March 23, 2010

Expanded Horizons

Mauer Present Value

by Tommy Bennett

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Question of the Day

What if I told you that, right now, you could buy Joe Mauer’s age-35 season for $13.5 million. Would you take it? How likely would you be to regret it?

The Art of the Big Deal

After long negotiations, Joe Mauer and the Twins have agreed to an eight-year, $184-million contract extension that will keep the catcher and reigning American League MVP in his native Minnesota through 2018. Not only is it the fourth-largest contract ever signed (in nominal dollars), it is by far the largest contract for a catcher in major-league history. As Christina Kahrl noted, it’s also the first time the Twins have locked up someone who has been a truly elite player for the team. This is both a big deal and a big deal.

After the cries of joy erupted and settled in the Twin Cities, a bit of doubt began to creep into the Land of 10,000 Lakes. After all, eight (plus one) years is a long time. The Simpsons will be rounding out its 30^th season by the time Mauer’s deal is up. Besides, the deal includes a full no-trade clause, the very mention of which can conjure up terrible thoughts of albatross contracts. On Twitter, I witnessed a quick backlash against the length of the deal. Many argued that the Twins would come to regret signing the deal just as the Rockies had regretted signing Todd Helton. Given Mauer’s back injuries and increasing time as designated hitter, most are operating under the assumption that Mauer will change positions somewhere along the road. There is truth in each of these concerns, and the number of successful catchers playing the position at age 35 is small.

The Twin Aims of Contract Structure

The funny thing about this deal is that it is not back loaded. In fact, Mauer will earn exactly $23 million in each of the eight seasons from 2011-18. Why is that funny? Let me back up for a minute.

I have a theory about contracts for baseball players. Normally, we assume that for a contract to be good for a team, it should pay the player the least amount of money possible. The less money spent, the greater the surplus the team has for other players. And there is clearly a theoretical sense in which this is true. You may have learned in Econ 101 that rational firms seek to maximize profits, and that means allocating resources in the most efficient manner possible. A little hand-wavey stuff later, and we’ve got a simple model.

Except that this theory suggests the very best thing a team can do is give out heavily back loaded contracts. Why? Because of the time value of money (it’s better to have a dollar today than a dollar tomorrow), teams that backload contracts end up effectively paying less for their players. If instead the Twins had offered Mauer a $1-million salary for the first seven seasons and a $177-million salary in 2018, they would without a doubt be paying less than they are under the current deal.

So they got jobbed because they didn’t backload the contract? But isn’t that exactly what everyone says is so bad about the Helton deal? That contract, signed nine years ago this month, escalated in salary from $10.6 million in 2003 to an eventual $19.1 million in 2011 (since renegotiated). It was effectively impossible for Colorado to trade Helton, it was often said, because they had this terrible back-loaded contract. How can this be the case if they were actually saving money by back loading the deal?

My theory of baseball contracts adds the wrinkle that teams want to pay players an amount that is approximately commensurate with their value on the field in that year. Because Helton was aging, the deal paid him more exactly as he was declining in value. Mauer’s deal pays him a constant amount each year of the deal. But importantly, it doesn’t pay him the same amount in present-value dollars, that is to say after we’ve corrected for inflation and the amount of interest the Twins could have earned on alternative investments. In fact, by the time Mauer is 35 years old and in the final year of the contract, the Twins will be paying him the equivalent of approximately $13.5 million in 2010 dollars.

Below, I’ve used two different discounting models to translate the amount Mauer will make in present millions of dollars. The first model, labeled “Constant” assumes a constant discount rate of seven percent (a common choice for such calculations). The second column, labeled “Variable,” accounts for the fact that inflation is very low at the moment but is likely to rise in the future (the discount rate rises from five percent to eight percent over the life of the deal). The differences between the columns are small.

In other words, if Joe Mauer had the same discount rate as either of my assumptions, he would be just as willing to accept a lump sum of about $140 million today as he was to accept the deal he just signed (making certain assumptions about his risk tolerance). One interesting tidbit about this table is that changing the discount rate can affect the calculations significantly. If instead we choose an eight-percent discount rate, say because we are worried about inflation in the coming years, the present value of the deal drops to $132 million. A nine-percent rate (which doesn’t mean nine-percent inflation, by the way) drops the value of the deal another $5 million.

Is it plausible that the Twins front office bothered with things like a discount rate? Only if you think the Pohlad sons are paying attention to the Twins. The Pohlads own a host of companies, including two banks and a financial services firm. If the Pohlads and their financial advisers anticipate very high inflation in coming years, they are expecting to pay Mauer even less in present dollars than I have indicated.

Sliding Down the Age Curve With Dignity

All this makes sense, I think. As Mauer ages he will likely decline in value. If the team can effectively pay him less in those future years, it can allocate its revenue to going after players who can help them win that year. Baseball teams don’t have magic money trees, and raising money to pay for back-loaded contracts can be very difficult. A more sensible and manageable approach matches up production with salary. Now, I don’t purport to know if Joe Mauer will be worth $13.5 million or so in 2018. But just for fun, let’s have a graph anyway:

The two blue dotted lines marked “Constant” and “Variable” correspond to the present value of the payments the Twins are making each year (including 2010, before the contract goes into effect), given the two discount models described above (read from the left-hand axis). The salmon-colored dotted line represents PECOTA’s long-term projection for Mauer’s value in WARP3 (read from the right-hand axis). The axes are scaled according to early returns from some of Matt Swartz’s work on MORP and the cost of buying WARP3 (or WARP per 162 games) in 2010.

For fun and comparison’s sake, I included a few of the greatest catchers in baseball history. However, instead of showing all the messy WARP3 data points (by age), I fit a quadratic curve to each player’s career and included the portion from his age-26 season to his age-36 season. Before we start up the war over aging curves again, let me just disclaim any scientific accuracy here; the quadratic fits are messy, anecdotal, and have absolutely zero predictive value. It is important to keep in mind that these catchers (Johnny Bench, Yogi Berra, Carlton Fisk, Mike Piazza) are remembered as great in part because they survived long enough as catchers in the major leagues.

Nevertheless, we can see the kinds of career arcs that Mauer might have if he is lucky. Some (like Bench in red) would have Mauer continue his dizzying heights of the last two seasons (his ‘09 WARP3 is an off-the-chart 8.8). Others (like Fisk in black) would be relatively flat. You’ll notice that PECOTA’s bullish projection traces somewhat like a combination of the late careers of Berra and Piazza. Nice work, as they say, if you can get it.

Will the Twins regret this deal come 2018? Of course, the big question here is how long Mauer can stay behind the plate. Bench and his precipitous decline were never given the respite of the designated hitter spot, of course, and perhaps that wrinkle will retard the deterioration of Mauer’s back and knees. I’ll leave that question to smarter minds, but one thing I can be sure of is that Joe Mauer will cost the Twins less in 2018 than he will in 2011.