Sports Philosophy II
(Part 1 of a 3-part series, time permitting)
Ultimately, the goal of any sport is to determine who the best team is. Now, of course, the question of what the "best" team is a difficult philosophical nut to crack in the first place, and often you'll see heated arguments on this subject when the participants don't even agree on the fundamental goals they're trying to prove. So I'll try to tackle the question of what makes a better team from several different angles. In the scientist's way, I'll start out with a deliberately simplified model.
Consider three teams (which, for lack of imagination, I'll call A, B, and C). They play a round robin, at the end of which each team is 1-1. This is the classic Circle of Death you'll see in quizbowl tournaments all the time. To make the example a little more fleshed-out, add, say, five more teams which always lose to A, B, and C, so we have a eight-team division with three teams at 6-1 and three teams at 2-5. Now, let's make an assumption that these results fairly reflect the quality of the three teams. This is arguably not a safe assumption, but we're not going to get interesting results without dong something, so we'll make it. And I can certainly think of quizbowl tournaments where this would be an accurate thing to say. Okay, now it's pretty obvious that we can say that A, B, and C are of the same intrinsic quality (assuming that it's meaningful to speak of an "intrinsic quality" in the first place; again, without making this assumption we're not going to get very far, so I'm just going to say it and move on).
Now, let's conduct a little gedanken experiment. Suppose team C's bus gets stuck in snow, or they forfeit all of their games due to their star player accepting throwback jerseys, or something else happens to take them out of the picture. All of a sudden, we have a pretty surprising result: team A is now 6-0 and team B is 5-1, so pretty much anyone sane would say that team A has done better than team B, despite the fact that our assumption that their intrinsic qualities are the same still holds.
All right, this might seem a little excessively contrived, but let's add another little wrench into the gedanken experiment. Let's say team A suffers a loss to team F somewhere along the line, so now team A and B are both 5-1. Now, we've made team A worse than its previous baseline, so if our previous assumption still holds true (and I sure haven't done anything to change it), then team B's intrinsic ability is actually a little better than team A. And yet, based on the fact that team A has beaten team B head-to-head, you'd see most people agree that team A is the better one.
At this point, I suppose you're going to say that this experiment is arguably a little silly. And so it is -- after all, just because our mythical team C exists in this case doesn't mean that we can always add a mythical team C to any given setup like the one above. Nevertheless, I think this serves to illustrate a broader point: many people, given two teams with equal records, will value a "good" win over a "bad" win, especially in the case of a head-to-head tiebreaker. But the team who loses the head-to-head tiebreaker has suffered a "better" loss than the other team, by definition. Why should we believe there's any a priori reason that a "good" win plus a "bad" loss is somehow indicative of a stronger team quality than a "bad" win plus a "good" loss?
This is not to say I oppose looking at indicators like strength of schedule -- in fact, I think it's something all-too-frequently overlooked (I'll talk about this more in the next part). But unfortunately, a lot of the time, strength of schedule is used by boosters of a particular team who will say things like, "Well, our team beat X, Y, and Z, and they're all good teams, so that must mean they're good!" while completely overlooking that the team also lost to J, K, and L, which were pretty bad teams. There are two sides to every coin, and if a good win is accompanied by a bad loss, then there's no basis to judge it better than a good loss and a bad win (in the absence of other information, of course). Trying to get further rankings out of this basis is merely trying to get something from nothing, and is essentially circular reasoning.
In the next part, I'll try to actually accomplish something productive.