Sherwin Rosen, in the American Scholar, writes:

Performers of first rank comprise a limited handful out of these small totals and have very large incomes. There are also known to be substantial differences in income between them and those in the second rank, even though most consumers would have difficulty detecting more than minor differences in a “blind” hearing.

What Sherwin Rosen says is that there are very few differences in talents at the very top.

The elusive quality of “box office appeal,” the ability to attract an audience and generate a large volume of transactions, is the issue that must be confronted. Recognition that one’s personal market scale is important, in the theory of income distribution has a long history, but the idea has not been developed very extensively in the literature.

Rest assured that prospective impresarios will receive no guidance here on what makes for box office appeal, sometimes said to involve a combination of talent and charisma in uncertain proportions. In the formal model all that is taken for granted and represented by a single factor rather than by two, an index q labeled talent or quality.

Albert Rees is a good introduction to the size distribution of income. The selectivity effects of differential talent and comparative advantage on the skew in income distributions are spelled out in my 1978 article, also see the references there. Melvin Reder’s survey touches some of the issues raised here.

Of course social scientists and statisticians have had a long standing fascination with rank-size relationships, as perusal of the many entries in the Encyclopedia of the Social Sciences will attest.

Statistical Distributions for Superstars

We use the methods we saw in course 2 and plot the log rank on the y axis against the log of the outcome of interest (revenues, number of views, number of sales, etc.) We show that many of these distributions associated to superstar phenomena display a Pareto-like behavior in the tail: this means that there are very many observations which deviate substantially from the mean, and that earnings and success accrue disproportionately to the very top.

Pollstar Data

Table 1: List of most sold albums. Source: Pollstar
rank Artist Total
1 Lady Gaga 223300
2 Drake 98900
3 Michael Buble 97500
4 Pentatonix 81800
5 Korn 62600
6 twenty one pilots 49900
7 Trans-Siberian Orchestra 49700
8 Leonard Cohen 45300
9 The Weeknd 39800
10 Kanye West 38000
List of most sold albums. Source: Pollstar

Figure 1: List of most sold albums. Source: Pollstar

Most-downloaded songs in the United Kingdom

The data comes from the following Wikipedia entry: List of most-downloaded songs in the United Kingdom.

Table 2: List of most downloaded songs in the United Kingdom.
No. Artist Song Copies sold[a]
1 Pharrell Williams “Happy” 1,922,000[3]
2 Adele “Someone Like You” 1,637,000+[4]
3 Robin Thicke featuring T.I. and Pharrell Williams “Blurred Lines” 1,620,000+
4 Maroon 5 featuring Christina Aguilera “Moves Like Jagger” 1,500,000+
5 Gotye featuring Kimbra “Somebody That I Used to Know” 1,470,000+
6 Daft Punk featuring Pharrell Williams “Get Lucky” 1,400,000+
7 The Black Eyed Peas “I Gotta Feeling” 1,350,000+
8 Avicii “Wake Me Up” 1,340,000+
9 Rihanna featuring Calvin Harris “We Found Love” 1,337,000+
10 Kings of Leon “Sex on Fire” 1,293,000+
List of most downloaded songs in the United Kingdom, Pareto Plot.

Figure 2: List of most downloaded songs in the United Kingdom, Pareto Plot.

Most-streamed songs on Spotify

The data comes from the following Wikipedia entry: List of most-streamed songs on Spotify.

Table 3: List of most streamed songs on Spotify.
Rank song value date
1 Shape of You 2162 6 January 2017
2 One Dance 1681 5 April 2016
3 Rockstar 1549 15 September 2017
4 Closer 1535 29 July 2016
5 Thinking Out Loud 1326 21 June 2014
6 God’s Plan 1284 19 January 2018
7 Lean On 1232 2 March 2015
8 Despacito (Remix) 1228 17 April 2017
9 Havana 1217 3 August 2017
10 Love Yourself 1213 9 November 2015
List of most streamed songs on Spotify, Pareto Plot.

Figure 3: List of most streamed songs on Spotify, Pareto Plot.

Most-viewed YouTube videos

The data comes from the following Wikipedia entry: List of most-viewed YouTube videos.

