the cost of attendance in a number of sports; if the NCAA had to pay like a professional sports league. Again, this is what economic theory would predict.  The advantage of sports is that we have the data to examine this prediction.

Chapter Nine of Sports Economics begins with a story many may know (or not!).  The highest paid public employee in most states is either a head coach in college football or college basketball.  When we looked at revenue in Chapter Nine of the book, though, the amount paid seemed somewhat odd.  For example, Pete Carroll was paid $7 million by the Seattle Seahawks of the NFL in 2015; a team that had $377 million in revenue. That same year Nick Saban was paid $7.1 million by the University of Alabama. But the football program at the University of Alabama only reported $97 million in revenue.

While many of us think about the men's NCAA basketball tournament we should remember a similar revenue-salary story can be told in basketball.  USA Today recently reported the salaries of the head coaches in men's college basketball.  According to this report, Mike Krzyzewski of Duke University, John Calipari of Kentucky, and Chris Holtmann of Ohio State are all paid more than $7 million per year.  HoopsHype, though, says only three NBA head coaches -- Gregg Popovich, Doc Rivers, and Tom Thibodeau -- are paid this well.  But just like college and professional football, if we look at the revenues of men's college basketball and the NBA it is hard to understand why coaches in both levels of competition would be paid similar wages.

Well, it isn't that hard to understand. 

NBA teams pay their players 50% of their revenue. The NCAA, though, significantly restricts payments to college athletes. Therefore the money in generated in college basketball has to go someplace else.  One "someplace else" is in the paychecks of the head coaches.

Let's imagine a world, though, where college coaches were paid like the NBA. According to Forbes.com, the average NBA team generated $245.6 million in revenue in 2016-17 while HoopsHype says the average head coach is paid $5.9 million per year.  So the NBA pays on average 2.4% of its revenue to its head coach.  What if men's college head coaches were paid in the same fashion?

Universities report the revenue of each athletic team to the U.S. Department of Education. The last year the data is reported is from 2016.  If we assume those revenue numbers haven't changed too much (which may not be a great assumption!), then we can use these 2016 revenue numbers to calculate what each head coach in men's basketball would be paid if their pay was restricted to 2.4% of team revenue. 

For example, Duke University reported $34.3 million in revenue for men's basketball in 2016. If Coach Krzyzewski was paid 2.4% of team revenue his pay would be $823,498; or more than $8 million less than he is actually paid today.

Once again, USA Today reports what college men's basketball coaches are actually being paid by their schools. And here is what the thirty highest paid college coaches would be paid if they were paid like NBA head coaches:

  1. Mike Krzyzewski (Duke University): $823,498
  2. John Calipari (Kentucky University): $669,490
  3. Chris Holtmann (Ohio State University): $436,908
  4. Bill Self (Kansas University): $437,297
  5. Tom Izzo (Michigan State University): $420,115
  6. Sean Miller (Arizona University): $561,032
  7. Bob Huggins (West Virginia University): $163,895
  8. Larry Krystkowiak (University of Utah): $209,582
  9. John Beilein (University of Michigan): $404,903
  10. Archie Miller (Indiana University): $587,989
  11. Shaka Smart (University of Texas): $420,578
  12. Lon Kruger (University of Oklahoma): $315,788
  13. Gregg Marshall (Wichita State): $177,784
  14. Tony Bennett (University of Virginia): $204,811
  15. Avery Johnson (University of Alabama): $359,189
  16. Scott Drew (Baylor University): $217,789
  17. Frank Martin (University of South Carolina): $286,055
  18. Brad Underwood (University of Illinois): $378,902
  19. Buzz Williams (Virginia Tech): $225,720
  20. Mark Turgeon (University of Maryland): $424,729
  21. Dana Altman (University of Oregon): $266,927
  22. Cuonzo Martin (University of Missouri): $240,974
  23. Steve Alford (UCLA): $321,201
  24. Jay Wright (Villanova): $266,223
  25. Mike Anderson (University of Arkansas): $391,011
  26. Michael White (University of Florida): $339,960
  27. Bruce Pearl (Auburn University): $237,022
  28. Will Wade (LSU): $194,770
  29. Matt Painter (Purdue University): $243,510
  30. Mike Brey (Notre Dame): $93,289

