Valuing wins

Baseball Prospectus' Matt Swartz posted a fantastic article this week on the valuation of player contracts in Major League Baseball:

If baseball free agents were in a typical, perfectly competitive market like those you see in the first chapter of your introductory economics textbooks, the price per win would have to be linear. Basic economic theory of perfectly competitive markets would say that anything other than the same price for all wins would create arbitrage opportunities where teams could perpetually trade their way to the top of the league.

Later on:

In the case of baseball free agents, there are two main reasons why the baseline’s assumptions don’t apply. First, these markets aren't thick enough that teams can sign and trade players so easily and quickly swap out players for others like investors can do with shares of Microsoft. There are only so many teams, and there are limits to making this kind of move in general. Second, you can't employ 60 Garret Andersons on a team and suddenly become the best team in baseball. There are only 25 roster spots, and only so many players can realistically get enough playing time to realize their true value.

This a subject that I've given a lot of thought lately, to the point where I may actually do some original research on the matter in the near future.

In any case, my intuition is that teams should pay disproportionately more for a seven win player than a five win, three win, or one win player. I have a hard time seeing a team trading Alex Rodriguez for ten or twelve players barely above replacement level unless they are also saving money in the deal. I think Matt's reasoning is spot on: there are only twenty-five roster spots. You can't show up with sixty one WAR players and expect to make the playoffs.

That being said, I think there are really two questions here:

1. What do teams pay for wins?
2. What should teams pay for wins?

Any approach that uses existing contracts as its basis, like Matt's, is going to end up answering question number one. I'm really more interested in question number two. Unfortunately, answering question number one is much easier: we have a whole lot of data on how players performed (and how they were expected to perform) and what they were paid. The question is essentially positive. Question number two is a normative question that involves a variety of assumptions about why teams pay players. I'm not going to delve into those here.

I'm not sure if Matt's article is subscriber only or not, but if it isn't, it is worth your time.

Twenty-five days until pitchers and catchers report!

**EDIT** I had originally misspelled Matt's last name. I've fixed that.

A brief basketball note

I'm not a huge basketball fan, but I do enjoy the occasional University of Michigan game. This was the case on Sunday when I watched Michigan beat the University of Connecticut. It was a very good game and an important win for U of M.

However:

After the game was over, University of Michigan fans rushed the court to celebrate. This is embarrassing. The University of Michigan is not some small town university that just pulled of a once in a lifetime upset. We are large university that has no excuse for not being at least a minor contender in any major sport year in and year out.* That the basketball program has suffered as it has over the last decade is shameful.

UConn was ranked 15th. 15th! The University of Michigan itself was ranked that highly earlier this year. This is a Michigan team that is viewed to be underachieving! We made the second round of the NCAA tournament last year! More was expected this year. This wasn't some scrappy underdog rising up to take down an elite, once-in-a-lifetime, superstar team. It wasn't even a program in an off year beating a hated rival. It was a non-conference game at home against a good quality opponent. We should expect to beat a team like UConn. Indeed, here is the AP's first sentence in their writeup (emphasis added):

Michigan looked like the team it expected to be while No. 15 Connecticut struggled -- again.

Rushing the court sends the message that you viewed your team as massively inferior to the team you just beat. It says that you view the victory as one of the greatest victories in school history. It is something that should be reserved for wins that define an entire program, not wins that ought to be a matter of course for a team that should be in the NCAA tournament more often than not.

I sincerely hope that Michigan fans, especially the student fans, will learn how to behave as if they root for a team that aspires to be "the leaders and best," not just a bloated, underachieving, has-been in college basketball.

* Here pause and weep for the football program.

On making predictions

If you're up for reading an economics post from the most verbose writer on the Internet, try this post from Scott Sumner.

Yes, but if we don’t have standards, if we aren’t going to hold people to their words, then what do we really have? Suppose I said; “I predict a major 20% to 30% drop in the S&P500 within the next 4 years. And if it doesn’t happen, but happens sometime later, I should still get credit.” Would you take me seriously? People don’t seem to understand that unless a prediction is both accurate and timely, it really isn’t of much value.

I would phrase this differently. I would say that the timeliness of a prediction is part of its accuracy.

If I predicted every year from 1919 through 2004 that the Boston Red Sox would win the World Series, should anyone give me credit for a successful prediction in 2004 despite being wrong in each and every other year?

The answer, of course, is that it depends. If my predictions were based on an objective model with independently demonstrated accuracy, then, yes, I should be given credit. Of course, this is an extremely unlikely scenario, since we would probably never be able to identify a model that fails in a such a spectacular fashion as this one as actually being accurate. Nevertheless, it's the process that's important, not the results, because the process is what we can control ex ante. If I am known to have the correct (or most correct, given available information) prediction process, then the results don't matter; I have made the best prediction I could.*

On the other hand, if my predictions are unsystematic and wildly subjective, then I should be vigorously laughed at for making such predictions. I should receive no credit for a successful prediction in 2004. As the saying goes, "Even a stopped clock tells the right time twice a day." We don't give the stopped clock any credit for this.

