One of them is a team that won just eight games in the 2012-13 season and was picked to finish 10th in the 11-team MAAC this season by league coaches in their preseason poll.
That would be Siena, which grinded out a 54-52 victory over Penn State in the CBI quarterfinals Monday night at the Times Union Center in Albany, N.Y.
Siena, now 17-17 overall, moves on to a tournament semifinal-round meeting with Illinois State Wednesday at 7 p.m. at the TUC.
Monday's outcome precipitated a rare on-court celebration in which hundreds of students and Siena fans stormed the court at the final buzzer, a scene not that different from March of 2010 when the team won the last of its three consecutive MAAC post-season tournament championships on its home court.
Monday's hero was reserve guard Evan Hymes, at 5-foot-8 the smallest player on the court at the end.
Hymes only got into late-game play when starting point guard Marquis Wright was knocked to the ground and struck his head on a baseline cameraman's knee after a driving layup attempt with 18 seconds remaining, and could not return.
Saints' forward Lavon Long was chose to take the resultant foul shots, and made one of two to give Siena a 52-50 advantage.
The Nittany Lions' Brandon Taylor tied it with 9.3 second remaining on a put-back bucket.
The Saints then inbounded to Hymes, who faked a handoff to junior teammate Rob Poole, burst past Penn St.'s perimeter defense and got to the basket to get off the game-winning layup just beyond the reach of Taylor with 3.2 seconds remaining.
Penn State guard D.J. Newbill then stepped out of bounds at the sidelines near midcourt when trying to get around a Siena defender, costing his team a chance for a legitimate last-second play.
Ironically, Hymes' presence in a Siena uniform this season is almost as unexpected as Siena's advancement in post-season play.
The junior guard initially announced last spring that he would leave the program to play closer to his North Carolina home. He subsequently rescinded that decision over the summer months to remain with the Saints.
"We owe it all to teams in the MAAC to play hard, because they taught us to play hard," Siena coach Jimmy Patsos said afterwards. "I thought we did a lot of the little things that were kind of griding and that's just the way the MAAC is."
The victory gives Siena a 5-1 record against BCS schools at the TUC in the past 10 seasons and Monday's contest is believed to be the first time a Big Ten program played a game against Siena on the Saints' home court.
Sophomore forward led the winners with a 12-point, 12-rebound effort while Poole added 11 points and eight rebounds.
Siena's roster doesn't include a single senior on scholarship.
"They're going to be a very good team in that league next year," Penn State coach Pat Chambers told reporters after Monday's game.