WAR! What Is it Good For? (And How Much Is it Worth?)

Howdy, y'all.

I hope you will forgive the rushed nature of this post, but I find myself with a bare amount of time in which to try and compose something. My apologies.

You know, I was in my automocar yesterday afternoon, flying across the alkali flats of Fenton, when a particular ad came on the radio. The ad in question is, I suppose, more of a public service announcement than a proper advertisement, warning against the dangers of buzzed driving. (Apparently it is the same as drunk driving, according to the Ad Council.) Anyhow, there's a pair of young women driving home from a party of some sort, partially inebriated. They're joking about the lame pickup lines guys at the party tried on them, giggling merrily, when suddenly the sounds of screams and crashing kicks in.

After the apparent crash, the girl driving asks her friend if she's alright, and the other girl starts crying and moaning about her broken arm. The driver gives her the, "I was only a little buzzed," defense, at which point the passenger decides she much be alright, then, cheers up, and apparently resets her arm. Of course, it doesn't last, the girl rebreaks her arm and starts wailing away, everyone winces at the sound effect and feels bad for the injured party, and the tagline comes in about not driving buzzed. It's a fairly effective spot, and the voice actor playing the injured girl does an especially nice job conveying both pain and panic.

There's only one problem with the spot, at least for me. The passenger who gets injured is name Becky, and when the crash occurs the driver turns to her and says, "Oh my god, Becky. Are you all right?"

Here's the problem: when she says those first four words, "Oh my god Becky," I actually experience this Pavlovian response mechanism and my brain immediately follows those words with, "Look at her butt." Of course, once that happens the rest of the song kicks in and the message of the PSA is completely lost in my adolescent giggles. While the voice actress playing Becky is vamping her heart out telling the world how much her arm hurts, I'm thinking of the circumstances under which my anaconda (shout out to Roy Halladay), don't want none and missing the point by a fairly large margin. It negatively impacts the effectiveness of the spot for me.

Does anyone else have this problem?

All through the offseason, more than I can ever remember before, there's been a lot of discussion about player value centered around WAR. You know, such and such is worth X amount of wins, wins are valued at Y dollars apiece, ergo the player in question is worth Z per season and his contract is a good or bad one.

This has gotten me to thinking, and since I'm short on time and ideas today I thought I would throw this out there. I understand the concept behind the cost of adding marginal wins. In a given year, teams spend so much per win across baseball. The number takes into account good contracts, bad contracts, and those that come in right at market value. It's not a perfect way to look at valuation, but it's certainly good enough for those quick back of the envelope calculations we all do when we see what a given player got.

But I've been thinking lately that this method of player valuation really underrates great players and overrates mediocre ones. We know that not all wins are valued equally; i.e. there's a certain spot on the quality curve where it's very cost-effective to buy wins and other places on the curve where the cost is too high for the benefit gained. But we sort of accept that players are valued very linearly, when I don't know that's a very good way to look at it.

Say for the sake of ease that a win this year will be 'worth' $5 million. That means a player posting 1.0 WAR should be worth $5 million, while a player posting 3.0 WAR should be earning $15 million on the open market. It makes sense, right? You expect to spend $5 million per win on the open market, the player worth three wins is worth thrice as many wins as the first guy. Simple equation.

Here's my problem, though: there are certain advantages gained with a player worth a large number of wins on his own, largely in the form of the smaller percentage of the roster he takes up. There's also a problem of scarcity, in that players worth five wins simply aren't as available as one win players and thus represent a much more in-demand commodity, driving up the relative price.

Ignoring the scarcity aspect for a moment, think of the roster bit this way: say you have five players, all worth 2.0 WAR. League-average players, in other words. Now, on the other hand, consider a pair of 5.0 WAR players in place of those first five hypothetical guys. In the first example, you have 20% of your roster producing 10 wins. That leaves you with 80% of your total roster space to add additional quality. In the second roster example, you have just 8% of your total roster producing those same 10 wins. Simple subtraction, you still have 92% of your roster left to try and add wins to your team. Given that the size of MLB rosters has a concrete limit, there's an opportunity cost to taking up more roster spots to add a similar amount of value. In the more balanced roster posited above, you simply have fewer opportunities left on the roster to improve the team than in the top-heavy model.

