The Difficulty in Projecting Contracts
Written by Brendan Gawlowski on November 30, 2012 @ 01:20AM      Jump To Comments

One theme that struck me after the B.J. Upton signing was the variation in opinions regarding the terms of the contract. Upton signed for 5 years and $75 million, and there were no shortage of people claiming that Upton was paid fairly (or even slightly underpaid). But there were also several commenters arguing that Upton made out like a bandit, including Fangraphs's usually pinpoint contract crowdsourcing tool, which was a year and $20+ million short in their projection of his deal.

Is it surprising that we saw such divergent estimates? On the one hand, yes. Reasonable people differed in their estimates of Upton's worth by over $20 million, not an insubstantial amount of money. But on the other, a quick look at some of the inputs for a basic contract estimator reveal how easy it is to produce two widely divergent values.

As an example, let's revisit the basic regression and salary inflation model I borrowed from Dave Cameron back in my Nick Swisher post. Cameron argues that teams will pay about $5.5 million per win in 2013, and that we can expect that number to rise by about 5% each off-season (meaning that he predicts teams will pay about $5.78 million per win in 2014, $6.06 million in 2016, etc.) For now, we'll also employ Cameron's projection that players, in the aggregate, lose about half a win per season as they age.

Using this model, we can estimate Upton's value. For the sake of simplicity, we'll begin by projecting Upton to be a 3.5 win player in 2013. We'll also only project for five years, the lifetime of the contract he signed with the Braves:

2013: 3.5 WAR at $5.5 million apiece = $19.25 million
2014: 3 WAR at $5.78 million apiece = $17.34 million
2015: 2.5 WAR at $6.06 million apiece =$15.16 million
2016: 2 WAR at $6.36 million apiece = $12.72 million
2017: 1.5 WAR at $6.67 million apiece = $10 million
Total value: $74.5 million

That's actually kind of amazing: Using this simple formula, we've essentially come to the same consensus as Frank Wren and the Atlanta organization.

But what if we were a little more pessimistic, and instead of projecting Upton for 3.5 wins in 2013, we choose to knock half a WAR off his 2012 total (like we do everywhere else in the model) and start him with 2.8? After running the numbers, we get:

2013: 2.8 WAR at $5.5 million apiece = $15.4 million
2014: 2.3 WAR at $5.78 million apiece = $13.29 million
2015: 1.8 WAR at $6.06 million apiece = $10.90 million
2016: 1.3 WAR at $6.36 million apiece = $8.26 million
2017: 0.8 WAR at $6.67 million apiece = $5.33 million
Total value: $53.8 million.

Now we've employed a mechanism similar to what the collective readers of Fangraphs had in mind when they projected Upton's salary total at $52 million. I can't see an organization handing a five year deal to a player one might expect to serve in a platoon role by the end of season three, but that's neither here nor there. Regardless, this example reveals how a simple adjustment to our model can produce substantially different values.

We can also demonstrate this effect by shifting our model the opposite direction. Let's start Upton at 3.7 wins for 2013, a figure halfway between what he posted in 2011 and 2012. We'll also bullishly assume that Upton's athleticism will help him avoid the injury bug and age much more gracefully than his counterparts (hardly an outlandish or unreasonable claim), and only project him to lose .3 WAR per season. Here's how that shakes out:

2013: 3.7 WAR at $5.5 million apiece = $20.35 million
2014: 3.4 WAR at $5.78 million apiece = $19.65 million
2015: 3.1 WAR at $6.06 million apiece = $18.78 million
2016: 2.8 WAR at $6.36 million apiece = $17.08 million
2017: 2.5 WAR at $6.67 million apiece = $16.67 million
Total value: $92.5 million

That's a pretty substantial difference from our previous two models. All of these models use reasonable assumptions, none have enormously different inputs (we didn't even alter the $5.5 million dollars per win assumption for 2013 or the 5% inflation projection), and yet these three evaluations have a $40 million range. Yes, this is a somewhat simplistic and dramatic demonstration, but I think it successfully illustrates the difficulty of valuing a player's performance. Rational people can radically disagree on the value of a free agent .

I think it's also worth mentioning that this exercise illuminates one reason why it's so hard to get a bargain in free agency. A talented player like Upton, who presumably had numerous bidders for his services, has the benefit of not only selecting the highest available bid, but also the opportunity to pit one franchise's aggressive offer against what other teams might be willing to pay. Players are likely to sign with the highest bidder and as we just saw above, some teams will pay quite a bit more than others for a free agent. If x teams want a player, inevitably, one of them will use higher inputs than the others. The result is an inflationary effect that cascades onto other available players.

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