Gini Coefficient of Major League Baseball Player Salaries (2007)

I was thinking about unionization and it's typical effects. Normally, unionization permits groups of laborers to increase their overall portion of the revenues of a company, by putting them on equal footing with the capitalists (those who own the capital assets which are used in production, i.e. the owners of the company and their agents i.e. management).

You would expect that this would also lead to a harmonization of the Lorenz curve with the perfect equality curve (where x = y, because every person receives equal income, and therefore the percentage of total income for any given percentage of the population is equal to that percentage of the population).

In the case of Major League Baseball...that didn't happen.

Even the lowest paid baseball players make a lot of money. Based on USA Today's 2007 MLB salary data for players on opening day rosters, the lowest paid players received $380,000 for the season. That's a fair chunk of change that immediately puts them in the top echelons of individual incomes in the United States.

However, when you look at the entire data series, and create a Lorenz curve from that data, you find that in fact it does not remotely approximate a perfect distribution. Using the trapezoid method (actually accurate in this case, given that I have the complete dataset), I calculated the Gini coefficient to be 0.6112. The Gini coefficient measures the ratio of the area between the perfect distribution curve and the Lorenz curve to the area between the Lorenz curve and the chart axes (the chart is plotted from 0 to 1 on both the X and the Y axis). In the case where the actual distribution is completely equal, the Gini coefficient would be zero, and in a case where one person has all of the assets, the coefficient would be one.

This ratio is quite high in comparison to, for instance, the coefficient typically presented for the United States (which is high currently compared to it's historical values). The 2005 US Gini coefficient was 0.469 according to the U.S. Census Bureau.

I assume that the players aren't aware of this, or they'd be voting in new union management.

I'm attaching a chart to this post that shows the Lorenz Curve for MLB 2007 salaries. As you can see, the bottom 50 percent of MLB players are only taking in 10% of the total MLB salaries. That's a sufficient number to take control of their union, so I don't know what the fuck they're thinking.

Oh, BTW, Excel has a lot of problems with statistics. Most likely that regression formula is wrong. I got some bizarre numbers when I attempted to integrate it. I'm not sure if that is because of a deficiency in the formula, or a deficiency in my ability to use a new (to me) stat package. Probably some of both, but a friend had similar problems, which is why ultimately I used the trapezoid method.