Let me preface this article with the admission that I'm really not sure I still believe Shin-Soo Choo is worth 20 AAV for 7 years. Perhaps that's just the market, but it's a lot of money (and would be the first contract exceeding 100 MM for a player never even voted in an ASG). However, I think you can make a compelling argument that it's the case, as long as we are willing to believe some relatively shaky assumptions.
First, let's look at the assumption that players depreciate at half a win a year. This is a nice rule on it's face; as a player moves from his peak (usually age-28 season), the player's ability erodes at a greater and greater rate, taking on a larger portion of his remaining skillset. The idea is that those two weights sort-of counterbalance, resulting in the standard half-win depreciation.
The problem is that it's fairly false, and it's easily proved. Let's take two players: Superstar Sam and Mediocre Mel. Sam is 30 and just came off of a 5 WAR season; Mel is also 30 but just had a season where he was 2 WAR. If Sam loses a half a win off of his value, that's a loss of 10% of his value. That same half a win is worth 25% of Mel's value. Does this seem correct to you? Barry Bonds put up 10.6 WARP in his age-39 season. Should we expect 5.6 WARP from him in 2014?
The "half-a-win" depreciation is a nice shotgun approach to establishing a value for someone, but if we're painting in broadstrokes, let's at least use a proper aging curve (h/t to the inimitable Nate Silver). Shin-Soo Choo is a centerfielder (albeit an extremely poor one). He'll probably move to a corner as soon as instantly, so we'll just use the Corner OF aging curve for him, which is as follows:
|Age||Percentage of Max Talent|
Pretty damning, right? The average cornerfielder is half as useful at 35 as he was at 26 – and we only get him for the ride down (ages 31-37). These percentages are from his peak value. What is Choo's peak?
Well, it was probably last year. BP had Choo at 6.4 last year (and 5.8 at 26, 5.4 at 27, prime years). Choo was 5.9 fWAR at 27 and 5.2 this year. Choo was 6.3 bWAR last year and 5.4 at 27. I think it's reasonable to Give Choo an implied peak of 6 platonic WAR. If the prevailing market rate is $6 MM a win (and it really is 7, but I'll take 6) and inflation is a tidy 3%, let's look at that table again.
|Age||% of max||WAR||Value||Total Value|
It's a 7-year deal, so if you got the "over 3 years" discount, that's $15.6 million off, which leaves us with 7 years, $140.8 million dollars. I'd argue that since his best year just happened, that he might actually age better than the normal person (though you could come at be with old-people vs. young-people skills). I'm not willing to take either side of either argument. All I'm stating is that it's not entirely unreasonable to envision 7 and $140 for Choo.
As a bonus, look how eminently valuable he still is in 2015 through 2019! Those are our "contention years." He's still worth a role at the top of an order until around age-37.