College football is the ultimate small-sample sport. We determine champions and all-time greats and hirings and firings and massive salaries based on incomplete impressions and only 12-15 games.

Combine that with the size of the FBS itself -- throughout its history, college football's top-division roster has typically featured well over 100 teams -- and you're going to end up with one heck of a list of amazing teams that never won the national title. (Of course, schools sometimes solve this issue by claiming national titles that voters didn't vote for.)

Below are the my top 25 best teams that took the field in the AP-poll era (1935 to present) and didn't finish a season as national champion per either the AP or coaches' polls. I used my historical SP+ rankings as a starting point, then took creative control from there.

25. 1947 Michigan (10-0)

The 1947 season produced two unbelievable teams: Frank Leahy's Notre Dame and Fritz Crisler's Michigan. They didn't play each other, however, primarily because by 1947, no one liked Notre Dame. The Fighting Irish were a burgeoning powerhouse, and Leahy didn't mind running the score up a bit when he had the chance. After a 35-12 Irish win in 1943, Michigan wouldn't agree to play them again for 35 years.

That's a shame because Michigan was Notre Dame's equal in 1947. The Wolverines outscored opponents by an average of 39-5. Future college Hall of Famers Bob Chappuis and Bump Elliott were dominant via both run and pass, while future pro Hall of Famer Len Ford was rampant on the edge. The Irish had already locked up the national title vote before the bowls, so Michigan responded by making an example of USC in the Rose Bowl, winning 49-0.

This entry does come with an asterisk, by the way. After Michigan's Rose Bowl romp, a Detroit AP voter arranged an unofficial postseason poll, and Michigan won it. It didn't officially count, but Michigan claimed a title all the same.

24. 2011 LSU (13-1)

In the year-end 2011 top-10 rankings, Alabama finished first, Oregon fourth and Arkansas fifth. LSU beat them all. The Tigers also beat No. 17 West Virginia and No. 19 Georgia by a combined 89-31. Florida, Auburn and Mississippi State all finished with seven-plus wins; LSU beat them by a combined 105-27. They were second in scoring defense thanks to one of the most raucous, fun secondaries in the history of the sport -- cornerback Morris Claiborne was a unanimous All-American and "honey badger" Tyrann Mathieu a Heisman finalist.