Contracts Made Easy

It wouldn't be too hard to argue that the top two outfielders in this year's class of impending free agents--Carl Crawford and Jayson Werth--are a better pair than Matt Holliday and Jason Bay were last year. You probably wouldn't pick any of these players to build a franchise with, they're older, don't play up the middle, and probably most importantly come with a steep price tag. But teams in the market for big money free agents aren't generally of the rebuilding variety anyway, and a team reasonably close to contention would be hard pressed to do better than one of the four above at one of their outfield corners.

Exactly which teams will empty their coffers for the privilege of employing these talented gentlemen is a question better left to someone more informed than I, perhaps someone working in baseball, perhaps Nostradamus. But how much it will set back the team to be named later is something I might be of use addressing.

Addressed below.

Commonly a free agent contract will involve an equal salary for the life thereof. Given a free agent's production can generally be expected to decline over the life of his contract, paying a player an equal amount each year doesn't seem like the most logical way to structure the deal. But if we've learned anything it's that things are not always as they seem, and after a little bit of digging the notion holds true in this case. In the event of an equal-salary contract (we'll call it) it might be true that the player is paid the same amount each year, but the notion of him costing the team the same amount is an illusion, for several reasons. Reason number one is the money's time value. While a player may be paid $12.5 million a year 2009 through 2012, $12.5 million in 2012 isn't as valuable as $12.5 million in 2009. Inflation drives the value of the money down, so we can't look at a contract without adjusting for inflation. Otherwise we'd be comparing apples to artificially inflated apples.

The other reason is the economic cost of the multi-year deal in year one is almost always greater than the dollar amount written down when the accountants balance the books. You see, in order to secure the player's services for $12.5 million in 2009, the team had to commit three additional years at $12.5 million. We might expect the player to contribute $20 million worth of on-field value in year one, $15 million in year two, $10 million in year three, and $5 million in year four. The following table represents the hypothetical contract discussed above, listing the player's salary, expected value of production, and expected surplus value for the life of the contract:

 

 

An accountant might call it a good deal in 2009 and 2010 and a bad deal in 2011 and 2012. An economist would prefer to view the contract with a smaller zoom lens by simply calling it a fair deal. Even if the economist picked up the accountant's microscope, he'd probably come to a different conclusion than the accountant did. Recognizing the privilege of employing a player for $12.5 million comes with the stipulation of employing the player for three more years at the same rate changes our figurin'. So the cost isn't the salary, rather the salary plus some of the future opportunity lost as a result of paying a $5 million player $12.5 million in 2012. It's a beautiful lesson in monopoly bargaining. Teams signing high dollar free agents would prefer to save some money now at the expense of some opportunity in the future in order to increase their postseason odds or the odds of winning the tournament now. And the player whose being paid enough to feed a small nation for a year probably doesn't mind if he gets $12.5 million a year rather than $20 million now and $5 million later, it's more than he could possibly spend either way.

The equal-salary contract structure works. The theory I've discussed above is ample evidence of this, but I find the fact that we see it executed in MLB so frequently to be a much more compelling piece of evidence.

So, how do we calculate "how much"? We need several parameters. Parameter one is the length of the contract. Parameter two is the player's production, his win value (usually some version of Wins Above Replacement), in each year of the contract. Parameter three is the rate of return, or interest rate. Parameter four is the market rate of a win. Defining these parameters is tough and there isn't much of a definitive correct answer, so I'd prefer to be an enabler rather than a do'er. Therefore, I've created a calculator that spits back a number tailored to your liking. We'll get to that in a second after I explain what the calculator is doing.

If we know the market rate for a win and we know how many wins a player is going to be worth, we can calculate how valuable a player will be over a given time period in 2010 dollars. In theory, this number should equal the player's salary in 2010 dollars. The issue is the player won't be compensated entirely in 2010 dollars. If we set "x" equal to the player's yearly salary in an equal-salary deal, the following equation should hold true:

 

 

Where "n" is the number of years in the contract. If you're not familiar with mathematical notation, it's a simplistic way to state what I have in the paragraph above, the value in 2010 dollars should equal the player's salary in 2010 dollars. Solve for "x" and you have the player's yearly salary.

I'm not good enough to come up with an easy way to empirically solve that equation, it's a bear. What I can do is let excel simplify it for me, turning it into something I can very easily solve. Plot several hypothetical yearly salaries against the output (what you get when you plug the salary into that equation) and every time you can draw a linear regression equation with an intercept of zero and an R^2 virtually indistinguishable from one (aka a very strong relationship that correctly models reality and is extremely easy to work with)*. Divide the total value by the slope of the equation and you have your yearly salary. Multiply by the years, and that's how much it costs.

*I should mention it's necessary to go through this process for every 'length of contract scenario'. I've already set up the calculator for contracts of 1-10 years in length, I may have to update it if Albert Pujols eventually reaches free agency.

But like I said, you don't have to do any of this. Here's all you have to do.

1) Download this file.

2) Fill in the rate of return, win values, and the market rate for a win (the green cells).

3) Note the length of the contract, find that number in the "ID" column. If it's a 4-year contract, you want ID 4, for example.

4) Note the AAV (aka yearly salary) and Total $ (the blue cells) corresponding to the appropriate ID.

And that's it.

Let's try one, Carl Crawford, 5 wins in 2011 with a 0.5 win/year linear decline, $4.4 million per win, 8 percent rate of return (add 100 to your ROR, by the way, for computation purposes), 7 year contract:

 

 

We get just a bit over $19.5 million a year, or close to $137 million for 7 years.

One final note on draft pick compensation. I've included a $5 million bonus for the first five years of the contract and a $2 million bonus during the subsequent three for draft pick compensation after the contract's expiration. If you'd like to change that (you'll probably want to), click on the cells in the "Adjusted" column and change the constant (in the formula bar).

I've conveniently avoided answering a tough question, but I suppose sometimes it's better to let the reader decide. I only hope this tool enables you to bring more to the table with less work involved when discussing potential free agent deals. As for Crawford and Werth, playing around with the tool will quickly reveal they're going to get paid a whole lot.  Combined they should easily clear the $186 million Holliday and Bay were guaranteed last off season.  I'm assuming a normal aging pattern here, and given Crawford and Werth are better athletes than Holliday and Bay I think it's a fair assumption.

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