We then display the first rows of the data:
Table 4: List of most viewed YouTube videos.
Rank video value
1 Despacito[17] 6.20
2 Shape of You[22] 4.21
3 See You Again[23] 4.11
4 †Masha and the Bear – Recipe for Disaster[30] 3.59
5 Uptown Funk[31] 3.56
6 Gangnam Style[32] 3.35
7 Sorry[37] 3.13
8 Sugar[38] 2.96
9 Roar[39] 2.82
10 Baby Shark Dance[40] 2.78

The first 100 top Youtube videos have been seen a couple billion times:
- Luis Fonsi - Despacito ft. Daddy Yankee: 5.7 Billion
- Ed Sheeran - Shape of You: 3.88 Billion
- Wiz Khalifa - See You Again ft. Charlie Puth: 3.84 Billion
- etc.

List of most viewed Youtube videos, Pareto Plot.

Figure 4: List of most viewed Youtube videos, Pareto Plot.

Highest paid American television stars

The data comes from the following Wikipedia entry: List of highest paid American television stars.

Network primetime salaries per episode

We then display the first rows of the data:
Table 5: Highest paid American Television Stars.
Name Program Role Salary
Simon Cowell The X Factor Judge $75 million
Katy Perry American Idol Judge $25 million
Jennifer Lopez American Idol Judge $20 million
Mariah Carey American Idol Judge $18 million
Christina Aguilera The Voice Coach $17 million
Hugh Laurie House Gregory House $15 million
Ryan Seacrest American Idol Host $15 million
Britney Spears The X Factor Judge $15 million
Miley Cyrus The Voice Coach $13 million
Adam Levine The Voice Coach $13 million

Highest grossing concert tours

The data comes from the following Wikipedia entry: List of highest-grossing concert tours. We first input the data from the Wikipedia page, using the rvest package to extract tables from the html source code:

We then display the first rows of the data:
Table 6: List of Highest Grossing Concert Tours.
Rank Actual gross Gross Infl Adj Artist
1 $736,421,584 $820,194,986 U2
2 $573,300,000 $573,300,000 Ed Sheeran
3 $563,300,000 $563,300,000 Guns N’ Roses
4 $558,255,524 $674,547,559 The Rolling Stones
5 $523,033,675 $546,023,369 Coldplay
6 $458,673,798 $493,336,432 Roger Waters
7 $441,121,000 $506,821,305 AC/DC
8 $407,713,266 $476,474,639 Madonna
9 $389,047,636 $483,515,954 U2
10 $364,300,000 $364,300,000 Garth Brooks and Trisha Yearwood
List of Highest Grossing Concerts, Pareto Plot.

Figure 5: List of Highest Grossing Concerts, Pareto Plot.

Highest paid film actors

The data comes from the following Wikipedia entry: List of highest paid film actors. We first input the data from the Wikipedia page, using the rvest package to extract tables from the html source code:

We then display the first rows of the data:
Table 7: List of Highest Paid Film Actors.
Actor Film Year Salary Total income
Keanu Reeves The Matrix ReloadedThe Matrix Revolutions 2003 $30,000,000 $156,000,000
Bruce Willis The Sixth Sense 1999 $14,000,000 $100,000,000
Tom Cruise Mission: Impossible 2 2000 $100,000,000
Tom Cruise War of the Worlds 2005 $100,000,000
Will Smith Men in Black 3 2012 $100,000,000
Robert Downey, Jr. Avengers: Infinity War 2018 $75,000,000+
Robert Downey, Jr. Iron Man 3 2013 $75,000,000
Sandra Bullock Gravity 2013 $20,000,000 $70,000,000+
Tom Hanks Forrest Gump 1994 $70,000,000
Tom Cruise Mission: Impossible 1996 $70,000,000
Harrison Ford Indiana Jones and the Kingdom of the Crystal Skull 2008 $65,000,000
Jack Nicholson Batman 1989 $6,000,000 $60,000,000
Leonardo DiCaprio Inception 2010 $59,000,000
Robert Downey, Jr. Captain America: Civil War 2016 $40,000,000 $40,000,000+
Robert Downey, Jr. Avengers: Age of Ultron 2015 $40,000,000

Largest sports contracts

The data comes from the following Wikipedia entry: List of largest sports contracts.

We then display the first rows of the data:
Table 8: Largest Sports Contracts.
Player Sport length value
Mike Trout Baseball 12 years (2019–2030) $426,500,000
Canelo Álvarez Boxing 5 years (2018–2023) $365,000,000
Bryce Harper Baseball 13 years (2019–2031) $330,000,000
Giancarlo Stanton Baseball 13 years (2015–2027) $325,000,000
Manny Machado Baseball 10 years (2019–2028) $300,000,000
Alex Rodriguez1R Baseball 10 years (2008–2017) $275,000,000
Nolan Arenado Baseball 8 years (2019-2026) $260,000,000
Alex Rodriguez2R Baseball 10 years (2001–2010) $252,000,000
Miguel Cabrera Baseball 8 years (2016–2023) $247,000,000
Robinson Canó Baseball 10 years (2014–2023) $240,000,000

Other examples

Billionaires from Forbes

Preparing the data from the Forbes Website.

