Well, it all started back in my early college days in 1979 while I was
earning my Bachelor's Degree in Applied Math at Georgia Tech, when I first
really noticed that the college football national champion was chosen by a
very arbitrary method. I knew there had to be a better way, a way that
would be more objective and less subjective.
As luck would have it, it just so happened that at that time I played
tournament chess. The United States Chess Federation uses a rating system
developed by chemist/statistician/computer consultant/musician Arpad Elo
that bases its ratings on the difference between the two opponents previous
ratings and the possible outcome of the game (win, lose, draw). I decided
that the same could be done for college football since the results are the
same, so I analyzed the Elo rating system and found that if you plotted the
amount a player's rating changed vs the rating of his opponent, those plots
for each result very much fit an inverse tangent curve (with the proper
scaling and constants added).
That knowledge in hand, I designed my first system. That first system, and
in actuality even the system today that it evolved into, was designed first
and foremost for one goal: to give each team an objective rating at the
end of the season. That rating was based on an equation that used an
inverse tangent function along with the rating difference between the two
teams going into a game to produce new ratings for each team based on the
result of the game.
Since then I've been tinkering with the formula quite a bit, so much so that
it doesn't resemble the original all that much anymore. In fact, I even went
so far as to replace that inverse tangent equation a few years ago with a
more linear one when I decided to simplify the system a bit and make it an
iterative process instead of a straight plug-and-chug equation.
I also have included some obvious factors in computing a rating that chess
doesn't. For example, the Elo system doesn't distinguish between a player
losing by getting crushed or a player barely losing, but in college football
the score is somewhat (repeat, somewhat) indicative of that distinction, so
I added in a graduated factor for the score difference, making sure to limit
it in case of blowouts of course, so that teams that barely lose get more
credit than teams that get blown out.
Also, the Elo system doesn't distinguish between who has the white pieces
(the first move advantage), whereas in college football the team that is at
home (the home field advantage is somewhat akin to the first move advantage)
has a significant advantage, so I incorporated that into my system.
There are some other factors, but I don't want to bore you with too many
details. But basically that's the how and where my system got started.
Over time, people asked me if I could produce intermediate results during
the season, so that they could see what my system's ratings were after each
week. While the system wasn't designed to do that, I modified it a bit so
that it would be able to take the limited amount of data available during
the season and produce a reasonable rating for each team. Hence the move
to the iterative process ... otherwise, having only a few games for each
team wouldn't allow enough movement to be really indicative of a team that
had gotten much better or much worse since the previous season. The 1996
Northwestern team was a prime example. Without the iterative process, it
would have taken all season for them to rise from their starting point
(their very low final rating from the previous season) to where they
truly belonged in 1996. With the iterative process, it took only a few
weeks.
Also, people asked if my system could predict point spreads for each game.
Now that definitely wasn't something I even dreamed of trying to do with
this system, but after comparing the difference between the ratings of
several sets of two opposing teams to the point spreads out of Vegas, I
started to notice that, with proper scaling and adjustment for such factors
as home/away, turf/grass, etc, I could come up with an equation based on
two teams' ratings that would give something reasonably close to the Vegas
line for most matchups, and occasionally a surprise disagreement with Vegas
when my rating for a team differs from what most other experts think. And
that's the predictions you see posted today on my Web page. Remember there
are no guarantees as to the accuracy of the predictions, so you are at your
own risk if you use them for anything beyond just looking at them for your
own enjoyment and amusement. I don't keep track of how correct those
predictions have been, either against the spread or straight up, so don't
ask ... I only post them for fun. There are others on the Internet that
do track the results though, so look for them if you're interested.
It's interesting to watch the numbers change over the course of a season.
As more games are played, more data is accumulated, and the numbers get
more accurate as to the true strength of each team. By the same token,
sometimes early in the season you may see a team's rating be different
by quite a large margin from what most people would think it would be or
from what it ends up at the end of the season. Such is the way with
computer ratings ... they are data-dependent, so trying to come up with
a valid number early in the season when there isn't much data sometimes
produces humorous results. I've found that by about the 5th week of the
season, there is enough data in place to have fairly reasonable results.
Finally, there's always the question of what rating does a team start
with. I gave up years ago trying to guess how much a team's rating
should be adjusted at the start of a season based on what players left
or graduated from the team, what players returned or joined, or what
coaches came and went. My guesses were as often wrong as they were
right. So now I just start with my final ratings from the previous
season, adjusted for the addition of new teams to or deletion of old
teams from the I-A level, and let the teams results during the season
move their ratings up and down accordingly. If a team is much better
or worse than the previous season, the rating's iterative process will
reflect that soon enough once a few games makes it apparent.
Anyway, that's the scoop. Enjoy the numbers.