Monday, September 12, 2011

Theories of value

By Jason Wojciechowski

To begin

The passing of September 1 in baseball is like hitting Thanksgiving in the real world. Christmas sales, holiday music in the department stores, and making lists for Santa are sanctioned the second we stop stuffing ourselves with turkey while the Lions lose on TV. In baseball, we've been talking about awards all year, tracking who's in the lead both by the stats and the narrative, but come the expansion of rosters, the awards talk gains legitimacy. Starters only have a handful of chances to improve their standing and position players have their last shot at a 20-RBI month that'll impress the 73-year-old beat writer 2000 miles away.

My last post here proposed a new award system, but that's fantasy-land. I'll still be giving you my Willie Mays Award winners come the end of the year, but I know that's not what everyone else will be thinking about. Instead, the real Most Valuable Player trophy is at stake. As ever, then, the baseball commentariat has created a grand foofaraw over the meaning of "valuable." Some think the MVP can only come from a winning team in contention for the playoffs. Others believe that an individual's work must be taken as far out of his team's context as sabermetricians can manage before his "value" can be properly determined. This debate has often broken down on old-school vs. new-school lines, though that's hardly black-and-white -- Andre Dawson won in 1987 for a bad Cubs team long before internet baseball nerds had any sway, and Steve Slowinski recently wrote at Fangraphs that valuing the work of players on contenders more highly than equivalent work on bad teams actually makes sense.

We'd all be a lot better off, I've come to believe, if we weren't quite so quick to jump down each other's throats about what "value" means, pretending that there's only one sensible definition and that it's somehow inherent in the world "value" and instead tightened up our individual understandings of value into something intellectually defensible that does not serve as a mere post-hoc rationale for our favored candidate. This would leave us more time to focus on what our theory of value leads us to in terms of which player deserves the award.

I think we can identify two reasonable definitions of player value for the purpose of awards, as well as two not-crazy definitions that simply aren't workable. None of the following four theories of value are, I believe, subject to attack on the grounds that they have no intellectually honest grounding in language or baseball.


Taking the extreme view that every baseball team is a business and every player merely an asset to be exploited, we could given the MVP award to the player responsible for the most revenue generated for his employer. Call this theory REVENUE+. It has the advantage of reflecting some part of the reality of how baseball teams go about choosing their players. Still, there are at least three major stumbling blocks.

First, REVENUE+ is just not fun. Who wants to acknowledge that baseball is a business, that the efforts of the players on the field are, in significant fashion, merely counted like poker chips by the Lords of the Realm?

Second, REVENUE+ is impractical. Baseball's books are closed, so figuring out jersey sales, team estimates for additional park revenue and TV ratings generated by certain players (or by additional wins generated by those players) is probably close enough to impossible that it's not worth the effort. We could develop proxies and guesses, but those would probably just come down to how many wins a player generated with a fudge factor for popularity. Since we're trying to lock down theories of value that allow principled decisions on awards, not more groundless arguments with little in the way of fact supporting them, this theory fails, though, notably, not for reasons inherent in the underlying theory itself.

Finally, a Yankee would win every year.


Were the MVP not explicitly a regular season award ("Only regular-season performances are to be taken into consideration."), we could use CHAMPIONSHIP+ as our theory of value. What, after all, is supposed to be the goal of every team in baseball but maximizing the number of World Series banners it gets to hang in its home park?

This is an idealized world, of course, one in which there are no Pohlad Twins or Pretty Much Any Period of Time Ever A's taking the low-cost approach to making money at the expense of making full efforts for rings. Still, on the grounds, as mentioned above, that fun is an important consideration in determining how we're going to vote on awards, I think we could dismiss the revenue-sharing hogs from our mind were it not for the pesky requirement that the post-season not be considered.

Without being allowed to consider actual post-season exploits, those who want to use CHAMPIONSHIP+ would be stuck giving theoretical extra-credit for players who are most important in a post-season, like the relief pitchers who preserve wins in the tighter confines of playoff run differentials or the top-line starting pitchers who, due to off-days, start a higher percentage of their teams' games in the playoffs than normal. We'd want to quantify how important those kinds of players typically were and then somehow figure out a way to apportion some expected value to players of that type.

All of this seems rather fantastical, especially given that many dislike using FIP to determine pitcher WAR (as Fangraphs does) on the grounds that it describes what should have happened, not what did happen. (I don't think this view is accurate, but that's neither here nor there -- the point is that, for dealing with award-voting, fans don't seem to be a big fan of theories of value that carry a whiff of speculative fiction.)


