My Wang Problem

[Sky's note: we're getting to the time of year where prospects will be changing hands in return for current major league talent.  Valuing prospects is tricky, but thankfully Victor Wang did a bunch of heavy lifting a couple years ago.  Colin's FanPost, which I've bumped to the front page below, raises some questions about using the numbers from the study.  He also links to a bunch of relevant articles, so if you're unfamiliar with Wang's research, you can quickly catch up.]

This isn't a particularly big deal, but I think it's going to lead to some errant analysis so it's worth bringing up.  Victor Wang's ridiculously awesome research in THT's '09 Annual has given us approximate surplus values for prospects.  This obviously makes analysis of prospects-for-stars deals (like the recent Cliff Lee deal) very doable.  But I have two issues.  One, I wish we would talk about surplus value in wins rather than dollars.  Dollars inflate and deflate, so the surplus value chart is going to change year to year.  Wins are stable.  Fortunately in Victor's summary article at THT, we still get WAB to refer back to. 

Two, I think this means that Sky's chart hasn't been adjusted for inflation properly.  Victor notes in his research that he was using $4.88MM per win.  Last season, free agents went for $3.5MM and right now consensus says we're in the 4-4.4 range afaik.  And the result is that when I calculate Smoak's surplus value on my own, I get significantly different values than are found in Sky's chart.  I.e. to calculate Smoak's value, let's say he provides 1.5 wins per season over those 6 seasons.  That makes him a smidge better than a top 10 hitting prospect in Victor's terms, using the 8% discount.

1.5*6 yields 9 wins times $4MM per win is $36MM in total value.  Now we must subtract the dollars paid above the minimum for arb years.  So that's 1.5*4*.4 + 1.5*4*.6 + 1.5*4+.8 - 3*.5 ~$9MM.  And the total surplus value becomes $27MM.  So what was for the M's a crazy good deal is now a merely very good deal, assuming you really like Justin Smoak.

And in case you want to calculate surplus value in the future given an expected wins per season, I think the formula looks like this:

4.2*wins per season*dollars per win +1.5

Top 10 Hitter in 2010 ~ $27MM

Top 11-25 Hitter in 2010 ~ $18MM

Top 75-100 Hitter in 2010 ~$9MM

Using that formula very nearly gives me Sky's chart if I use $4.88MM per win.  It's probably a little low because I used a slightly different method for arb accounting.

That all said, there's still a very decent chance I'm just skipping a step somewhere.  What I really want is to be able to do this stuff for my handful of readers and ironing out these issues would be a real help, particularly if Kenny Williams pays some price for Adam Dunn or whomever in the upcoming weeks.