I did this on the B1G board, but all it got was mocked by their resident asshole and the made an identical, new post about it.
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Here's a take on the 16-team SEC with 3 annual rivals for each team. Remember, no divisions.
Alabama - Auburn, Tennessee, Ole Miss
Auburn - Alabama, Georgia, Miss St
Georgia - Auburn, Florida, Carolina
Florida - Georgia, Carolina, Vanderbilt
Carolina - Florida, Kentucky, Georgia
Kentucky - Carolina, Missouri, Tenneessee
Missouri - Kentucky, Oklahoma, Arkansas
OU - Missouri, A&M, Texas
A&M - OU, Texas, LSU
Texas - A&M, Arkansas, OU
Arkansas - Texas, LSU, Missouri
LSU - Arkansas, Miss St, A&M
Miss St - LSU, Ole Miss, Auburn
Ole Miss - Vanderbiilt, Miss St, Alabama
Vanderbilt - Ole Miss, Tennessee, Florida
Tennessee - Vanderbilt, Alabama, Kentucky
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Some notes:
Usually, for an entire conference, you'd have trouble spreading out games vs big-boy programs, but here, we have plenty of those
A&M probably has the toughest trio here
Someone has to/gets to play Vandy
Each team has at least 2 it would love to play
The weakest links among those is probably UK-MIZ, OU-MIZ, and VAN-OM
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I've heard that SEC teams will submit 5 preferred teams they'd like to be among their annual 3, and the SEC will work to make that happen. The difficulty is whether the strong programs wanting to play other strong programs (relevance) vs weak ones (built-in wins) and the opposite - the weak programs preferring strong or weak opponents.