With the season finally opening, the 25-man rosters have been set. With set rosters comes a set Opening Day payroll. Plenty of people analyze Opening Day payrolls in the context of their own teams - what does this year's payroll mean? Is the team spending more or less? Plenty of people also analyze the same concepts while comparing the teams against each other. This analysis is more of the latter.
However, I wanted to put a twist on it. As a Royals fan, I noticed that the team has a large Opening Day payroll this year, at least by the Royals' standards. It's at $131,487,125 for Opening Day according to Cot's, which is really middle-of-the-road these days. What makes that interesting, besides a tight-wallet owner opening up his pocketbook for a winning team, is that Alex Gordon is the only player making at least $10 million for the Royals. I first wondered how common that was, but my real question is this: How does the variance in pay among the teams compare?
I gathered data for each team using Cot's and did some cleaning. I eliminated any rows of data in which a player was listed but did not have a salary; these are generally players on the 40-man roster but not in the majors. The second bit of cleaning might result in some skewed results, but I don't think it will affect the data that much. I filtered out the rows of data in which one team was paying for the salary of a player on a different team, like Josh Hamilton. This is a small number of players and a relatively small amount of money, Hamilton aside. The goal is to look at distribution of money for players on a team, as long as they are on still within the organization. There could be a better way to deal with these players' salaries, but I felt fine enough.
In order to look at variance, a person would normally look at standard deviations. This gives an idea of how much, on average, a particular salary differs from the mean salary. However, there's a problem with this method in this case. Small market teams like the Rays have a smaller payroll and therefore smaller numbers. The standard deviation will naturally be smaller. The Yankees, on the other hand, will almost certainly have a larger standard deviation since so many players make tens of millions of dollars on their team.
The way to adjust for the above issue is to use the coefficient of variation (CV). The CV is calculated in this way - standard deviation divided by the mean. Pretty simple, yes? This calculation adjusts for the different "baseline" levels of spending per team. A loose guideline of values is that a CV of one means a dataset is roughly "medium" variance, a CV less than one means low variance, and a CV more than 1 means a high variance.
Below you'll find a scatterplot of CV on the x axis and Opening Day payrolls on the y axis. I've also added reference lines to show the average of each number.
There are a few things to notice at a high level. First, the average CV is about 1.3, which means teams in general are on the higher side of variance. This makes sense - there is a stark difference in pay between free agents and those still in the first six years of service time. Second, average pay here is about $134 million, rounding up. That seems crazy to me, but I think that's just another indicator of how flush with cash MLB really is. Third, there are not any teams with both a high payroll and a high CV. It would seem that having a slew of highly-paid players is a requirement to have a high payroll, rather than having a few very highly paid players and a bunch of league minimum guys.
Back to the Royals - they are an outlier. Their CV is 0.74; the next-closest team is the Pirates at 0.946. What they are doing appears to be a little rare. They are paying a large number of players similar middle-of-the-road salaries. This also makes sense; their core basically came up together and is getting paid at around the same time. In addition, they have not replaced any players with cheaper ones from the minors in the past few years. Alex Gordon makes the most at $12 million, but the Royals have 15 players making between $4 million and $10 million (including Jason Vargas, recovering from Tommy John surgery). There is unparalleled parity in salary in Kansas City.
Then there are the Brewers. Not only are the Brewers a small-market team, but they are also undergoing a full-blown rebuild. They have been selling off pieces like crazy, but they have retained their high-priced talent. At the top are Ryan Braun, Matt Garza, and Aaron Hill, whose salary is being paid in part by the Diamondbacks. All three of those players are making above $10 million. Literally every other player is making under $5 million.
There could be some adjustments to these data, but I think the lesson is that large market and small market teams don't necessarily structure their payrolls according to expectations. Large market teams can still spread the wealth equally, while small market teams can still be imbalanced.