I think most people know this intuitively, but I think a couple things happen that cause people to take unsystematic predictions more seriously than they ought to:

1. We have a cognitive bias that causes us to remember successful predictions more often than unsuccessful predictions. Unsuccessful predictions are everywhere. Successful predictions, especially successful predictions of really spectacular events, stand out to us. We then grant undue expert status to the successful predictor causing us to overweight his analysis in the future.
2. We are fooled into perceiving patterns and systems where none exist, giving us the illusion that we are operating systematically. For example, there were people who argued that the Yankees would never win a World Series with Alex Rodriguez for any number of reasons. Most if not all of the reasoning in these predictions involved extrapolating from small sets of data to proclaim large significant patterns. We see how well that worked out.

So you have to have a system, but you also have to let the system speak for itself. You can't say, "Well, I predicted the Red Sox would win sometime between 2000 and 2003, but they won in 2004... hey, I was pretty close!" If your system did not predict this, then you cannot call it a success because your system provided no useful information ex ante.

It's important to keep all of this in mind when you hear experts going on and on making wild predictions, whether those predictions are about baseball or economics. We must insist that we operate with in an objective, systematic framework or we will find ourselves falling victim to a whole host of epistemological charlatans and stopped clocks.

* Of course, the best way to evaluate or process is by the results it produces. A process that consistently produces poor results must eventually be rejected. The key is that any one outcome of a process is not sufficient evidence. We must have a large sample of unbiased outcomes before we can make a correct determination on the efficacy of a particular process.

**EDIT** See also: Robin Hanson. He's talking about economics, but the lessons are applicable everywhere.

Let's talk some baseball

I'm starting to get my baseball juices flowing again. So here's some notes on some stuff that happened at some point in the past month or three:

• The Hall of Fame gained a new member: Andre Dawson. I probably would not have voted for Dawson. Indeed, I've written against his candidacy in the past. Still, it isn't an atrocious choice. Nonetheless, the most positive development of this year's voting is that Bert Blyleven is now only five votes shy of enshrinement. It's highly likely he'll make it in next year and pass the title of "Most Clearly Deserving Player Not In The Hall of Fame" to someone else.
• Mark McGwire admitted to using steroids during his career. I wish Mark would have said this to Congress five years ago. I don't know why he felt he could not. Nonetheless, his statement is one of the better ones you'll read on the subject, keeping in mind all of the problems that plague these sort of things. Even though it's been suspected for a long time that he used, it was good to see him come forward more or less of his own volition. See also: Rob Neyer's take on the situation.
• The Yankees traded for Curtis Granderson. There's not much to say: in short, it was, in baseball terms, a good deal for New York, though the nature of it did prolong my apathy by a few more days. I have two essentially incompatible wishes: for the Yankees to win a gazillion World Series and for them to do it with a ton of homegrown players. And since the latter wish is dependent on the former, they might as well do their best at winning as many World Series as they can and let my feelings on the nature of their victories sort themselves out.
• Ditto for Javier Vazquez, though I will root harder for him than Granderson, given his shoddy treatment in New York the first time around.
• There are only thirty-seven days until Christmas in February. I cannot even begin to tell you how much I'm looking forward to watching a baseball game with no implications other than the sublime meaning in taking the extra base, turning a double play, hitting a triple into the gap, painting the corner with wicked curveball, drinking an extra beer, putting Stadium Mustard on a grilled Kosher hot dog, and doing nothing all weekend but basking in baseball, glorious baseball.

A world without Ernie Harwell is a worse world...

...so we should probably start steeling ourselves for it. In the meantime, here's yet more evidence, if in puff piece form, of how awesome Ernie really is.

The Colts suck

Apologies for another football post, but...

This.

I'm sick and tired of the idea that somehow winning the Super Bowl is so important that a team would risk an undefeated season for the smallest hint of an improvement in their chances of winning one. Have these people gone totally crazy?

Why play sports? Why compete? If you're any kind of athlete it's for one reason: because you love the competition itself. It's the striving to be the best, the greatest, the undisputed champions that makes the competition great. No one plays a sport with the opportunity to become an alright player. No one plays a sport to go 9-7 or 84-78. What Olympic sprinter dreams of setting the second fastest time in the history of the world?

No athlete does this. Not one. Not even the scrub wide receiver on a Class D high school football team who only got to play because the team was too small to cut anyone (trust me).

So why, why, why do professional football teams insist that winning a single season championship is worth more than being able to say that you accomplished THE GREATEST ACHIEVEMENT IN THE HISTORY OF YOUR SPORT?!?!?!??! It's absolute madness.