A few notes on this list.  First, the average salary for this group is $3.5 million and this average pay works out to 27.1% of average reported revenues. If these coaches were paid like the NBA, though, the average pay of these coaches would only be $344,031.  So if these coaches were paid like NBA coaches then on average each would see a pay cut of about $3 million (similar to what I said about Sean Miller at the University of Arizona earlier this month).

In addition, none of these head coaches would be paid as much as a million dollars per year. And Mike Brey's pay wouldn't be much different than a professor at Notre Dame. Brey's school only reported $3.9 million in revenue in 2016 from their men's basketball team and his currently salary is 61% of this total. But if NCAA paid like the NBA, Brey would receive less than $100,000 per year. 

To the best of my knowledge, no college coach has come forward to advocate that the NCAA pay players and coaches as they are in the NBA.  And given these numbers, there isn't much incentive for any coach to advocate such a change.  But it is interesting to see what a less restricted market would look like.  The picture painted suggests that many NCAA coaches are not going to want to live in a world where NCAA athletes are better compensated for their efforts and coaches… well, they get much, much less.

Chapter Nine of Sports Economics begins with a story many may know (or not!).  The highest paid public employee in most states is either a head coach in college football or college basketball.  When we looked at revenue in Chapter Nine of the book, though, the amount paid seemed somewhat odd.  For example, Pete Carroll was paid $7 million by the Seattle Seahawks of the NFL in 2015; a team that had $377 million in revenue. That same year Nick Saban was paid $7.1 million by the University of Alabama. But the football program at the University of Alabama only reported $97 million in revenue.

While many of us think about the men's NCAA basketball tournament we should remember a similar revenue-salary story can be told in basketball.  USA Today recently reported the salaries of the head coaches in men's college basketball.  According to this report, Mike Krzyzewski of Duke University, John Calipari of Kentucky, and Chris Holtmann of Ohio State are all paid more than $7 million per year.  HoopsHype, though, says only three NBA head coaches -- Gregg Popovich, Doc Rivers, and Tom Thibodeau -- are paid this well.  But just like college and professional football, if we look at the revenues of men's college basketball and the NBA it is hard to understand why coaches in both levels of competition would be paid similar wages.

Well, it isn't that hard to understand. 

NBA teams pay their players 50% of their revenue. The NCAA, though, significantly restricts payments to college athletes. Therefore the money in generated in college basketball has to go someplace else.  One "someplace else" is in the paychecks of the head coaches.

Let's imagine a world, though, where college coaches were paid like the NBA. According to Forbes.com, the average NBA team generated $245.6 million in revenue in 2016-17 while HoopsHype says the average head coach is paid $5.9 million per year.  So the NBA pays on average 2.4% of its revenue to its head coach.  What if men's college head coaches were paid in the same fashion?

Universities report the revenue of each athletic team to the U.S. Department of Education. The last year the data is reported is from 2016.  If we assume those revenue numbers haven't changed too much (which may not be a great assumption!), then we can use these 2016 revenue numbers to calculate what each head coach in men's basketball would be paid if their pay was restricted to 2.4% of team revenue. 

For example, Duke University reported $34.3 million in revenue for men's basketball in 2016. If Coach Krzyzewski was paid 2.4% of team revenue his pay would be $823,498; or more than $8 million less than he is actually paid today.

