I'm a little psyched based on our current win streak, so I'm going to type way more than I should. I started following the team in 94-95, so I remember all these seasons well. I'm not going to give my answer to the OP's question, but instead I'm going to focus on our actual NCAA tournament play in each of those seasons, in chronological order:
1998- We were probably one of the last teams to get in. We got upset in the first round of the Big East Tournament by a mediocre Georgetown team, and I think most of us thought we were NIT bound. We drew UCLA, and while we were down most of the game, we got hot in the last five minutes and either took the lead or had a chance to win at the end (I can't remember which). We fell in a close one, but it was a valiant effort.
1999-Lafayette didn't know what hit it in the 2-15 matchup. I still to this day don't know what happened to us in the 2nd round vs. Purdue. Probably the worst Canes basketball game I have ever watched. Inexcusable.
2000- We drew the last timeslot on Friday night, so we were one of the last first round games, and we easily beat Arkansas, who I think only got in because they surprisingly won the SEC tourney. The second round game against Ohio State was awesome. The team played great. The Sweet 16 game I didn't get to see much of, as this was back when only 1 game per timeslot was broadcast, and we were in the same timeslot as the Duke vs. Florida game, so if you didn't live in Miami or Tulsa, you only got to watch a few snippets when Duke was at halftime. I remember Tulsa getting out to a big early lead, and we did manage to come back and tie it up or even go up by 1, but then Tulsa pulled back ahead for good. Tulsa was coached by Bill Self. I think that was his last season there before he went to Illinois (which only lasted a few years due to Roy Williams leaving Kansas).
2002-Perry Clark coached team. We were the noon tipoff on Thursday, were down probably by close to 20 before the first half was done, and cheating Quinn Snyder and #12 seed Mizzou wound up going all the way to the Elite 8 that year. This was by far our worst NCAA tournament of all of these. I think we were the first team eliminated.
2008-St. Mary's first round game was good. This was a McClinton team. We made a valiant comeback against a very good Texas team in round 2 and fell just short. Great effort. The only kind thing I can say about Frank Haith is that he had this team ready for the tournament.
2013-I remember listening to Marquette vs. Davidson in the first round driving home from work, and 14 seed Davidson was choking away the game. They should have upset Marquette. I just had a feeling this would come back to haunt us. We of course easily dispatched Pacific. We did not play well against Illinois. We got lucky on a blown call in the last minute (before they used tv replay to review plays late in the game). It went out on us, but the refs called it the other way. I think we would have lost that game without that call going in our favor. That Marquette loss was tough. We couldn't hit shots in the first half.
2016-Buffalo gave us all we could handle. I remember watching that game and thinking that their coach (Nate Oats) was going places. He's coaching Alabama now. I loved our performance against Wichita State. We started off so hot and dominating, and even after Wichita State made their run and even took the lead (I think) we came right back. A great game. I remember when the bracket came out, we all kind of knew we were going to be a 3 seed, and a lot of us, myself included, were happy we got the regional where Villanova was the 2 seed. We all thought they were the weakest 2, and we were all wrong. While we lost by over 20 to Villanova in the Sweet 16, I still to this day think that was our best Sweet 16 performance, up until last year of course, and Villanova was just playing elite basketball.
2017-We were up 10-0 or something like that. We were also playing a Tom Izzo coached team. It was a tough loss, but I have no bitter feelings about it.
2018-Until last year when we finally got good again after 3 poor seasons, I thought we were forever cursed by Lonnie Walker missing the front end of the 1 and 1. I remember when the brackets came out thinking we got the worst 6-11 matchup. Loyola proved all season, and especially in the tournament, that they were very good. I thought we played a good game. Just lost to a good cinderella on a clutch 3 pointer. Other than the Lonnie Walker free throw miss, I can't remember anything else bad about our performance.
2022-We almost blew that USC game in the last minute. (Just like we almost blew the UVa regular season game this year, and did blow the Pitt game this year). The Auburn game was probably our best single NCAA game ever. Iowa State somehow played good enough defense to upset their way into the Sweet 16 and wasn't much trouble for us. (Though I can see a possible rematch with them in this year's tournament, and their good defense could give our best offense ever some fits). It's not often that a 10 seed gets to wear their home uniforms in the Sweet 16 like we did. It was so awesome to finally make an Elite 8. A little bit of our thunder was stolen by St. Peters beating Purdue that same night we beat Iowa State. We played a great first half against Kansas.