Who
is #1
I was planning
not to write a column this week since most people were busy making noise
about the voting issue and no one is going to read this week's [SCIENCE
FOR EVERYONE] column. However, after watching Saturday's college football
games, I changed my mind and decided to write about FOOTBALL. I know that
many people are more interested in watching football games and reading
football news than reading [NOISE] on the computer. I hope this article
may relax some people and divert their minds away from the voting issue
for a while.
Last Saturday,
whenever I turned on the TV, I heard "Who is #1? Penn. State or Nebraska?",
even before the games. After these two teams have played and won impressively
over ranking opponents, the discussion on "Who is #1" appeared
more intense. So which team is really #1?
This morning,
I read in the newspaper that the Associated Press poll has given the #1
ranking to U. Nebraska while the USA Today-CNN coaches' poll gave Penn.
State U. the #1 ranking. Are these polls credible? Are the voters fair
and knowledgable? Which poll is the better one? If you are in the US and
went to a Big Ten school or a school in the East, you may think that Penn.
State deserve the #1 ranking and so the USA Today-CNN poll is the better
one. However, if you are (or were) associating with a Big Eight school
or a school in the South, you may think the AP is better and Nebraska is
#1. You can probably see that, due to the human characteristics which all
the voters in both polls have, it is not easy to have an unbiased opinion.
That brings up the issue about the credibility of the polls. What is needed
is a way to rate the teams without human prejudice. A computer with some
mathematical formulas can give an answer. I scanned through the Sports
Section of my local newspaper and two national newspapers, looking for
the rankings from computer polls, and unfortunately, I did not see any.
Ten years
ago, the mathematician James P. Keener of U. of Utah gave the idea "of
ranking the teams using a mathematical model" some thought after Utah's
arch rival Brigham Young U. was voted #1 based on its undefeated season.
But its victories had come against generally weak opponents. It was then
apparent to him that the voters' polls were voting for the teams with best
records instead of the best teams.
Perturbed
by the polls' results, Keener set out to see whether a mathematical scheme,
which automatically takes into account the strength of a team's opponents,
would provide a more satisfactory answer. In the simplest possible scheme,
one can assign a single point for a win, half a point for a draw, and zero
for a loss... and calculate rankings on this basis. Keener's scheme is
a little bit more complicated. A relatively obscure mathematical result
known as the Perron-Frobenius theorem was used as a recipe for calculating
such a ranking. Keener chose to allocate the value per game between the
two competing teams on the basis of the game score, and he explored various
ways of making this distribution. Each method he looked at showed certain
biases in different ways. Nonetheless, once the rules, however arbitrary,
are set, the scheme produces the required rankings. It is interesting to
note that none of the various methods that he tried made BYU #1 or even
#2. The method he finally adopted even placed BYU out of the top 10.
Today, there
are many computer polls (New York Times, USA Today-CNN, ..., and individuals)
that rank the teams based on many different mathematical formulas. The
poll or rating that is used the most (?) is probably the Latest Line from
Las-Vegas, Nevada. The ratings provide a numerical measure of a team's
relative strength and have some value in predicting the outcome of future
games. Each different ranking or rating method gives different results
because each weighs important factors differently. So now the problem with
computer polls is which model predicts best? There seems to be no easy
answer for that just like the "which voters' poll is the best"
problem.
For the fans,
being human, it is hard to swallow the results from the computers, especially
when they play down their favorite teams. Besides, those computer polls
don't even agree among themselves.
In the end,
when it comes to rating or ranking teams, the value of any particular method
resides in the mind of the beholder. So let the games begin, and may the
best numbers win.
Reference:
"Who's Really #1?", I. Peterson, Science News, Vol. 144, pp.
412-413 (December 18 & 25, 1993).
