The Cost Of A Free Agent

Every year fans argue about what kind of contract a given player deserves or whether free agency is a good avenue for building a team. Inevitably, fans think some players were overpaid or lament the fact that their team largely sat out the feeding frenzy. In order to better inform these discussions, I wanted to take a quantitative look at how much production costs on the free agent market, and see if there are any insights to be gained along the way. I'll also take a look at a couple of the Browns' recent free agent acquisitions to see how they stack up.

Before we begin, a word on the data. I compiled a list of 182 unrestricted free agent signees from the 2015 offseason. I took my contract data from spotrac, including total contract value, guaranteed money, contract length, and 2015 cap hit. In order to tie this to production on the field, I used Pro Football Reference's AV metric, which is meant to be an all-encompassing representation of player value. It's not great for comparing individual players, but is ideal for sorting large data sets and looking at overall trends. In this article I've compiled each player's career total AV, their AV for the past three years, and their AV in 2014. I want to point out that compiling this dataset was a pain in the butt, since it's impossible to find salary data and AV in the same place, and each site's list of free agents was different. Well over 200 players changed teams this offseason, but I could only find complete records for 182. Most of the players missing were signed to the league minimum and will likely not make much of a difference on the field, if they even make a team. If you want to take a look at the raw data but don't want to torture yourself with putting it together, shoot me an email and I'll pass it along.

With that out of the way, let's make some comparisons. Let's start by looking at the distribution of average yearly salaries. From this histogram, we can see that the vast majority of free agents are making less than $5 million per year, and there were really only a small number of big contracts handed out.

Now, NFL contracts aren't guaranteed, so looking only at the average salary may not be indicative of the actual price a team is paying. Let's compare average yearly salary to guaranteed money and 2015 cap hit to get a more complete picture. Each of the plots below have been normalized so all of the data are between zero and one, which allows me to plot everything together, but higher numbers still correspond to higher salaries. The important thing isn't the actual numbers (we'll get there), for now it's just the trend we're interested in.

The salary data is correlated pretty well, but it's interesting to see where players maybe sacrificed guaranteed money for a higher average salary, or vice versa. As an aside, some of you more mathematically inclined readers might be wondering why I plotted this on a linear scale instead of logarithmically, which would show the variation a little better. I wanted to keep consistency between all of the figures, and as you'll see shortly, the AV data is decidedly not logarithmic. If all of that sounded like gibberish to you, don't sweat it, it's not important.

Now that we know that we can treat guaranteed money, cap hit, and average salary more or less the same, let's look at what all that cash actually pays for. Here's how average salary compares to total career AV, three year AV, and 2014 AV.

As you can see, there's a huge amount of variation in AV, and that makes it hard to see much relationship between salary and production. If that sounds strange to you, you're not alone. It's precisely this lack of a tight relationship between on-field value and cost that makes free agency a crap-shoot, almost as much as the draft. There are so many other factors that go into a player's value to a team besides just production on the field, and AV is far from perfect to begin with. Things like age, intangibles, or scheme fit may make a player more valuable to one team than another. As you might expect, the three year AV plot shows the best relationship, to the extent that there is one. That's because one year of AV can be deceiving, and a whole career's worth might not accurately reflect who a player is today. From this plot, we can see that while better players tend to cost more money, the price goes up faster than the production. This leads to some diminishing returns, which can be more easily seen by combining the two lines on that plot. Below, I've plotted AV/year per million dollars. This plot is not normalized, these are the actual values. On this plot, the most expensive players are still on the far right, but you can see that at the higher average salaries, one million dollars buys you less AV. Another way to think of this is that "five nickels don't add up to a quarter" in the NFL. One all-pro is worth more than five rotational players, even if their AV comes out the same.

Another way to visualize this data is as a histogram, which will help us see what the average cost of a free agent is in terms of AV per million dollars and give a good idea of how widely that number varies. This is similar to a concept familiar to some baseball fans, "the cost of a win." What we're looking at here is a little different, though. Since we aren't projecting future performance, we can't say a team is likely to get a certain amount of AV in the future for a given amount of money. We could look up historical data to see how well players have produced in the past after signing their free agent deals, but putting this data together was enough torture for now. What these numbers really tell us is how much a player should expect to get in free agency based on past performance. But enough of that babbling, let's look at the distribution.

With the exception of a few steals, a player can expect to earn a million dollars for roughly every 1-4 AV per year. For those who want to put a single number on it, the distribution above peaks at 1.25 AV/year per million dollars and has a mean of about 2.4 AV/year per million dollars. For context, that's somewhere between Johnson Bademosi and Jim Leonhard. There's obviously a lot of noise here though, so I strongly urge you not to use these numbers as a definite cut-off and instead consider whether or not a player's contract puts them somewhere in the middle of the above distribution before making a judgment on whether they are over or underpaid.

Finally, for those of you still with me, let's see how the Donte Whitner and Karlos Dansby contracts stack up to this analysis. In the three years before he became a Brown, Whitner compiled 23 AV, or about 7.6 per year. Whitner makes an average of $7 million per year, so he clocks in at 1.08 AV/year per million dollars. That's a little on the low end, but it's well within the expected values. Last year Whitner had 8 AV for the Browns, which means so far his play is in line with his contract. Keep in mind there are diminishing returns involved here, so it's not surprising that a good player like Whitner might cost a little more, relatively speaking.

Following the same procedure for Dansby, we get 35 AV in the three years before he became a Brown, or 11.6 per year. His contract pays him $6 million per year, so he comes in at 1.9 AV/year per million dollars. This is a relative steal for a player as good as Dansby, once again keeping in mind diminishing returns. Of course, Dansby is a little older and his contract goes for four years, so the Browns had to risk Dansby declining and sacrifice some flexibility in return for his relatively low yearly cost. Based on these two test cases, it seems the current Browns front office is making good use of free agency.

So there you have it, now you know how much a free agent costs in the NFL. When looking at these numbers, it's important to remember that each negotiation is an individual event, and there's always more going on than simple production vs. cost. But hopefully after reading all of this you feel a little more informed about what constitutes a good contract in the NFL, and hey, it's always nice to see that the people in charge of our favorite team seem to know what they're doing.