Finally into the realm of the plausible, the theory of value that seems to be most popular among the internet baseball nerd crowd could be called WINS+. It is straight-forward: which player's actions on the baseball field resulted in the most wins for his team, without respect for the questions of whether that team made the playoffs, how much money the team made from those wins, or any other considerations outside of raw wins and losses?

Using WINS+ is not the same as simply making a list of your favorite WAR implementation and voting that way, though. There are all sorts of statistics that you might believe tell you about which player added wins to his team -- the various WARs on the internet, your own custom WAR, WPA as displayed at Fangraphs or Baseball-Reference, or, to some poor lost misguided souls, batting average or RBI. Your theory of value is a distinct inquiry from your method of arriving at value. Some fans might truly believe that the player with the highest batting average adds the most wins to his team. Those straw people are wrong, of course, but that doesn't mean their underlying theory of value is flawed, and when we seek to educate them on better ways of understanding player value, we should acknowledge that their theory of value is perfectly plausible.


The more controversial theory of value, of the two plausible possibilities, could be called PLAYOFFS+. As Steve Slowinski wrote in the article linked above, the marginal value of a win for a team on the cusp of the playoffs is greater than the marginal value of a win for a team in last place. (This sounds vaguely question-begging because I haven't defined what "marginal value" means for a team in this situation. I think it's fair to say that it's true whether the team values revenue (the playoffs are worth $$$), simply being in the playoffs, or winning a trophy (can't win it all unless you're in the tournament).)

There are a couple of ways that you could implement PLAYOFFS+. Of the four playoff teams in a league, you could take the team that came closest (in a final standings sense) to missing making the playoffs and award that team's best player the MVP. You could construct a curve assigning multipliers to certain win numbers and apply that curve to the individual win totals of the best player from each team. There are probably other ways I'm missing.

People who like WINS+ will rebel against PLAYOFFS+, perhaps on fairness grounds (Alex Rodriguez didn't put together those Rangers teams). Fans of bad teams will chafe at the fact that a team's 74th win might be given a multiplier of zero (no team makes the playoffs with 74 wins, so going from 73 to 74 has zero value in PLAYOFFS+) because the emotional difference for a fan between a mediocre team (74 wins) and a bad one (64 wins) is not insubstantial.

These, however, are reasons to personally prefer one theory of value over another. They do not expose the invalidity of PLAYOFFS+ as a theory -- they do not show that PLAYOFFS+ is unrelated to ideas of the word "valuable" that we experience in everyday life or baseball. Similarly, there are plenty of MVP arguments that profess to use PLAYOFFS+ but really are engaging in selecting reasoning for the sake of defending a favored candidate. Again, however, that does not make PLAYOFFS+ itself unusuable any more than writers misusing WAR counts as an argument against WAR itself.

You may not like PLAYOFFS+ (I don't, as a matter of fact), but I think it is important to identify it as a plausible and internally consistent foundation upon which an edifice for deciding who should win the MVP can be built.

In sum

When your friend argues that Jose Bautista or Matt Kemp shouldn't be MVP, don't dismiss him out of hand for foolishly listening to the Jon Heymans of the world. She might just have a different theory of value than you do, and as long as she's applying that theory consistently, you can save yourselves a lot of trouble by recognizing that.


Bill said...

I really like this piece, but I'm going to continue dismissing the ambiguously gendered Jon Heyman adherent out of hand. Because the problem isn't that that line of thinking is unrelated to a consistent theory of value; the problem is that that theory of value makes no sense in this context. There are certainly definitions of "value" and "valuable" which can be applied to make very-good-player-on-a-pennant-winner A more "valuable" than great-player-on-a-loser B, and I don't think that's ever really been the issue. (It's the PLAYOFFS+ crowd that's always saying "it's called the Most VALUABLE Player," as though that word means one definite thing.)

But. It's an individual award, meant to recognize individual accomplishments, and it's looked back on fifty or sixty years after the fact as a marker of a great individual season. So of all of the plausible definitions of the word "valuable," it simply makes no sense at all to apply the one that ties a player's "value" to things that are almost completely out of his control.

So I continue to think it's a position that can't be defended and, for the most part, deserves to be mocked. Just not because of the definition of the word "value" itself.

David said...

