By Chris St. John
This post has been in the work for five months. I wanted to see for myself how good each free agent signing was in terms of the market, so throughout the off-season, I kept track of how much money each Major League free agent signed for. I used each player's past three seasons and included an aging curve to estimate how useful he will be to his team for the length of the contract. These are their stories (dun-dun):
I found the average of each player's previous three years WAR from Fangraphs, Baseball-Reference and Baseball Prospectus. Then I used an aging curve to determine what a team might be expecting from the player in the future.
I split relief pitchers from all other players because their market is different than everyone else.
Buyouts are included in the guaranteed salary, but options are not. If a player has a 3 million dollar option with a 1 million dollar buyout, only the guaranteed buyout money is included in the average yearly figure. I also tried to exclude non-guaranteed contracts, though some may have slipped through the cracks (I barely caught Casey Blake's).
This isn't meant to be a highly precise representation of how teams valued players. If you read my work for any amount of time, you can tell that I shy away from factoring everything into an analysis. I prefer to do quick and dirty, in the ballpark type of stuff, while acknowledging the limitations of what I have done. So take this for what it is: a simple career average plus aging curve dollar per win graph.
The trend-lines on the graph are equal to ($/WAR)*(Yearly War)+$500,000. I made 500k the y-intercept, since even a replacement player will make the minimum salary. I used average yearly values instead of overall values for this graph so Albert Pujols's $240 million contract wouldn't squeeze all of the $1 million contracts together.
A polynomial trend-line actually fits both data sets better, but non-linear dollars per win is an argument in itself. This data set is obviously not large or technical enough to draw those types of conclusions from.
Here are the top five overpaid and underpaid players by total salary. I excluded relievers from this section, because the high $/WAR figure creates large negative values for below-replacement relievers.
Jonathan Papelbon actually rates as an underpay according to this linear model. Since he is projected for 5.4 wins over the length of his contract and relievers are paid over $11 million per win, this gives him an expected salary of nearly $60 million. However, this excludes the increased injury risk of signing a reliever to a four-year contract. A polynomial model would show him as an overpay.
Relief pitchers were paid over double per win this off-season than other players were. We can not continue to view their contracts in the $5 million per win light, as that is simply not how the market works. Also, none of this takes into account team success. If the Tigers win the world series with Prince Fielder, does it make overpaying him worth it? He is certainly more valuable to them than he is to the Baltimore Orioles, a team that wouldn't make the playoffs anyway.
I would loved to have done this with an interactive Tableau graphic, but have been unable to get those to work with the blogging software on this website.
As always, you can contact me in the comments or on Twitter @stealofhome.