Free Agency Contract Calculator

Free Agency is almost upon us yet again. The hectic time of the year often features dozens of multi-million dollar contracts being handed out within a span of only a few days. I attempt to capitalize on the free agency contracts of years past by creating a system that can predict the contract a new free agent will receive.

The Methodology

When designing the system, I wanted to base it off the two major determiners of a free-agent contract: fWAR and age at time of signing. More often than not, a player with a healthy three-year span of WAR and a younger age would be offered the largest contracts. As expected, older players with poor WAR totals often received close to league minimum or minor league contracts.

I started out by collecting free agency contract data from ESPN's database. The results were limited to only 2006 and beyond for two reasons: contract market inflation (which I will address later in this article) and lack of database support. Nowadays, contracts scrape the $100 million mark with relative ease compared to what players were making more than a decade ago. The scary part is that teams are willing to spend more and more each season. As a side note, international free agents were also excluded because of the lack of analogous value measurements.

Once all the data were collected on player contracts (signing age, contract length, etc.), information on WAR was retrieved for every player for the three years preceding their time in free agency. For example, someone poised to enter the market at the end of the 2010 season would need data from the 2010, 2009, and 2008 seasons. Subsequently, the WAR figures were weighted toward their more recent seasons, meaning that the season that just occurred would be three times as impactful as the season three years ago. The same reasoning applied to the middle year (2009 in this case), as it would be worth twice as much as the preceding year (2008). This is how you end up with a player's weighted WAR, or wWAR.

wWAR is not the final step, though. Age needs to be factored into the equation to truly get a better look at a player's total value. Note that the ages at the time of signing may not be perfect, because the ESPN contract database uses current day ages for players. As a result, years had to be subtracted from every contract situation in regard to the years removed from the free agency period. Once all the ages were collected and stored in the spreadsheet, they were normally distributed based on the average wWAR. The product of these two numbers results in what I call "Free Agency Score". I know, very creative.

Free Agency Score is the index for most of the subsequent research I did, and the first step to that was finding the line of best fit, in this case a polynomial trendline. On the x-axis was the player's Free Agency Score, and on the y-axis was the player's salary per season, or average annual value (AAV). Originally, I was going to simply use this singular trendline as my basis for every player; however, upon further research, I came to realize that some positions are paid drastically different salaries even if their wWAR is exactly the same. For that reason, players were filtered by position (for the sake of simplicity, position was decided by where the player played the most innings in 2014 -- for example, someone who player 500 innings at 2B and 600 innings at SS would be considered a shortstop) and those data were used to find position-based trendlines. These are the algorithms in which a player's information can be entered and their expected contract can be outputted.

I noticed a few particular facts that I would not have expected by breaking up the data. First of all, the bullpen market is the most inconsistent and hard to predict. Relief pitchers that are considered capable of handling the ninth inning, a.k.a closers, are handed the most money, even if they are not worth as much as a good set-up man. All things considered, relief pitchers as a whole are very much overpaid for their services when looked at by this heavily WAR-based system.

The position players at almost every position besides first base and right field are underpaid. Currently, trends seem to inaccurately weight in-game power over skills such as defense and OBP%. Power is hardly the way to judge a player, but it is the same reason a player such as Adam LaRoche will be completely overpaid this offseason. Yes, he did hit 26 home runs, but he only produced 1.6 WAR the entire season. That ranked 162nd among all players in 2014, tied with the likes of Peter Bourjos and Brandon Guyer.

As you can see from the chart below, constructed by inputting the same Free Agency Score with the lone change being the position, first baseman make almost exactly the average salary and much more than their infield counterparts that rely on other skills. Similarly, designated hitters make about 31% more money for the same exact amount of production.

Position	AAV%	Difference
C	$4,511,260	-19.00%
1B	$5,572,538	0.10%
2B	$4,080,349	-26.70%
SS	$4,824,765	-13.30%
3B	$3,964,007	-28.80%
LF	$5,132,049	-7.80%
CF	$4,925,073	-11.50%
RF	$6,203,969	11.50%
DH	$7,293,416	31.00%
SP	$6,518,288	17.10%
RP	$8,200,788	47.30%

Inflation was quite tricky to work into the calculator. but I think I accomplished it after some minor adjustments. I knew that the market had changed since 2006. To be sure, the average amount a team would pay per season for same worth was graphed out. I noticed an immediate trend.

2006 started out with a $4,329,047 price tag for a player with a Free Agency Score of 1.01 (the mean of all 848 contracts on record). Prices kept falling until 2010, when the economy climbed out of the recession for a large part. It turns out, the recession actually played a major role in the willingness of teams to pay top-dollar. Things changed, and teams began paying higher prices for the same quality of player, leading to a large increase every year up through 2013. This offseason's projected inflation is extrapolated from the 2006-2013 data on hand in order to come up with the figure: $6,241,037. A high price indeed. as teams are willing to pay more and more for the same amount of talent every year for various reasons. All salary data were then adjusted according to this projected ratio.

YEAR	AAV FOR EQUIVALENT PLAYER
2006	$4,329,047
2007	$4,070,007
2008	$3,954,313
2009	$3,029,029
2010	$3,923,799
2011	$4,023,746
2012	$4,555,818
2013	$5,479,134
2014	$6,241,037

The Results

This contract calculator will be able to accurately predict the general area a player's contract should be in by their seasonal salary. The most important thing to note, however, is that the market dictates a large part of the equation, and it is hard to fully assess a player's expected payday without some context. This offseason will lack many impact bats, and as a result, mediocre batters such as Corey Hart will be paid much more than they should be. The market usually has a fair amount of sway, so all users should be hereby warned that this calculator is not an exact, input-output, kind of function. A keen baseball knowledge will go a long way in determining just how much the result should be adjusted.

This Microsoft Online table will tell you my exact prediction on what any player should be paid this offseason on an annual basis. The beige boxes are for user input. Start by inputting the desired player's position using the standard abbreviated terms, and select whether or not you would like to see the inflation adjusted rate. The inflated rate is more accurate and relevant to today's market, but I made it an option in case someone would like to see the non-inflated price. Age and fWAR for the previous three years can be found on FanGraphs. Once everything is in place, the calculator will run the numbers through the equations and spew out an average annual value.

I think Tableau is the much more visual way of looking at scenarios, and often, much more contextual. This Tableau graph will be able to show you the closest comparable contracts to the one someone is likely to receive on an annual basis. The sliders on the right can be adjusted to your liking, but I recommend using a 1.0 wWAR and two years of age range on either side. With those markers in place, you should be able to find the most comparable contracts for players.

I want to say thank you to everyone who helped me with this project.

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All statistics courtesy of FanGraphs, ESPN and Baseball-Reference.

Justin Perline is a writer for Beyond the Box Score and The Wild Pitch. You can follow him on Twitter at @jperline.