Once again, USA Today reports what college men's basketball coaches are actually being paid by their schools. And here is what the thirty highest paid college coaches would be paid if they were paid like NBA head coaches:

  1. Mike Krzyzewski (Duke University): $823,498
  2. John Calipari (Kentucky University): $669,490
  3. Chris Holtmann (Ohio State University): $436,908
  4. Bill Self (Kansas University): $437,297
  5. Tom Izzo (Michigan State University): $420,115
  6. Sean Miller (Arizona University): $561,032
  7. Bob Huggins (West Virginia University): $163,895
  8. Larry Krystkowiak (University of Utah): $209,582
  9. John Beilein (University of Michigan): $404,903
  10. Archie Miller (Indiana University): $587,989
  11. Shaka Smart (University of Texas): $420,578
  12. Lon Kruger (University of Oklahoma): $315,788
  13. Gregg Marshall (Wichita State): $177,784
  14. Tony Bennett (University of Virginia): $204,811
  15. Avery Johnson (University of Alabama): $359,189
  16. Scott Drew (Baylor University): $217,789
  17. Frank Martin (University of South Carolina): $286,055
  18. Brad Underwood (University of Illinois): $378,902
  19. Buzz Williams (Virginia Tech): $225,720
  20. Mark Turgeon (University of Maryland): $424,729
  21. Dana Altman (University of Oregon): $266,927
  22. Cuonzo Martin (University of Missouri): $240,974
  23. Steve Alford (UCLA): $321,201
  24. Jay Wright (Villanova): $266,223
  25. Mike Anderson (University of Arkansas): $391,011
  26. Michael White (University of Florida): $339,960
  27. Bruce Pearl (Auburn University): $237,022
  28. Will Wade (LSU): $194,770
  29. Matt Painter (Purdue University): $243,510
  30. Mike Brey (Notre Dame): $93,289

A few notes on this list.  First, the average salary for this group is $3.5 million and this average pay works out to 27.1% of average reported revenues. If these coaches were paid like the NBA, though, the average pay of these coaches would only be $344,031.  So if these coaches were paid like NBA coaches then on average each would see a pay cut of about $3 million (similar to what I said about Sean Miller at the University of Arizona earlier this month).

In addition, none of these head coaches would be paid as much as a million dollars per year. And Mike Brey's pay wouldn't be much different than a professor at Notre Dame. Brey's school only reported $3.9 million in revenue in 2016 from their men's basketball team and his currently salary is 61% of this total. But if NCAA paid like the NBA, Brey would receive less than $100,000 per year. 

To the best of my knowledge, no college coach has come forward to advocate that the NCAA pay players and coaches as they are in the NBA.  And given these numbers, there isn't much incentive for any coach to advocate such a change.  But it is interesting to see what a less restricted market would look like.  The picture painted suggests that many NCAA coaches are not going to want to live in a world where NCAA athletes are better compensated for their efforts and coaches… well, they get much, much less.

One of the stories told in Sports Economics is that we can use data from sports to measure the economic value -- or what economists refer to as "marginal revenue product" -- of an athlete.  All one needs is a measure of a worker's productivity and data on revenue from the sport.  In fact -- as I recently demonstrated at Forbes.com -- sometimes you can make an estimate with just data on revenue.   

Sports Economics reviews three different approaches to measuring a worker's value. The one I prefer is the approach taken in Chapter Nine to measure the economic value of each member of the men's basketball team at Duke University. Here is how this was measured:

  • The U.S. Department of Education reports that revenue for the men's basketball team at Duke University was $33.8 million in 2014.
  • In the NBA (as well as the NHL), the players are paid 50% of league revenue.  If Duke University followed that approach, then $16.9 million would be paid to the players that season.
  • If this revenue was allocated according to how many wins each player produced for this team, then a player like Jahill Okafor -- who produced 6.5 wins in 2014-15 -- would be worth more than $3 million. Obviously, this is far more than the cost of attending Duke University.
  • And that means Okafor was paid less than the revenue he generated. That also means -- by definition -- he was exploited.

In November I applied the same approach at Forbes.com to the study of women's college basketball. This analysis indicated that Gabby Williams -- who produced 11.0 wins for the University of Connecticut in 2016-17 -- was worth about $550,000.  And once again -- as we saw with Okafor -- this means Williams was exploited.