I just cannot get over this. A Super Bowl title is given out, well, every single year. Yeah, it's great. Yes, you strive to win one. Yes, it's every team's ultimate goal, but only because going undefeated and winning it all is so damn hard that teams don't even consider it realistic enough to make it a goal in the first place! It's like saying, "Man, my goal was to save up my money and buy a Cadillac, so I guess I'll turn down this chance to own the freaking Batmobile." Why blow it when you have the chance?

And to blow it for almost nothing! The advantage you get by resting your best players, if it even exists, is nearly infinitesimal. Yes, they might have gotten hurt, but the odds of that happening are stunningly long. And if they did, where's the shame in getting up to the podium and saying, "You know what? We had a shot at immortality, at accomplishing the ultimate feat in our sport, at being the best there ever was, and we took it. It didn't work out. But we played our best every minute of every game this year and we can walk away from this knowing that we didn't leave anything on the table."

If there is such a thing as football justice, the Colts will lose in the first round. We have simply got to start the meme that resting your players and punting on undefeated seasons hurts your football karma, because if we ever needed a good bout of irrationality, getting professional teams to actually try to reach the true pinnacle of their sport would be a good place to start.

This is a shitty, shitty day for sports fans. The Colts ought to be ashamed of themselves.

Baseball apathy

So I found myself in a very weird place a month and a half ago: I suddenly found myself not that interested in baseball. I haven't been to this place in over a decade. In fact, I haven't been there since I started caring about sports in general, sometime in middle school.

But more strange and more troubling than just my general nonchalance vis-à-vis baseball was the fact that the event that triggered this creeping malaise was my favorite team winning the World Series.

This is not how it's supposed to be. Apathy is not the reaction sought for by one who invests so much emotionally in something as unimportant as baseball. Indeed, the realization that I was not super excited about his development disconcerted me greatly. What the hell is wrong with me? I've been asking myself that question for weeks now.

It's not as though I don't care greatly about the success of the New York Yankees. If you've read this blog, or watched a Yankee game with me, or needled me about the Red Sox, you know this isn't true. Indeed, I even had an email conversation with a friend in the last year in which I admitted that the first three things that came to mind as things for which I would trade time off my life were all Yankee-related events (specifically: winning the 2001 World Series, winning the 2004 ALCS, and getting Mike Mussina his 27th out).

Furthermore, there were times during this postseason when I was literally sick to my stomach because of the tension. I enjoyed the whole postseason thoroughly. Why didn't I get the emotional payoff I expected?

The first thing that occurred to me was that my predominant immediate reaction to the Yankee win was relief. Relief that we didn't blow the Series; relief that we had vindicated our position as the best team in baseball; relief that A-Rod and CC had put those inane monkeys on their backs to rest. I think that this relief was in part due to the nature of the final game (it wasn't close) and in part due to the nature of the Yankees' season as a whole (again, it wasn't close). By the time it was over, it was so blatantly obvious that the Yankees were the best team in baseball that winning the World Series was almost the thing that they had to do so that they wouldn't embarrass themselves. Actually winning was practically anticlimactic, especially given the nature of the final game.

Then there was the timing of the Yankee World Series "drought:" it lasted exactly as long as Mike Mussina's tenure as a New York Yankee. No more. No less. This was and is absolutely maddening to me, because even though I know it's just random, it still seems so cosmically unfair. This ground on me for days after the World Series win.

The Yankee victory also meant the end of baseball for 2009. That's a depressing thought, even if the Yankees went out the best way possible. It also meant that I would now have to hear about how my team "bought" a World Series and (worse) that I would have to admit to myself that the accusation was essentially true.

I've spent so much time preaching about how there's no moral component to baseball, no higher power at work directing the fates of the players, no overarching story waiting to be told, no reason why our guys "deserved" to win or had more "heart" or "wanted it more" that when my guys actually win I can't self-assuredly pat myself on the back about how awesome I am for rooting for "the good guys."

None of which is to say that I wasn't happy when they won. I was. Nor is it to say that I haven't experienced the delirium of winning a World Championship recently: I was ecstatic for weeks when the Giants beat the Patriots.

So why? Why did I react the way I did to the 2009 New York Yankees' World Championship? Why did I sit on the edge of my seat all throughout October if not for this? Why did I follow the Yankees day in and day out all year if not for this? What the hell was I expecting to happen?

I don't know. I don't think I'm ever gonna know. And that's the trouble. I've spent weeks dwelling on this and I don't have an answer.

And so that's how I found myself in this place of not caring about baseball. Indeed, I've almost dreaded baseball news because it reminds me of the weird place I'm in.

I have thoughts on the Yankees offseason, but I'm gonna save them for another time, a time, hopefully, when I will actually care.