In the accompanying article, for example, Oklahoma State management science associate professor Rick Wilson's crunched numbers give the nod to Penn State (with one caveat). Wilson is far from alone in naming the Nittany Lions No. 1. The New York Times and Jeff Sagarin (published in USA Today) both rated Penn State over Nebraska, and both employed statistical methods in their analysis.
Hal Stern, an associate professor in the Department of Statistics at Iowa State University, puts in yet another statistically based vote for the Nittany Lions in his paper, "Who's Number 1 in College Football?. . .; And How Might We Decide?" The paper appears in a recent issue of Chance [Vol. 8, No. 3, 1995], the magazine of the American Statistical Association.
It is interesting to note that Stern and Wilson take different roads but arrive at essentially the same conclusion: Penn State on top. Wilson takes a neural net approach; Stern uses the statistical idea of least squares. Wilson makes it clear that his model is not intended as a prediction tool; Stern says the difference between the least squares ratings of two teams is an estimate of the number of points by which one team should beat the other at a neutral site. Penn State is No. 1 in Stern's book by a wide margin (and beats Nebraska by five points in a hypothetical game); Wilson's analysis gives a slight edge to the Nittany Lions, but details at least one scenario in which Nebraska edges Penn State out of the No. 1 spot.
There are a number of philosophical similarities between the two approaches. Both models reward teams handsomely for playing difficult schedules. Both models attempt to minimize the effect of blow-out victories against weak opponents. The same can't be said for human pollsters who apparently reward teams for running up the score and penalize them for not winning by big enough margins.
Last season, for example, Penn State was No. 1 in both "human" polls until midway through the season when the Nittany Lions played Indiana. Ahead by three touchdowns in the fourth quarter, Penn State Coach Joe Paterno called off the dogs and put in his second string whereupon Indiana scored two meaningless touchdowns to make the final score more respectable. Meanwhile, Nebraska cruised to another lopsided win. The Cornhuskers passed Penn State in the polls that week and never looked back. Judging from the huge numbers run up during the early part of the current season, the top-10 teams learned a lesson: don't let up, it could cost you in the polls.
Computers may not be swayed by 50-point wins over terrible teams, but former TIMS President Don Morrison reminds us that computerized ratings are still subject to biases. The difference is, the computerized biases are known, the human biases are not.
"These computerized ratings explicitly state what their objective function is," says Morrison, a professor at the Anderson Graduate School of Management at UCLA and UCLA's faculty athletics representative. "They tell you, `This is how is how I'm going to value certain victories.' The rankings you get are consistent with the objective functions. If you agree with the objective functions, you buy into the rankings.
"With the coaches and sportswriters polls, it's unclear what the objective function is. You have multiple voters with different objective functions. You end up with something that is hard to interpret.
"The point is, there is no such thing as a biased-free, objective rating system," continues Morrison, co-editor of a special issue of Management Science some years ago that dealt with the mathematics of sports. "It depends on what variables you use, how you scale them and how you weight them. Some count a win as a win. Some count the margin of victory. Some count the quality of the opposition. What you do late in a season vs. early in the season. All of these things, whether you call it neutral networks, least squares or whatever, have some objective function that is inherently subjective."
The least squares and neural net models produce their share of quirks. A 7-5 Illinois team finishes seventh in Stern's unmodified ratings, 10 places ahead of an undefeated Texas A&M squad. An unheralded Bowling Green squad, which didn't show up on any one's ranking radar, finishes a lofty 16th in one Wilson scenario, well ahead of Pac-10 champion Oregon. Some college football fans may have trouble digesting the idea that Nebraska's 49-point win over Pacific actually cost the Huskers the neutral net national title - not because the margin of victory wasn't impressive, but because the game was even played.
Explains Wilson: "Basically, a team IS penalized for playing poor teams - there is really no way around this. If a team is rewarded for playing and defeating good teams, a corollary of this is that a team is NOT rewarded, i.e., penalized, for playing and defeating (poor) teams. Is this really fair to the teams, since schedules are made long in advance? Maybe not, but the only objective information that one can go on is game result and opponent strength."
There is one point on which all parties seem to agree: the best way to determine college football championships is on the field, not via polls or computers.
- Peter Horner