Friday, June 20, 2008

Simple Head-to-Head

An irate fan calls into the local sports talk radio station Monday evening so angry he can barely get the words out. Between the coughing, gagging, and spitting, he manages to say: “This is ridiculous. It’s nonsense. How can they rank the Cartersville Skunks #5 ahead of my Waynesboro Lemmings. The Lemmings beat the skunks 17-14 the third week of the season. The rankings are stupid. It’s simple head-to-head. Simple head-to-head. I’ve got nothing more to say.” Click.

Amazingly, there are more than a few fans who think they’ve got it all figured out. The problem is, they’ve never taken a pencil and tried to do what they insist makes so much sense – just rank the teams so that the winners in each game are ranked higher than the losers.

Funny thing is, early in the season this is still possible, and yet fans fuss at the rankings because they don’t want to believe that the few games played are actually representative of how good (or bad) their team is. However, by midseason, this kind of ranking is no longer possible. Sooner or later, team A beats team B who beats team C who beat team A. Or some team beats a 10-1 team and loses to a 1-10 team.

As geeks who do computer rankings, we do understand the frustration. In fact, in the “ranking community,” we even have a lingo to describe all this stuff – “retrodiction,” “ranking violations,” “ranking by pairwise comparison,” and the like.

Before you’re tempted to call your local sports talk radio program, let me offer up a slightly different way to assess a set of rankings. Suppose a team is 12-0 at the end of the season. It would be reasonable for them to be ranked somewhere above all twelve of their opponents. Another team goes 0-12. It would seem reasonable for them to be ranked somewhere below all twelve of their opponents. Consider another team that goes 6-6. Would it not seem reasonable for them to be ranked above six of their opponents and below six others? Here’s the catch. Would this not seem reasonable even if this team actually beat one or two of their higher ranked opponents while losing to one or two of their lower ranked opponents? After all, teams have good days and bad days. Upsets are what makes football exciting, right?

For what it’s worth, any decent ranking method will approximately do just this? Why not exactly this, you might ask? Well, consider this one example of why it can’t always be done. Suppose no one goes undefeated. Someone must still be ranked #1. Since they have one loss, they are ranked above a team to whom they lost.

There is another problem with this scheme. If a team goes 12-0 against a schedule that includes no top 25 opponents, exactly how high should they be ranked? Somewhere between #1 and their best opponent, but where?

The bottom line is that ranking football teams is a really hard problem. Probably harder than any other sport because the teams play so few games.

Back to the irate caller. He’s got it all figured out. We just move the Lemmings up to #4. Of course, the Lemmings lost to the 4-6 Hedgehogs, so we’ll have to move the Hedgehogs up to #3. But the Hedgehogs lost to six other teams, and we don’t have enough slots for them, so we’ll have to move the Hedgehogs, Lemmings, and Skunks down to make room. Wait, one of those teams was the Skunks. I thought this was SIMPLE head-to-head.

Thursday, June 19, 2008

On the Current BCS System

The current BCS system.  Exactly what is it?

I would characterize it as a two-team playoff system.  As such, it's better than the old pure poll-based system of days gone by (AP, UPI, etc.) where we never really knew who the national champion was, but it's not nearly as much fun as the playoffs enjoyed by the other divisions and associations (FCS, II, III, and NAIA).

So, as much as most FBS fans call for a "real" playoff system (i.e., four or more teams) and criticize the BCS in the same breath, I still think the BCS is a step in the right direction.  After all, a two-team playoff is better than no playoff at all.