From Ace to Albatross?

Ben Sheets is finding himself in a most precarious situation this offseason. He had started to become the face of a franchise, the once in a decade find that a general manager finds solace in. Now Ben Sheets finds himself in the purgatory of the oft-injured. No one doubts his usefulness as the ace of a staff when healthy, but all too often the Milwaukee Brewers found themselves waiting for his return to the disabled list.
Even after a relatively healthy season by Sheets' standards, GMs are reluctant to commit to him even for a short-term deal.
How big of a risk is Sheets?
Let's take a look at Sheets' projected value over the next couple of years. According to CHONE, Sheets will be worth $12.6 million in 2009 and $12.0 million in 2010. This factors in Sheets' injury history by projecting him to pitch 148 and 133 innings in 2009 and 2010 respectively.
Let's suppose that things are even more dire than that. Suppose that there's a 75% chance that Sheets pitches 148 innings next year and a 25% chance that Sheets does not pitch at all. Similarly for 2010 assume there is a 70% chance that Sheets pitches the 133 innings as expected, and a 30% chance that he doesn't pitch at all.
These are very extreme assumptions, especially considering that Sheets is yet to miss an entire season in his major league career. Furthermore, there is strong evidence that Sheets is less of a health risk than A.J. Burnett who just signed a 5 year $82.5 million deal with the Yankees. (This is something we will take a closer look at in another post).
Using a similar 6.75% discount rate as in the Lowe article we find that a 2 year deal for Ben Sheets worth $17.9 million paid out under equal annual amounts is a fair deal. But of course this amount takes into account the worst-case scenarios, i.e. Sheets doesn't pitch at all. Strictly using the dollar amounts above, we have Sheets' value at $24.62 mil over two years (payments distributed evenly). But if Sheets is able to perform at the level he has most of his career his value would be slightly higher, at roughly $26 million.
Now projecting in a best-case/worst-case scenario let's suppose Sheets has a 20% chance of pitching 200+innings, a 25% chance of not pitching at all and a 55% chance of pitching based on the above projections. Sheets' value then becomes $23.79 million. Making a 20% assumption that Sheets pitches 200+ innings is not that far-fetched considering that he has pitched 200+ innings on three occasions in his career and he's coming off of a 198.1 inning season.
It seems that the market for Sheets is currently moving toward roughly 2/$20. That would be quite the bargain based on CHONE's standardized projections.

Lowe seeking a contract

We've seen mixed approaches to signing players this offseason. The Mets were able to acquire Francisco Rodriguez at a reasonable amount for a reasonable length of time. The Yankees however bid against themselves for CC Sabathia, blew competition out of the water for Burnett, and stayed with competition for Teixeira. Many players remain on the market and are expected to take lower salaries than was originally anticipated.
Derek Lowe was originally thought to be looking for 5 years $90 million. After seeing a slowing market the Mets made an initial offer of 3/$36. Two very disparate numbers. Scott Boras and Derek Lowe countered by saying Lowe is looking to other suitors for $16 mil per.

Let's use CHONE's projections to formulate the present value of Lowe's worth to a team. We will use a present value formulated from a discount rate based on current bond models. Using a combination of Citigroup's Discount Rate Curve, Moody's Discount Rate, and a portfolio of high rated corporate bonds, a reasonable discount rate is 6.75%. Furthermore, let's assume a middle of year payment for each year of Lowe's valued worth. CHONE projects Lowe's worth at:
2009: $15.5 mil
2010: $14.8
2011: $14.2
2012: $13.4
That gives us a present value of $51.14 mil.
Now, it is important to note that these discount rates do factor in current economic conditions. While we may be tempted to adjust the discount rate going forward, it is really unreasonable to do so given the current economic turbulence.
So now any team wanting to match the value of Lowe's worth, but not wanting to give Lowe 4 years guaranteed could backload some of the dollars of both the guaranteed portion of the contract as well as a fourth year vesting option.
Based on the Mets' three year offer a fourth year vesting option seems highly likely. To make the contract more appealing to Derek Lowe you need to make the vesting condition fairly easy to attain. Something that he has an 85%+ chance of attaining. Perhaps that would be pitching something like 170+ innings in 2011.
Suppose that a team offers Derek Lowe 3/$40, with a payment schedule of 2009 - $12 mil, 2010 - $13, 2011 - $15. In order to match the present value of Lowe's worth, the 85% likely vesting option would have to be $22.18 million; a pretty hefty vesting option.
Now if instead a team makes a more reasonable offer of 3/$42 without backloading; the vesting option would only need to be $19.23 mil. This seems like the type of offer Lowe would be happy with. Either way, he's probably looking for a bit too much in $16 mil per and the Mets started off too low at 3/$36, even given the current economic situation.