Given the value of concentrating quality into fewer roster spots in terms of an opportunity cost, I wonder if players shouldn't really be valued in a linear fashion, but rather exponentially. In other words, as we look at it now, we know a 4.0 WAR player is twice as valuable as a 2.0 WAR player. What I'm suggesting, though is that such a viewpoint undervalues the four win player due to the extra roster spot necessary to equal the value that single player provides. In other words, while we know a player worth four wins is going to produce twice as much value as the two-win guy, the four-win player is actually worth more than twice as much as his league average counterpart and should be valued as such.

There's an issue of scarcity here, too, in that the higher you move up the wins-per-season ladder the more difficult players are to find. A guy worth 6.0 WAR is so much more rare than one worth, say, 3.0 WAR that, again, I think those extra wins should actually be valued more highly than the wins the lesser player provides.

That scarcity works in reverse, as well, of course. Players worth one win are common enough -- and add little enough value relative to the amount of roster space they occupy -- that they shouldn't get full credit for that single win they add. Both the 6.0 win player and the 1.0 win players take up the same 4% of the roster; the excess value provide by the better player shouldn't be subject to the same linear calculation as the below-average production from the other player is.

There is another side to this, in that the potential downside of receiving the bulk of your production adds to the possibility of catastrophic failure due to injury or simple poor play. If your 2.0 league-average guy gets hurt or just falls off a cliff, you're talking about a much smaller percentage of your overall production down the tubes for the season than if your 5.0 WAR staff ace goes down with Tommy John surgery in spring training. (Not that that has ever happened, of course.) Concentrating the value also concentrates the risk, much like a stock portfolio built on just a handful of high-growth holdings. So there is definitely a point against my thought that high-end players are worth exponentially more than lower value players.

Even so, given the larger risk of losing a huge amount of production in one fell swoop, I still think on balance the concrete dollar amount per win method of player valuation tends to underrate those players capable of producing a large amount of value from a smaller percentage of the roster. You should never, ever pay anything beyond league minimum for replacement level, but then the first win above that is immediately worth just as much as the win value a given player produces above, say, league-average level. I tend to think that's overvaluing a relatively commonplace commodity, while undervaluing a significantly less common one.

Then again, perhaps the market already corrects for this and I just don't realise it. After all, there are plenty of one- to two-win players who sign for peanuts in any given year due to health concerns or just the simple crunch of needing a job as spring training approaches. There are people on other boards I've seen scoffing at Edwin Jackson's current contract demands, when his career performance record suggests he will be worth what he's asking in all likelihood. The perception of him as enigmatic and perhaps a bit of an underachiever may very well drive his price down below what he'll be worth, in which case he would essentially serve as a balance against some other contract which overvalues a mediocre player.

I also worry I'm conflating two somewhat unrelated ideas in that the market value for a win is determined by what teams across the game spend in a given year, while player salaries and valuation are much more subject to individual vagaries. Perhaps directly equating the value of a player to what the market says his production is worth in a given season is a mistaken premise from which to start. Still, it's something that's been kicking around in my head recently due to the thrust of so much of our offseason discussions and I thought it would be suitable for a quick (though not so quick now; looking at the word count below this I've rambled on far, far longer than I had planned on), Wednesday discussion thread.

In the end, I'm not really arguing for paying more per win; rather, I wonder -- though in a rather vague sort of way -- if the first win or two worth of value you receive from a player shouldn't be much less valuable than what we think, while those wins you receive from players like Matt Holliday or, dare I say it, Albert Pujols should be placed on a sliding scale, with the fifth and sixth wins worth far more than what we give credit for.

So this is my question to you: do you feel like a linear style of player valuation, in which a player worth five wins is worth exactly five times as much as a player worth one win, is the most accurate and useful method? Or do you feel an exponential valuation, in which higher-quality players are worth more per win beyond a certain number would be more reflective of how valuable said players actually are?

Feel free to tell me I'm way off base here; I'm no economist and there's a whole lot of stuff going on here that probably makes my initial hypothesis a poor starting point. But it's January, there is no new news, and I wasn't quite ready to start on my draft reports for 2012 yet. (I'll likely start those either next week or the week after, mid-ish January seems to be about the time I need to start to get a solid number of them done.) So here is this rather long but poorly thought-out post for you to consider and perhaps argue over.

Have a nice Wednesday, and I shall see you all again next week. Take care.