Then this past week I used a somewhat similar approach at Forbes.com to measure the economic value of women in college hockey. Because I don't have data on how many wins each hockey player produces, though, I took a slightly different approach. If we assume the NHL can measure wins (not entirely sure that is correct!) and that the NHL is paying players for their wins production (not entirely sure that is correct!) then we can use the distribution of salaries in the NHL to see how revenue would be allocated in women's college hockey if colleges followed the NHL model.

The results indicated that -- on average -- the women of Team USA generated more than $140,000 in revenue their last year in college. And given the value of a scholarship, that suggest many of these women were exploited.

There have been two objections raised to this analysis.  First, people wonder about teams who have expenses greater than their revenues.  In discussing expense data in colleges we must first note -- as mentioned in Chapter Nine ofSports Economics -- that this data seems problematic.  Specifically, for about half the women's college basketball teams analyzed the revenue data self-reported to the U.S. Department of Education was exactly equal to the expense data that was self-reported. This is odd because - as any student of economics should understand -- the process that determines a firm's revenue is largely independent from the process that determines its costs.  For these two numbers to be exactly equal suggests something unusual happening. 

In Sports Economics it was argue that "something unusual" was related to the non-profit status of schools. Non-profits -- like universities -- have an incentive to spend all their revenues.  So as revenues rise so will expenses.  And if athletic departments can, they will spend even more than the revenues that are accrued.  In other words, expenses can exceed revenues.

Can workers be exploited if expenses exceed revenues? Again -- as any student of economics should understand -- that is most definitely possible. A worker's value is a function of how much output that worker produces and the revenue that output generates. It is entirely possible for a firm to receive more revenue from a worker than it pays the worker in wages; and through mismanagement of the rest of the firm end up having total costs in excess of total revenues. When that happens, the worker is still exploited. 

Let me give an example to illustrate this point. Imagine you worked for a firm and you generated $50,000 in value but the firm only paid you $30,000.  By definition, you are exploited.  But let's say your boss now told you that the firm was losing money. Does that mean you are no longer exploited?  Of course not. You are still generating more money than you are paid.  The fact your boss can't manage the firm doesn't change the definition of exploitation.

Now that we understand what it means to be exploited we should emphasize that not all college athletes are producing more revenue than what they receive in a scholarship.  This leads to another issue people have raised.  Should players who are not exploited be paying for some of their college education?

I imagine that is a possible outcome. But I think that's unlikely. One issue to remember is that the revenue numbers reported to the U.S. Department of Education are about ticket sales, broadcasting revenue and donations (yes, donations count!).  But these numbers do not include a measure of how sports promote the name of a university. For example, how many people in the nation would know about Gonzaga University without its men's basketball team? That marketing effect is part of the value of athletics to a college. Therefore, it might make sense for a school to spend more on athletes than the explicit revenue the athletes generate.

So how much should athletes ultimately be paid?  Patrick Hruby offered this answer to that question a few days ago.

"So what is the best plan for paying players? No plan at all. If Kentucky wants to offer basketball recruits $500,000 signing bonuses, fine. If Notre Dame doesn’t want to offer football recruits a penny more than their athletic scholarships, that’s also fine."

I would agree with this plan.  Outside of college sports firms and workers are free to negotiate any deal that is consistent with the nation's labor laws.  So, if Duke University wanted to pay Jahill Okafor $3 million, that should be fine. Likewise, the University of Connecticut can pay Gabby Williams $550,000 and the University of Wisconsin can pay Meghan Duggan more than $230,000 or Hilary Knight more than $700,000.

Of course, it's possible these athletes might also negotiate a salary that is less than these values. In the end, though, this should not be the business of the NCAA or the government.  What wage these athletes get paid should simply be the business of the schools and the athletes.

Of course, if those deals result in an athlete generating more revenue than they are paid then once again, we would say they are exploited.  But the reason now would be different.  Now we know college athletes are exploited because of the rules created by the NCAA.  If exploitation existed when these rules were eliminated we would then have to think harder about what is going on in the labor market. And that will be a story we will discuss, if and when that ever happens!