[EM] Round Robins

[Gervase Lam]

> Date: Sun, 13 Mar 2005 19:17:22 -0800 (PST)
> From: Alex Small
> Subject: RE: [EM] Round Robins

> Say we have a round robin tournament
> between soccer teams from USC, UCLA, and UCSB.  Say that USC beats UCLA 
> 2-1, UCLA beats UCSB 4-1, and UCSB beats USC 2-0. 
> Who would be declared the winner of that round robin and advance to the
> next level of competition?

For each team, the winning margins versus the other teams are added up, 
with losses being denoted by a negative winning margin.  The team with 
highest net total (known as "goal difference" in soccer) is the winner.

In this case UCLA is the winner because:

UCLA +2 = -1 + 3
UCSB -1 = -3 + 2
USC -1 = +1 - 2

For team sports in general, I think the best analogy is "recursive" 
Copeland.  For any teams who are given the same Copeland score, Copeland 
is then run again on the tied teams.

However, soccer or ice/field hockey don't use Copeland.  Instead, a number 
of points are given for wins and a lower number of points for ties.  
Nevertheless, soccer and hockey fans should easily understand Copeland.

Thanks,
Gervase.