The first 25 billionaires are:
Table 9: First 25 Billionaires.
Rank Billionaire wealth source
1 Bill Gates 79.2 Microsoft
2 Carlos Slim Helu & family 77.1 telecom
3 Warren Buffett 72.7 Berkshire Hathaway
4 Amancio Ortega 64.5 Zara
5 Larry Ellison 54.3 Oracle
6 Charles Koch 42.9 diversified
6 David Koch 42.9 diversified
8 Christy Walton & family 41.7 Wal-Mart
9 Jim Walton 40.6 Wal-Mart
10 Liliane Bettencourt & family 40.1 L’Oreal
11 Alice Walton 39.4 Wal-Mart
12 S Robson Walton 39.1 Wal-Mart
13 Bernard Arnault & family 37.2 LVMH
14 Michael Bloomberg 35.5 Bloomberg LP
15 Jeff Bezos 34.8 Amazon.com
16 Mark Zuckerberg 33.4 Facebook
17 Li Ka-shing 33.3 diversified
18 Sheldon Adelson 31.4 casinos
19 Larry Page 29.7 Google
20 Sergey Brin 29.2 Google
21 Georg Schaeffler 26.9 ball bearings
22 Forrest Mars Jr 26.6 candy
22 Jacqueline Mars 26.6 candy
22 John Mars 26.6 candy
25 David Thomson & family 25.5 media
List of Top Wealth Holders according to Forbes, Pareto Plot.

Figure 6: List of Top Wealth Holders according to Forbes, Pareto Plot.

The Pareto distribution does not work very well for the very top (Bill Gates is not rich enough!)

List of Top Wealth Holders according to Forbes (> 30 billion), Pareto Plot.

Figure 7: List of Top Wealth Holders according to Forbes (> 30 billion), Pareto Plot.

Salaries at the University of California (UC)

The salaries at the University of California are public and available at this website: https://ucannualwage.ucop.edu/wage/

The distribution in the tail at the University of California is really well approximated by a Pareto distribution. Below is the plot of wages higher than $250K.

Distribution of Wage Incomes in the UC System (>250 K), Pareto Plot.

Figure 8: Distribution of Wage Incomes in the UC System (>250 K), Pareto Plot.

The distribution in the tail at the University of California is really well approximated by a Pareto distribution. Below is the plot of wages higher than $400K.

Distribution of Wage Incomes in the UC System (>400 K), Pareto Plot.

Figure 9: Distribution of Wage Incomes in the UC System (>400 K), Pareto Plot.

Below is a zoom on the distribution of wages higher than 1.5 million annual. You can see that the highest paid superstars on campus are the Head Coaches, and superstar physicians. Again, it is striking that these distributions are very well approximated by a Pareto distribution.

Distribution of Wage Incomes in the UC System (>400 K), Pareto Plot.

Figure 10: Distribution of Wage Incomes in the UC System (>400 K), Pareto Plot.

Market for Executive Officers in large firms

Again, from Sherwin Rosen:

Such considerations are important for understanding the market for executive officers in large firms. Unusually good information on executive compensation is available from public proxy statements circulated to stockholders by requirement of the Securities and Exchange Commission. Examination of these statements is instructive. They reveal Superstar-scale rewards that are highly concentrated among the top half-dozen executives in these firms. More detailed study indicates that the top incomes vary systematically with the size of the organization. Large firms pay executives more than smaller firms do. Even the occasional, well-publicized dollar-a-year man falls in line once stock options, pensions, and other forms of deferred compensation are properly accounted. The value to the organization of good top-level decisions and avoidance of bad decisions is abundantly clear once the nature of control of resources on such a vast scale is considered.

Common use of the term Officer for corporate executives Suggests certain parallels with the military. A good or bad decision by a platoon leader does not have much effect on the overall fortunes of war, but the same cannot be said of decisions made by the chief strategists. The value of extra talent is much larger at the top of the organizational hierarchy than at the bottom because those decisions percolate through the enterprise, and they have much further to travel in a larger enterprise than in a smaller one.