Inspired by, and with thanks to -
"This book ... is about the principles that govern chance, the development of those ideas, and the manner in which they play out in politics, business, medicine, economics, sports, leisure, and other areas of human affairs."
Prologue
The Drunkard's Walk: How Randomness Rules Our Lives
by Leonard Mlodinow
There has been talk for a long time about a single elimination tournament for the top tier of college football teams to replace the current BCS system. Usually it is thought of as an 8 team playoff.
However, according to the Huffington Post:
"A committee of university presidents approved a plan for a four-team playoff put forward by commissioners of the top football conferences. ...
No. 1 will play No. 4, and No. 2 will play No. 3 on Dec. 31 and/or Jan. 1. The sites of those games will rotate among the four current BCS bowls – Rose, Orange, Fiesta and Sugar – and two more to be determined. "
Note that in the illustration above the matchings have been chosen so that the first two bowls on the left have been chosen so that if what is planned for next year were applied this year, that is, 1 against 4 and 2 versus 3, with the winner playing for the championship in the following bowl. (All outlined in a red square.) In this case the strongest team wins, the "championship." But, note, it is not the final winner in the 8 team field.
On the right the results of ~100 retrials of this identical set up are shown. The two highest ranked teams, Notre Dame and Alabama, win about 1/3 of the time, but notice how well number 5, Kansas State, does.
The results for another 100 runs would differ, and be significantly differ if the original matchups were changed.
The problem with one loss and out tournaments is chance can play a big role, and in football, unlike baseball, multiple games between the same two teams to determine the "true" best team is not practicable.
That is the problem with single elimination tournaments, they are played only once, and although,
"May the best team win",
all to often it won't.
The application Playoff2012 is available to download free here. It is a simulation of a hypothetical single elimination 8-team playoff assumed to have occurred at the end of the 2012 season. The eight teams are chosen by the user from the 10 top teams in the final BCS standings in December 2012 (listed below):
| TEAM | BCS
Average | Assumed*
Strength |
| Notre Dame | 0.9978 | 10 |
| Alabama | 0.9441 | 9 |
| Florida | 0.8984 | 9 |
| Oregon | 0.8621 | 9 |
| Kansas State | 0.8226 | 8 |
| Stanford | 0.7683 | 8 |
| Georgia | 0.7583 | 8 |
| LSU | 0.7511 | 8 |
| Texas A&M | 0.6756 | 7 |
| South Carolina | 0.6604 | 7 |
*The Assumed Strength is 10 times the BCS Average rounded to the nearest Integer.
The user can choose the teams and change the strength of each to any number from 1 to 10.
Playoff2012 is setup so that, if a team of strength 8 plays a team of strength 2
a great number of times it will win 80% of the games.
In any given 100 such games this number may very from around 75% to 85%,
but usually will be close to 80%.
Finally the user picks the initial pairings.
All instructions are included in the application.
Downloads:
211 visits (1 today, 1 this week)