What In the World?
"I think I'm going crazy, Bill," said George. "I can't
figure out a good rating system for the state league.
I've got over a hundred teams and I need to come up with
a statewide rating system to rank all of those teams.&
Any ideas?"
"As a matter of fact, yes!" said Bill enthusiastically.
"Have you ever heard of the Harbin Football Team rating
system? I think they use it in Ohio. They use it to determine
the high school football teams that are eligible to compete
in post-season playoffs. Each team earns points for games
it wins and for games that a defeated opponent wins.
Here's how it works: Level 1 points are awarded
for each game a team wins. A level-2 point is awarded
for each game a defeated opponent wins."
"I hear ya, but I still don't
get it. How do you put all that together?" asked
George.
"Well," said Bill, "it's very
easy. We simply use a matrix."
Rank teams A, B, C, D, E, and F if you are given the
following information.
Team A beats F, and ties C;
Team B beats A, C, and F;
Team C beats E and F;
Team D ties A and beats F;
Team E beats A and F;
Team F beats C and ties D.
If two teams tie, enter 0.5 in the zero-one matrix instead
of 1.
