Question about Win Curves and Value

Watching Miguel Cabrera and Prince Fielder hit back-to-back for the next few years is going to be awesome. Despite the fact that it may not look so good 6 or so years from now, it will be awesome for a little while. That money, though, gives many pause as they begin to look at his contract, but as Mike Rogers pointed out, the value of adding wins isn’t constant. All of the research points to a win being worth around $4.5-5 million, but that isn’t true for each team. For teams in the 70-73 win range, it doesn’t make much sense to pay that much for a win when it won’t help. For teams in the 87-89 win range, the value of additional wins goes up because adding a win or two might be the difference between making the playoffs (thus having the opportunity to win the World Series and make tons of extra money) and not. The Tigers are that type of team, so paying a little extra for him makes sense. The question, however, becomes how much. Mike and I started talking on Twitter, and we discussed who exactly gets credit for those “additional wins”.

When I’ve seen some things on Jonathan Papelbon or Fielder’s contracts, people point out their respective team’s place on the win curve. As I’ve already said, teams in the 90-win range can justify spending a little extra for wins, but when it comes up, it almost seems as though those players are given all the credit for those additional wins. For instance, the Tigers are a (spitballing) 87-win team for 2012, but by adding Fielder, they are now a 91-92 win team. Thus, the Tigers should be okay spending a little extra for each win because Fielder is responsible for upping the win total. The thing is that I’m not sure that makes sense.

The team was constructed as an 87-win team before Fielder signed, so it seems like he is responsible for wins 88-92. But is that true? It’s not as if Fielder sits the bench until those wins are needed and then comes on to single-handedly win those four games. His value is spread throughout the season just like everyone else’s. Can you really give him credit for those wins?

And how would you react if you make multiple signings? What if you’re an 82-win team that adds two four-win players? Does the first player signed not get the added bonus because he was first? Does the second player get all of it because he was the last to sign? It doesn’t make sense to give both of them the bonus. The first one only put you into the mid-80s and shouldn’t get the bonus if you use the above line of reasoning. If you planned to sign both of the players but not necessarily the order, do you spread it evenly?

And how many years of the contract do you give him a bonus? If you think your window is 2 years but the contract is for 5, do you give him the bonus for all five years, knowing that he might not sign now if you don’t?

And say you sign a guy the year before to put you into the 90-win range, and you give him that bonus for the however many years of his contract. This off-season, you lost a four-win player, and you’re now going to sign another one (or the same one to a new contract). The player you must sign this off-season will technically now put you in the 90-win range. Does he get the bonus, too, even though you’ve already paid for those wins? And if he does and you did this again, just how many wins are you paying for, especially when you have that other guy who will be a free-agent next year?

Now let’s say you don’t pay for full wins. Instead, you pay by a ratio of wins added. Let’s say you predict (which is all you can do when you make the deal) to win 90 games and the player should add 4. That’s 4/(90-48=52) to get 7.6 or 8% of the possible bonus. You pay a little extra, but you won’t use it all. You can’t really split it evenly because you’ll still end up in a situation where you’re paying too much for wins as the contracts pile up (split it 2 ways this year but that won’t work next season).

I suppose this really just a on-the-fringes question, but it does puzzle me a bit. I understand the logic behind paying more for certain wins, but I’m not sure how much sense it really makes as you look at it further. You could argue that you just live with it because you’re just continually in that spot and that it only matters for free-agents, but you’ve decided on a number for those wins and continue to pay it to multiple people, though you only meant it for one. I’m entirely sure how to rectify it other than to say that this is the difference between theory and reality. In a one-year perspective, it makes sense, or at least more, but as you continue further out, it makes less and less sense as you move out further and further. Teams are responding to their situation, economic forces, market pressures, their placement on the win curve, and the need to win now and damn the future. It’s just a question. I have no official conclusion. It’s just something that’s been on my mind.