January 15, 2010 at 2:01 pm by Capitol Avenue Club under Atlanta Braves
Introducing the Time Value of Wins: Part I (Theory)
I’ve been discussing the time value of wins in this space a little bit over the past month. I’m fairly certain the concept has never been formally introduced or quantified. I intend to do both over a two-part series. This is part one, in which I formally introduce the theory of the time value of wins. Here we go.
Every year as July 31st approaches, the casually obsessed baseball fan is over run with trade rumors. Usually, they involve a team with no hope of contention trading away an expensive super star to a playoff contender for a small army of elite prospects. Much fan malcontent arises from said rumors and trades, usually from the fans of the team that traded away said super star. I can already hear the rabble on Padres’ message boards 6 months from now: “How the fuck can Hoyer trade Adrian Gonzalez or Heath Bell for a bunch of un proven prospects?”
That’s understandable. To expect average fans to be content with a team that is clearly rebuilding is to set entirely unrealistic expectations. However, from an objective and analytical standpoint, it’s important to remember that the rebuilding team is rebuilding for a reason. As Billy Beane said: “The way I look at it, you are either building something special or you have something special.” What Beane is saying, and he’s right, is that the ultimate goal is to build a winning team. If you don’t have one, you’re working on building one. The reason most teams rebuild is because their roster isn’t good enough to contend for a playoff berth. If that’s the case, the resources at hand should be dedicated toward winning in the future, seeing as winning now is practically impossible.
Hence, deadline deals. If the team has zero hope of contending, it’s probably best to go ahead and trade away the super star, because the wins he brings to the table have little meaning in the grand scheme of things. Other than PR, ticket sales, and other off-field issues, the super star’s presence on the team is virtually meaningless.
Take the 2007 Texas Rangers, for example. On July 29th, they owned a 46-59 w-l record. There was little chance of them making up a 16 game deficit in two months and receiving a playoff berth. So, they decided to trade Mark Teixeira–who would certainly depart via free agency after the 2008 campaign. If the Rangers had kept Teixeira, they probably would’ve won more games than the 75 they did. They may have even won 5 more games, finishing 3rd, rather than last, in the division. However, 3rd place ain’t in the money, and Teixeira’s potential presence during the season’s final two months had zero playoff implications–they weren’t making it, with or without Teixeira. The present wins they would’ve received from Teixeira’s on field production were of little tangible value, the future wins they received in the return for Teixeira (in the form of Neftali Feliz, Jarrod Saltalamacchia, Beau Jones, Elvis Andrus, and Matt Harrison) represented something that is actually useful to the organization.
All of this goes back to JC Bradbury’s good and valid point, “Trades Are Mutually Beneficial”. Observe:
At this point, I defer to the fundamental theorem of exchange: rational and self-interested parties will only voluntarily trade when both parties expect to be made better off by the exchange. Players change teams only because both GMs sees the new player as superior to the old. And this doesn’t necessarily mean playing quality: salary requirements, service time, age, and contract length also play important roles. In some cases, player skill-sets just fit better on different teams.
So far, I haven’t introduced anything new. Basically what I’ve said is, when evaluating a transaction, it’s important to consider how much utility a player brings to the organization.
As far as mainstream sabermetric transaction analysis goes, usually, the accounting is pretty close to correct. For example, say a 3-win free agent signs a 3-year, $30 million deal. We determine his projected win value over the three year period (usually by regressing his present win value based on an aging curve), account for the time value of money, and determine how much money a team paid for their wins. The less they paid per win, the better for the team.
However, it’s important to understand a team’s position on the win curve to evaluate the efficiency of a transaction. Adding a 3-win player at market rate is usually a good idea for a team with a true talent level of 85 wins–the three wins they gain from their free agent are disproportionately important. The difference between 85 and 88 wins is often a playoff berth. As a corollary, adding a 3-win player at market rate is usually a bad idea for a very bad or very good team, more so the former. Paying market rate for three extra wins, say, to boost a team from 75 to 78 wins, does very little. At the end of the day, the team is still sitting at home in October, and the $10 million could have been spent on something else, something that will actually help the team make the post season at some point.
But we see teams keep their players or sign free agents despite little hope of contention. Why do they do this? Well, there are a few explanations. One is they’re stupid and/or delusional, which could be true in some cases, but is certainly not the case all the time. Two is the player provides some sort of off-field value, be it leadership, ticket sales, TV Ratings, or something else. Again, this could be true some times, but certainly is not always true. The third reason is market inefficiencies. When a GM thinks he’s found one, he may exploit it despite little reason to believe the move will help the team contend. Everything can’t be chalked up to market inefficiencies, though. Maybe 5 years ago, not today. Explanation number four involves the theory I’m presenting here–the Time Value of Wins.
The future presents uncertainty. When investors consider various investments, they’re primarily concerned with two things–yield and risk. However, failing to consider a third thing, the scape of the future market, can lead to nasty results. Baseball teams operate under the same assumptions. When they decide how to spend on a free agent, a GM will probably ask the following: 1) how much production am I going to get out of this player, 2) how much risk is associated with him, 3) what is the scape of the market going to look like for the life of this contract, and 4) how does his production help my team?
That fourth one, giving the production a tangible context, is what the theory of the Time Value of Wins deals with.
The Theory: Because the future presents uncertainty, a context-neutral win today is more valuable than a context-neutral win a in the future.
Corollary one: The sum of the rate of win depreciation and the rate of win regression should be equal to the projected market rate of return (inflation) for contracts of equal salary distribution.
For instance, going back to our 3-win player at 3 years and $30 million. In the first year, he’s worth 3 2010 wins and is paid $10 million 2010 dollars. In the second year, he’s worth less than 3 2010 wins due to both a) regression and b) the time value of wins, however, he’s paid $10 million 2011 dollars, which is not as valuable as $10 million 2010 dollars. If the sum of the rate of regression (due to aging, presumably) and the rate of win depreciation (due to the Time Value of Wins) equals the rate of inflation, the contract is a time-neutral one. That is–it possesses the same trade value per contract length in 2010 that it does in 2012.
Exactly what the rate of win depreciation is will be difficult to quantify, seeing as I’m not an economist, but I make an honest attempt to do so in part II.
The practical application of the theory of the Time Value of Wins involves usage in context. I intend to take a look at where a team projects to be on the win curve so as to determine the utility of wins. By determining where a team projects to be on the win curve, we can estimate how valuable extra wins are to a team. We’ll get down to the mechanics of it all in part II. In the mean time, I suggest reading Steve Sommer’s research on win curves.
One of the ultimate goals of this endeavor is to modify the Trade Value Calculator to account for the time value of wins. With this tool, we’ll be able to evaluate not only how the market values a commodity, but how a specific team values it. T here are many other goals, but before we dive in, I thought I’d provide this little primer.
I’m off for the weekend. Take care.