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Inequality in offensive production (or, How the Pirates are like Luxembourg)

Ed Szczepanski-USA TODAY Sports

With Andrew McCutchen out of the lineup with a fractured rib, the Pirates are without their most important offensive contributor, at least for the next week or so. How much of an offensive contribution does McCutchen provide? As measured by wRC (weighted Runs Created), McCutchen is responsible for about 17.7 percent of the Pirates' offensive output. For comparison's sake, the average share of productivity provided by each team's most productive offensive player is 15.5 percent and, as a class, the top hitters account for 14.4 percent of total weighted runs created.

Obviously, the Pirates will not be able to fully make up for the loss of McCutchen. It will be even more difficult considering the uncertainty surrounding Neil Walker (back problems) and Pedro Alvarez (defensive issues). However, the Bucs still have five players with OPS+ figures over 100, plus a resurgent Gregory Polanco. (The league average team has 5.7 players with a OPS+ over 100.)

The Pirates' plight piqued my interest in the distribution of production within major league offenses. Specifically, how much inequality in production is typical? Is there any relationship between shared production and overall offensive output? And, finally, is there a simple way to conceptualize and describe the various offensive profiles?

To answer these questions, I used a common measure of inequality called the Gini Coefficient to measure shared production, and weighted runs created to measure total offensive production.

The Gini Coefficient

The Gini Coefficient is a statistical measure of statistical dispersion that is most often used to analyze income distribution. As described by the World Bank, "Gini index measures the extent to which the distribution of income or consumption expenditure among individuals or households within an economy deviates from a perfectly equal distribution."

The Gini Index runs from 0 to 100. A Gini Coefficient of 0 means that income is absolutely equally distributed throughout a population, while a score of 100 means perfect inequality.

For context, the Gini Coefficient for the United States is 48.6 before taxes and transfers, and 37.8 after taxes and transfers. The split in Canada is 44.4/32.4 and Sweden 42.6/25.9. Before taxes and transfers, the Gini Coefficient for Pennsylvania is 46.1, and Maine 43.7.

Applying the Gini Coefficient

Since the Gini Coefficient provides us with a simple measure of inequality, it offers an easy way to measure how production is distributed within team offenses. To that end, here's what I did:

  1. Using Fangraphs, I collected wRC stats for all players who have at least one plate appearance per team game played. At the time I gathered this data, that was all players with over 110 PA. I use the one plate appearance-per-game threshold to avoid teams getting high inequality Gini Coefficients simply because they have a lot of players with very few plate appearances.
  2. Arrange the players by team.
  3. Take each team's list of wRC and plug it into this Gini Coefficient Calculator.

Results

Teams are classified according to one of the four offensive profiles in the table below.

X and Y-axis explained

The intersection of the X and Y-axes is league average for both inequality (Gini Coefficient) and offensive productivity (wRC). The numbers are 29.42 and 431.36 respectively.

X-axis = This is the measure of shared production. Teams on the left of the Y-axis are sharing offensive production more equally than average.  In other words, there is not as much disparity in wRC scores. Teams on the right side are receiving more unequal production, meaning there is more dispersion in wRC.

Y-axis = This is the measure of production. Teams above the X-axis have a total team wRC that is above league average. In other words, they are the most productive offenses overall; teams below are performing below average.

Quadrants

Top left (blue) - "Successful Socialism." These teams are sharing production and producing above-league-average wRC.

Top right (orange) - "Trickle-Down." These teams are receiving a lot of production from a few players, and the whole team is benefiting in the form of above-league-average run creation.

Bottom left (brown) - "Howard Roark's Revenge." These teams are sharing production, but they're not producing much.

Bottom right (purple) - "Too Few Producers." Production is not being shared and not much is being produced.

American League

(Click to enlarge)

Americanleagueinequality_medium

Detroit is sharing production and performing well above league average. Toronto is getting the bulk of its offense from three players (Jose Bautista, Melky Cabrera, and Edwin Encarnacion), and then there is a steep drop-off. Robinson Cano and Kyle Seager are providing what little offense there is for Seattle. Kansas City is producing below league average and there is not much disparity between the hitters.

