What does (should) it mean to be crowned "National Champion"?

There is much debate now whether Utah or Texas ought to share in the college National Championship in some way, though it is unlikely that they actually will). From the WSJ's Daily Fix:

[I]n an open letter to the 72 members of the media who choose the Associated Press No. 1, the Washington Post’s John Feinstein makes a strong case for them to place undefeated Utah at the top of their ballot.

“The reason to vote for Utah is simple: This is the one and only way you can stand up to the BCS bullies — the university presidents, commissioners, athletic directors and the TV networks who enable them — and, to renew a catch phrase, just say no,” Feinstein argues. “Say no to this horrible, hypocritical, feed-the-big-boys system. Say no to the idea that fair competition doesn’t matter. Say no to all the hype surrounding the power conferences and power teams. To co-opt yet another catch phrase, say yes to change.”

Feinstein isn’t the only one who thinks Utah didn’t get a fair shake at the national championship. Yahoo Sports’ Dan Wetzel agrees, pointing out that some voters in the Harris Interactive poll, which determines the title-game participants, admit they didn’t see the Utes play at all this season. “Even by the absurd standards of the BCS, having voters not bother to watch an undefeated team play a single game is a new low,” Wetzel writes. “Whether Utah deserved to be ranked No. 1, 2 or 25 isn’t the point of this argument. The Utes deserved to have voters at least see them.”

But not all agree:

Gregg Doyel disagrees that Utah deserves to be No. 1. “People, please. Utah is the same team that beat Michigan 25-23. Michigan went 3-9 this season,” he writes at CBS Sports. “Utah is the same team that beat Air Force 30-23. Air Force went 8-5. Utah beat Weber State 37-21. Weber State isn’t even in Division I. Utah beat New Mexico 13-10. New Mexico went 4-8.”

I'm not sure if, given a vote, I would vote Utah #1, but Doyel's argument seems bizarre to me. There's a lot of weaknesses with arguing that, because, say, USC beat the Citadel by 20, while Ohio State only beat then by 10, then USC is better. And his argument is just a series of those assertions. I mean, that kind of thing happens all the time and no one believes those predictions because they are entirely unhelpful. All the time one team gets blown out only to turn around and beat a team that blew out the team that originally beat them. Some teams just match up differently; football teams are complex, and some just match up with others better. To paraphrase Herm Edwards, it's about who won. Nevertheless, we saw some of this reasoning this year with Oklahoma and Texas, where Texas's win over Oklahoma eventually counted for less than the subjective impressiveness of Oklahoma's victories down the stretch.

But, more fundamentally, all this made me wonder what the designation "National Champion" is supposed to capture, anyway. The baseline that everyone -- including the President-elect -- seems to push for is a playoff. So we can use that to ask about each view.

Doyel's argument seems to be that Utah doesn't deserve to be #1 because -- "People, please" -- you wouldn't really expect them to beat Texas, OU, or Florida, right? I mean, just look at all their bare victories over mediocre or mid-level teams. In other words, one could phrase the Doyel view as the "National Champion" is the team that you think is the absolute best team in the sense that, were they to be matched up against any other team in the country, they would always be favored to win.

That can't be right, though. That's not at all what a single-elimination playoff gives you. Had the 2007 Giants played the 2007 Patriots the week following the Giants' Super Bowl win, would Eli and Co. suddenly have become the favorite? I think not. In March Madness, with teams playing every couple of days, do we really think that the better team always wins each game? No, and that's kind of the point of a playoff.

Indeed, series-based playoff systems, like with MLB or the NBA, are presumably based on the very idea that one-game is not enough to determine the best team. So, if we still think the playoff is the best solution, then it makes no sense to say that Utah can't be the National Champion just because you think the other teams might actually be better overall. Though, if you subscribe to the Doyel view of "National Champion," then the BCS probably does a better job for you than a playoff would, because the system is all about crowning the perceived best overall team. Although it lacks the precision of a playoff, it gives you fudge-factors so that Florida's and Oklahoma's (though not Texas's) losses can be overlooked.

So, maybe instead of crowning as National Champion the best team in absolute terms, that distinction is a reward for having the best overall season. I don't really watch racing, but that seems to be what they go for with their points system. And many BCS defenders say that it makes "every week a playoff," so the best overall season gets rewarded (let's just pretend like that is true). Well, a playoff doesn't give you that either: Exhibit A - the 2007 New England Patriots. They played unbelievably all year, blew everyone out, and then lost. No one -- not even them -- tried to argue that they should get a share of the Super Bowl via media vote or whatnot.

And that sort of thing happens all the time in playoff systems. It seems like a lot of the recent Super Bowl winners haven't been that great overall, or certainly were not considered the best teams going into the playoffs. Even when the Colts won the Super Bowl, it was with arguably their worst team in something like four or five years. Luck and circumstance play a huge factor, and again, the playoffs are decided by single, permanently binding, contests.

So what does a playoff give you, and why is it probably a better solution for crowning a National Champion? Let me say first that I think it would be a better system than the current BCS morass. But the advantage the playoff gives you is not anything metaphysically correct. It probably does not crown the best team. And it does not reward the best season (sorry Utah).

It merely gives you relative certitude. It's not perfect -- some clunker teams can be crowned, some historically great teams will get the relative shaft -- but, before the season, during the season, and in the playoffs, everyone knows what it takes to be the champion: you must get into the playoffs, and you must win every game once you're there. The Patriots couldn't lobby for votes, they couldn't say that they got jerked around, and they even couldn't say that they didn't get their chance. They played and they lost. They were probably better, they might only have had a bad day, but hey, you knew what you were getting into.

Which is really the issue here. No one has any idea what being "National Champion" ought to mean -- especially in college football where you have over a hundred D-1 programs and no team can come close to playing all the others. A playoff would simply lay some ground rules people could follow. As it stands, without a playoff, everyone may mount their high horse and argue past each other.

Update: Rocky Top Talk and the good Senator both weigh in on this issue. And Bill James says that all self-respecting statiscians should boycott the BCS, because the computer side of the BCS is irrational, incomprehensible, and, worse still, used only to justify the coaches poll: "Throughout the 11 years of the BCS, whenever the 'computer' rankings have diverged markedly from the polls, the consensus reaction has been, we have to do something about those computers. And they have; whenever the computer rankings don't jibe with the 'human polls,' they fix the computers."