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A thought experiment on win valuation

Suppose I am playing fantasy baseball in a dynasty league. It is a 10-team league with a \$200 buy in--winner takes all (\$2000). At the trade deadline I am in 3rd place and I basically have two options. One, I could "buy", increasing my odds of winning now at the expense of winning in the future. Two, I could "sell", giving up on the proposition of making \$1800 this year in order to increase my chances of winning the \$2000 in the future.

Let's say if I "buy", I will stand a 30 per cent chance of winning this year and a 10 per cent chance of winning the next two years. If I "sell", I have no chance of winning this year, a 10 per cent chance of winning next year, and a 50 per cent chance of winning in two years. All things are equal after three years.

Now, to determine which is the better course of action, multiply the chances of winning by the reward for winning, adjust for the time value of money, and add them up. This is what I have done here (option 1 being "buy" and option 2 being "sell", 12 per cent rate of return assumed, time adjusted original investment subtracted from the "Total" row):

So, if I trusted these numbers, I would be inclined to sell. Suppose I did. I traded (and I'm just making this up, just like I made up the numbers) Roy Halladay for Stephen Strasburg, Jesus Montero, and Brett Wallace and I traded Mark Reynolds for Mike Stanton and Dustin Ackley. Without Reynolds' homers and Lincecum's strikeouts, I finish 6th, have a good draft, some players break out in year two, and my team looks really good heading into year three.

Except after year two the league commissioner gets a promotion at his law firm and no longer has time to manage the league, three other players decide to quit the league, and it dissolves before year three ever gets started.

Obviously I did not plan on the league dissolving, but the possibility is always there. I would have handled the situation at the year one trade deadline quite differently had I known what was in store. I am aware of no fully functioning crystal balls with psychic power, but if I know the probability of a scenario I can use that to help guide my decisions.

The future brings uncertainty and uncertainty breeds risk. In fact, one of the principles of risk management is: "risk management should explicitly address uncertainty". In estimating the probability of winning now and in the future, I explicitly addressed (in a very unscientific manner, albeit) the uncertainty surrounding my team's future quality. The tragic flaw here is my failure to address the uncertainty surrounding the team's future *environment*. Lesson 1: we can never assume the status quo with 100 per cent certainty.

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When you're evaluating a multi-year contract, I think it is important to consider what I will call "disaster scenarios". The league folds (highly unlikely in real baseball but not outside of the realm of possibilities), ownership decides to go really cheap, several stars break their legs and you no longer possess a contender's roster, et cetera.

The most sophisticated contract analysis examines the contract in context. It involves forecasting the player's future value based on past results, aging factors, and other baseball knowledge, and determining how much that's worth to the team. The latter part usually means examining how good the team is now, how good they want to be (and at the returns are diminishing in many, many cases, meaning it is never profitable to shoot for anything close to 162 wins), and how they are positioned for the future. Using least error projections, we can account for some of the uncertainty surrounding the player. I think it's crazy to stop there. I think that unless you consider other types of risk--particularly types that the player has nothing to do with--it's not as good as it could be. What are the chances my organization melts down and I'll be paying someone \$18 million to DH for my 65 win team in 2 years?

I don't know, but I know it's not zero. Assuming the probability of a disaster is zero was my tragic flaw in the fictional scenario above. And since the probability of a disaster is not zero, all other things equal, a win today is more valuable than a win in the future. Call it the time value of wins.

If you're familiar with a way to quantify it, I'd love to hear about it. But if not, I still think it's something to keep in mind.