I suppose, except for the fact that, when taken to its logical conclusion, PLAYOFFS+ makes absolutely no sense whatsoever. First of all, an excellent player on an excellent team should never win the award. The 1975 Reds won their division by 20 games. Therefore, Joe Morgan's 12.0 WAR was meaningless. They still would have won the division, with or without him. Therefore, worthless. Second, and by the same token, Joe Foy's contribution to the 1967 Red Sox (to the tune of 1.0 WAR) was more valuable than Al Kaline and his 7.3 WAR - the Red Sox don't win the league without Foy, and Detroit finished one game out, which means no one from that team could possibly be "most valuable." This is so beyond absurd that it's unbelievable anyone would make such an argument. But the PLAYOFFS+ model supports it. Now, I actually don't have any problem with writers just picking a narrative and going with it, as long as there are numbers to support it. But pretending players from non-playoff teams have no value (at least when it comes to MVP voting) is ludicrous.

studes said...

A few thoughts:

I think taking Playoffs+ to its logical conclusion would involve Championship WPA, which we've used in the THT Annual the last couple of years. That shows how absurd the interpretation could get, but you don't have to take the idea to its logical conclusion. Playoffs+ can still make sense.

I might add: throw out WAR for MVP consideration. Who cares about replacement level for awards? Just measure what actually happened on the field. Replacement level makes a lot of sense for a lot of things, but it doesn't have to be used for everything.

I've got an idea: Story+. Which players provided the most inspirational story over an extended period of time? Consider stats, but don't get carried away with them. MVP is all about perception and fan interest. It isn't about stats.

Jason Wojciechowski said...

David, your argument is against a particular implementation of the PLAYOFFS+ theory, the one that assigns zero value to Kaline's contributions because his team managed to miss the playoffs by one game. This, however, isn't the only possible construction. The more nuanced one I mentioned in the following sentence would assign multipliers to Kaline's value based on the fact that he helped his team win games number ... 87, 88, 89, ... (or whatever win numbers the implementation came out requiring). I'm not sure that this less extreme model is so broken as to call into question PLAYOFFS+ entirely.

Also, and this is a failing on my part for not thinking of this, PLAYOFFS+ probably isn't nearly as compelling for the period of time you're talking about -- in 1967, there were twenty teams and just two of them got to play extra games, so "making the playoffs" is not even a phrase that necessarily makes sense applied to that context.

Studes, I'm not immediately repulsed by STORY+, but I think it could take a lot of the fun out of end-of-season arguments. If we acknowledge that it's all purely subjective, then we're just stuck in the same land we are about painting or movies or books. You like X, I like Y, we can articulate why that's so, but we're just explaining things to each other. We have no real hope of convincing each other. That (illusion of?) possibility of convincing someone else that you're right is what I think brings a lot of energy to an awards debate that can be rendered relatively objective.

I only hinted at it in the piece, but since Bill brought it up -- on the merits of the various theories, I'm WINS+ all the way. Win curves or no, my inner sense of justice doesn't let me ignore a great season just because a player (e.g.) plays for a crummy owner.

William Tasker - Caribou, ME said...

Interesting post and just as interesting comments. Don't have much to add to such elegant thinking.

The Baseball Idiot said...

Seems to me that 'valuable' is in the eye of the beholder, or in this case, the voter.

The guys who vote, all of them, have earned the right to do so, even if we don't agree with their decisions. There are over 500 of them.

If the majority of them decide the same way, that's enough of a sample size to satisfy me. I might disagree, but I don't get a vote.

McNair: I can't say I'm very fond of the United States of America as a name for a new country.
John Hancock: I don't care what you think. You don't have a vote. YOU'RE NOT A MEMBER OF CONGRESS.

Bill said...

There are only 30-32 who get to vote, though, on each individual award (two writers from the market of each team in the league). It's a pretty tiny sample. And you always get at least one or two (like the one Seattle writer who voted for Miguel Cabrera over Mauer in 2009) who do things that just tell you that they're either not paying attention or don't know what they're doing.

And the BBWAA at large is full of people who haven't written about baseball in decades, some who have never written about baseball, but were sports editors or something once upon a time and now draw political cartoons or edit science magazines or something. If you're going go throwing blind faith around, the BBWAA isn't a good place for it to land.

The Baseball Idiot said...

I agree with you Bill, but that's the system we have.

More people seem to be worried about the definition of the award than the actual process of how it is given out. Change the process, the definition will change also.

Until then, there isn't much we can do about it. If the government says, "would you like to pay more taxes, or a lot more taxes", you take the best avaialble option until you change the system of who determines the tax in the first place.