National League

Nationalleagueinequality_medium

Colorado, Pittsburgh and Milwaukee are getting good production from many players. San Diego is getting little production without any players separating from the pack. In Miami, Giancarlo Stanton makes up a huge share of the offense, and while Casey McGehee and Christian Yelich are having good years, the Marlins' production is the least equal in the National League. Atlanta's offense looks a lot like that of the Marlins, with Freddie Freeman rather than Stanton leading the way.

Overall, there is no relationship between how much production is shared and how much is produced. However, perhaps one interesting thing this type of classification does reveal is which offenses are best positioned to deal with the loss of their top producers. Successful Socialist offenses are producing at an above-league-average clip and sharing the production in the process. This should make them more resistant to the boom-and-bust cycles that might prove jarring to Trickle Down offenses.

Average inequality and Inequality similarities

In the tables below, teams are organized according to their offensive profiles. Each team's Gini Coefficient is provided as well as the total weighted runs produced by their hitters with over 110 plate appearances. Additionally, for conceptual purposes and, well, just for the fun of it, I provide each team's most similar country by equating distribution of wRC equated to distribution wealth.

Offensive Profile: Successful Socialism

Team Gini wRC Income Inequality (before taxes and transfers) Income Inequality (after taxes and transfers)
Indians 24.09 462 Slovenia Slovenia
Athletics 25.82 479 Luxembourg Belgium
Rays 26.05 470 Slovakia Austria
Brewers 26.8 458 Finland Hungary
Rockies 27.08 504 Germany Hungary
Tigers 27.38 505 Romania Hungary
Twins 27.63 441 Romania Hungary
Angels 27.83 483 Iceland Hungary
Pirates 28.51 484 Switzerland Luxembourg
League 29.42 431 Kosovo Germany

Offensive Profile: Howard Roark's Revenge

Royals 17.77 402 Sweden Slovenia
Padres 20.4 307 Sweden Slovenia
Yankees 20.73 414 Sweden Slovenia
Reds 24.54 398 Montenegro Denmark
League 29.42 431 Kosovo Germany

Offensive Profile: Trickle Down

White Sox 29.64 460 Kosovo Germany
Orioles 31.35 447 Estonia South Korea
Blue Jays 33.71 502 Azerbaijan Italy
Marlins 37.56 442 Vietnam United States
Dodgers 30.7 470 France Greece
League 29.42 431 Kosovo Germany

Offensive Profile: Too Few Producers

Dbacks 29.95 414 Kosovo Iceland
Mets 30.16 391 Australia Iceland
Phillies 30.33 386 Australia Switzerland
Cardinals 31.28 404 Estonia South Korea
Red Sox 31.44 414 Estonia South Korea
Nationals 32.7 422 Nepal Japan
Cubs 33.24 392 Kyrgyzstan New Zealand
Astros 33.88 427 Ireland Italy
Rangers 34.31 378 Greece United Kingdom
Giants 34.57 390 Albania United Kingdom
Mariners 35.94 375 Bosnia and Herzegovina Portugal
Braves 37.2 422 Maldives Israel
League 29.42 431 Kosovo Germany

Finally, here are the Gini Coefficients for some of my favorite teams in history:

Team Gini wRC
'84 Tigers 24.73 810
'79 Pirates 25.05 724
'71 Pirates 32.98 731
'68 Tigers 32.12 621
'27 Yankees 36.38 944
'09 Pirates 20.14 620

Answers to the initial questions

How much inequality in production is typical?

The average major league offense distributes its offensive production like Germany distributes wealth after taxes and transfers.

Is there any relationship between shared production and overall offensive output?

No, R-Squared is zero for wRC and Gini-Coefficient.

Is there a simple way to conceptualize and describe the different types of offensive profiles?

I constructed four offensive profiles based on each offenses total output and total sharing of output: Successful Socialist, Roark's Revenge, Trickle Down and Too Few Producers.

The following are speculative descriptions of the character and plight of each offensive profile:

Successful Socialism: These are the most stable. They receive above-average offensive output and they have many solid contributors.

Roark's Revenge: These offenses are in the worst shape because they score high on shared production only because they don't have many good producers.

Trickle Down: These are the most volatile offenses and are subject to boom-and-bust cycles because they rely heavily on a few players.

Too Few Producers: These offenses live on the razor's edge of dropping out of sight as they already are producing below the league average, and the production they do receive is unequally distributed.

(Stats courtesy of Fangraphs, Central Intelligence Agency and World Bank. They were calculated on 8/3/2014.)