When is a win worth more?

I was thinking about Michael Bourn this morning, because I need psychiatric help. It kind of struck me that the Cubs could use Bourn more than most other teams… but taking a common approach to free agency, we shouldn’t be offering him more money than any other team (Bourn’s worth is more or less a constant), especially because we are so far away from contending. That’s obviously not true, but it is the assumption we essentially rely on when trying to compute a free agent’s worth. For instance:


Age-29 : 6.0 WAR

Age-30: 3.5 WAR (projected)

Age-31: 3.2 WAR (projected)

Age-32: 2.8 WAR (projected)

Age-33: 2.2 WAR (projected)

Age-34: 1.4 WAR (projected)

This is a back-of-the-napkin estimate, where I took Age-30 to be 3.5 and depreciated by 10/10/20/40 percent. If a free agent is “worth” 4.5 million in free agency, then this table becomes

3.5 * 4.5 = 15.75 million

3.2 * 4.5 * 1.05 (inflation) = 15.12 million

2.8 * 4.5 * 1.05^2 = 13.89 million

2.2 * 4.5 * 1.05^3 = 11.46 million

1.4 * 4.5 * 1.05^4 = 7.66 million

So, a 3-year pact would look like 44.76, a 4-year deal worth 50.60 (10% decrease for 4th-year premium- otherwise 56.22), and a 5-year deal worth 63.88/57.49)

Let’s simplify that to 3/45, 4/56, and 5/64, as those seem reasonable.

This is the inherent problem with “fair market value”, though: is Bourn worth that much to the Angels, who already have a loaded outfield? Of course not. We aren’t trying to buy wins above replacement, we are trying to buy wins above replacing our guy.

Last year, the Cubs trotted out a .230/.303/.337 line at CF. Using this WAR calculator, we can see that the Cubs got 0.4 WAR from their CF last year. Bourn would provide 3.5 WAR, but only 3.1 Wins Above Alternative. The Angels, on the other hand, put up a .292/.365/.470 line, for a WAR of 7.3; Bourn is worth -3.8 WAA for the Angels (which, of course, is one reason they aren’t bidding for him). Of course, the Angels could move Bourn to RF or LF, but that diminishes with WAR, so his WAA will certainly improve but not by much.

If we think of players as providing Wins Above Alternative instead of Wins Above Replacement, we can get a much clearer picture of who teams are targeting and why they should be targeting them. You could even sort of predict who should offer a player more (I haven’t done the research, but it’d be very impressive if a team had a greater need for Bourn than the Cubs do).

The value of a WAA is certainly higher than 4.5 million (the average FA is not replacing a 0 WAR player, but obviously they are paid the same in my formula), but we actually don’t need that precise value to compute who should offer the most (all else similar- obviously, team payrolls and where they are in the contention cycle matters also). It is simply the team with the greatest potential WAA.

Of course, FA is way, way more complicated then just coming up with this number; I just thought it would be interesting to note. This will be much, much more useful when the Cubs are only a player or two away from being really competitive.