Last season's pissing and moaning by TCU about being left out is only one reason for my topic.  The other reason goes back many years.

The opening game of the 1961 season was played in the Shoe against TCU.  The Buckeyes went into the game with a pre-season rank of #3.  In a big upset, TCU and the Buckeyes tied 7-7.  What was really disappointing was that TCU finished the season at 3-5-2.

The Buckeyes then ran the table and finished #2.  They did not go to the Rose Bowl that season despite being invited due to the faculty declining the bid.  That particular season the contract between the PAC8, Big Ten, and Rose Bowl had lapsed thus there was no contractual requirement that the Buckeyes accept the bid.

Alabama ended up at #1 as the only undefeated team.  Not counting undefeated Rutgers of course as they were ranked #15 but played a very poor schedule.

As an interesting aside, here is an excerpt from Wikipedia about that football season:

November 18 Texas Christian University had earlier tied Ohio State 6-6 in Columbus, and bested that with a win over #1 Texas in Austin, 6-0. After the 6-0 loss, legendary Texas coach Darrell Royal uttered his immortal description of TCU:

"They're like a bunch of cockroaches," Royal said. "It's not what they eat and tote off, it's what they fall into and mess up that hurts."

Despite their poor record that year, TCU knocked two teams out of a national championship as that was also Texas' only loss.