MANHATTAN, Kan. — At 8-2, The Kansas State Wildcats have nothing to apologize for.

They have won every game they were supposed to win, and they have picked up two victories away from Bramlage Coliseum. Their hopes of reaching a fourth straight NCAA Tournament remain within reach.

But because of a schedule that has matched them up against eight teams from small conferences and two national powers, their most memorable games were double-digit defeats. They couldn’t hang with No. 2 Michigan at Madison Square Garden and fell flat in the second half against No. 14 Gonzaga in Seattle.

For now, K-State is known as a team that can’t compete with college basketball’s elite. That won’t change until the Wildcats score a signature victory. That makes Saturday’s 7 p.m. clash with No. 8 Florida at the Sprint Center such an important game. It is the Wildcats’ last opportunity to beat a top-tier opponent, and build fan excitement back up to where it had been in previous seasons, before Big 12 play begins.

“If we win this game I think we will earn a lot more support,” guard Will Spradling said. “I feel like our fan base kinda doubts us a little bit. If we win this I feel like they will be behind us a little more.”

If K-State loses it has to wait until Jan. 5, when Oklahoma State comes to Manhattan for the Big 12 opener, for another chance to impress. In between it plays UMKC and South Dakota. So this game is definitely important.

“I don’t know if there is pressure. There’s opportunity,” K-State coach Bruce Weber said. “It’s a great opportunity for us. Does it make or break our season one way or the other? No, but it sure would be a nice boost to win and put us in a nice mind-set.”

Victory won’t come easy, though. Weber thinks the Gators, whose only loss came in the final seconds against Arizona, might be the best team the Wildcats have faced. Seniors Mike Rosario, Kenny Boynton and Erik Murphy are all scoring more than 11.6 points per game, and their coach, Billy Donovan, has won two national championships.

Florida beat K-State 57-44 two years ago on a neutral court in the Sunshine State by holding the Wildcats to 27.3 percent shooting. Spradling and the four other current K-State players who took the court in the game still wince when they think of how poorly that game went.

“It was ugly,” Spradling said.

The Wildcats hope to learn from their failures in that game, as well as their second-half breakdowns against Michigan and Gonzaga this year, and fight from start to finish.

Junior forward Shane Southwell expects K-State to accomplish that much. He blames the Wildcats’ two collapses on poor stamina. In practices leading up to those games, they were sharp most of the way but got sloppy at the end. Lately, though, he has seen his teammates finish practices just as strong as they start them.

K-State should also benefit from a large and friendly crowd. Team officials say more than 13,000 tickets had been sold for the game, which would give the team much more fan support than it has benefited from playing in front of sparse home crowds.

The Wildcats will take all the help they can get as they try to earn their first signature victory of the season.

“That should be extremely enlightening for our team,” Southwell said. “We haven’t played in a front of a huge K-State crowd. I know they are going to be there and they are going to be loud. Hopefully they give us that energy in the second half we haven’t had.”