re: You are not an "everything" school if you've never made a mens final 4

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Why is that the threshold and not a natty?

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If I had to guess, it would have to be the size and scope of the post-season for the specific sport.

Football, for the longest time, only had a 1 game post-season; then there was a 2 game post-season. Requiring a national title in that one makes sense.

Basketball and baseball, OTOH, require you to win 6 games in the post-season (basketball) or 10 games (baseball) - with basketball giving you 0 mulligans and baseball giving you a maximum of 4 mulligans, but only 1 per regional/series.

I think the lack of mulligans in basketball (especially when compared to the professional version, where playoff teams get best of 7 series at each round) is why most people start with Final Fours as the big indicator. Baseball has the "reached the CWS" but that seems to be less of a "banner" moment than, say, reaching the Final Four.

Or, more to the point (keep in mind, fluctuations in eligibility for teams makes these "close but not exact" - for example, there are teams that have won the NCAA basketball tournament that are no longer in Division 1 - like CCNY, who won back in 1950 but are now Division III.)

There have been 85 official NCAA tournaments:
91 teams have ever reached the Final Four, or 26% of all eligible NCAA teams.
66 teams have reached the national championship game, or 18.9%
37 different programs have won the national championship, or 10.6%.

Of the teams remaining, two have never won: Auburn and Houston.
If Florida wins, they will win their 3rd, making them one of only 9 teams (currently 8) to have won 3 or more titles. If Duke wins they will tie UConn and North Carolina at 6 each, behind only UCLA at 11 and Kentucky at 8.

27 teams have won a division 1 football national championship, or 20.3% of all division 1 football teams (based on recognized selectors per the NCAA)

86 teams have made it to the college world series, or 28.7%.
47 teams have made it to the final series of the CWS, or 15.7%
36 teams have won the CWS, or 12%

Order of rarity, from least rare to rarest:
Making the College World Series (final 8 teams) - 28.7%
Making the Final Four - 26%
Winning the CFB National Championship - 20.3%
Reaching the final game of the NCAA Tournament - 18.9%
Reaching the final series of the CWS - 15.7%
Winning the CWS - 12%
Winning the NCAA national championship - 10.6%

Of course, none of these numbers breaks down into "realistic" chances - these treat Alabama State has having the same odds (1 in 353) as Kentucky for winning. That would take a lot more calculation as well as defining what those parameters actually are. Does Vandy have a more realistic shot than Robert Morris, or even less because Robert Morris can get a shot by winning its conference, while Vandy has only won the conference twice - meaning they have had to rely on at-large bids way more often. Of course, Vandy has actually made it past the first round (even as far as the Elite 8 once) while Robert Morris' only wins have been in Preliminary or First Four games and has never advanced past the first round.