A thought experiment on win valuation

by PWHjort on May 22, 2010 3:47 PM EDT in Positional Reviews

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.

Continued below. You can continue reading this post by clicking the link below that says "Continue reading this post".

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.

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Comments

Interesting stuff. One of the greatest difficulties of

analyzing historical contracts (i.e. ones from 2 or 3 years prior) is reestablishing that context. I’ve heard the argument made — and I find it quite compelling — that the Cubs were willing to overpay Alfonso Soriano in 2007 because the signing increased interest among other free agents (Ted Lilly, for one).

In doing this, the Cubs had to sign Soriano well into his later years, meaning he would likely under-perform with respect to his contract. In other words, they went all in for the 2007 and 2008 seasons (in which they reached the playoffs), eschewing later contract difficulties (i.e. 2009 and later). If we examine the contract in a vacuum, it’s hard to understand the rationale of signing an aging slugger for so long, but context helps to clarify that — at least a little.

from Cubs Stats and Twitter @BradleyWoodrum

by BWoodrum on May 22, 2010 4:04 PM EDT reply actions

Fantastic.

by Tommy Bennett on May 22, 2010 4:58 PM EDT reply actions

Are you familiar with the CAPM model? That may answer the question of the asset’s(player) worth in the context of market risk.

It seems to me that a lot of stock valuation techniques could also work on basball players. But maybe that’s just because I’m a Finance guy.

With crappy overpaid vets of course!

by TheBravestWay To Block A Decent Prospect on May 22, 2010 5:54 PM EDT reply actions

That seems very helpful. I’ll take a look.

Thanks.

Beyond the Box Score / Capitol Avenue Club / shwitter: @CapitolAvenue

by PWHjort on May 22, 2010 6:31 PM EDT up reply actions

Not to get too snarky, but do stock valuation techniques actually work on stocks?

I’ve been through the B-School courses at undergrad and so no evidence that stock valuation was anywhere near as well understood as the techniques make it seem.

by Dan Turkenkopf on May 22, 2010 7:54 PM EDT up reply actions

The problems with the CAPM model

The CAPM model has two problems here. One is that is essentially impossible to pin down, since the “beta” is subject to fudging and there’s no set time horizon for measuring volatility. It might be better than nothing, and it might actually work better for baseball players (who, unlike stocks, tend to experience similar curves), but it’s not scientific.

The second, and greater problem, is that CAPM measures contextual risk, whereas you’re talking about exceptional, game-changing risk. What Nicholas Nassim Taleb and others call Black Swans, for lack of a better term. CAPM actually assumes the opposite; that accepted volatility levels will remain constant.

Measuring the potential for Black Swan risk will never be precise, but I could see a way to pro-rate that risk over a set number of years. In baseball terms, for example, one could ask about how often is there a work stoppage, and one could come up with an increasing risk level for every year following the last work stoppage. Of course, guarding against such things isn’t that hard to do in theory, but it’s close to impossible in reality, since the most you ever get for your time and money is a lack of disaster, for which people rarely continue to shell out resources.

by Greg Heller-LaBelle on May 22, 2010 9:57 PM EDT reply actions

Greg, I’m with you here:

Of course, guarding against such things isn’t that hard to do in theory, but it’s close to impossible in reality, since the most you ever get for your time and money is a lack of disaster, for which people rarely continue to shell out resources.

Beyond the Box Score / Capitol Avenue Club / shwitter: @CapitolAvenue

by PWHjort on May 23, 2010 1:09 PM EDT up reply actions

Great thought exercise that most fans don’t ponder.

Quantification is still, I believe, still stuck in the probabilities analysis you did up top. There might be upcoming theories in options you might want to check into, but I’ve been out of the loop, so I can’t tell you what they are, only that I’m aware of some theories regarding that and valuation. There might be some way of applying those theories to baseball, I don’t see why not. It may not be exactly the same as stocks, but I think that it should still yield analytical insight to the process.

Black Swan is probably a book you would like to read regarding qualitatively discussing this type of scenario. The author has written a couple of books on this topic, but Black Swan deals specifically with unexpected outcomes that nonetheless always seem to happen anyhow. Scenario Planning analysis is probably another topic area you should explore.

You might also want to check into Sam Savage. He wrote the book, The Flaw of Averages, and another book on analysis where he provides tools to look beyond simple averages. Monte Carlo simulation is a big part of his tool kit. I think the way he talks/writes turn off some people to his message, but I think he’s got something there.

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by obsessivegiantscompulsive on May 23, 2010 2:42 PM EDT reply actions

The only thing that can really "work" is if you can capture all the variables

or a large enough percentage of the uncertainty. Sure, the league could fold, and you want to capture that probability, but also the league could up the buy-in to $400 for the next season. All you have available to derive these variables and their probabilities is history and past experiences (and to an extent, intuition). When it’s baseball, there’s a good amount of data cataloging past experiences. When it’s management of fantasy leagues, not so much.

by SagehenMacGyver47 on May 24, 2010 7:28 PM EDT reply actions