I personally would put Purdue at #3...
OSU and UM are great, but they're not basketball schools.
Comparing just those three on the metrics that I mostly relied on in making the list:
League Titles:
- 24 Purdue
- 20 Ohio State
- 14 Michigan
NCAA Appearances:
- 30 Purdue
- 29 Ohio State
- 25 Michigan
S16's:
- 15 Michigan
- 14 Ohio State
- 12 Purdue
F4's:
- 10 Ohio State
- 6 Michigan
- 2 Purdue
NC's:
- 1 (tie) Ohio State
- 1 (tie) Michigan
- 0 Purdue
Purdue leads in two of the five but it is close in both and is last in three.
Michigan leads in one but it is close and they are tied for first in one and second in another. The knock for the Wolverines is that they are a distant third in League Titles and NCAA Appearances.
Ohio State leads in one category and is tied for first in another. They are a close second in the other three.
I went with Ohio State first because they don't have any glaring deficiencies. Unlike Purdue (F4's and NC's) and Michigan (League Titles and NCAA Appearances) the Buckeyes are respectable in every category finishing either first, tied for first, or a close second in all five.
I picked Michigan second because I feel like this is a sport much moreso than Football where what matters most is postseason success and Purdue is just not good there. Here are the three schools' rates of converting NCAA Appearances in postseason success:
- #1 Ohio State is #1 in the league in the rate of converting NCAA Appearances into F4's at 34.48%
- #2 Michigan is #2 in the league in the rate of converting NCAA Appearances into S16's at 60%
- #3 Michigan is #3 in the league in the rate of converting NCAA Appearanes into F4's at 24%
- #5 Ohio State is #5 in the league in the rate of converting NCAA Appearances into S16's at 48.28%
- #8 Purdue is #8 in the league in the rate of converting NCAA Appearanes into S16's at 40%
- #11 Purdue is #11 in the league in the rate of converting NCAA Appearances into F4's at 6.67%, this is only better than the three schools that have NEVER been to a F4 (MN, UNL, NU).
I can see the argument against Michigan because Purdue has significant leads over them in two categories but I can't see the argument against Ohio State where Purdue ha slim leads in league titles and NCAA Appearances while trailing in S16's, trailing badly in F4's, and having no NC's.
I'll also add this, when I was checking how MSU's 16 league titles compare since they joined (1951) I noticed that 13 of PU's 14 league titles were before that. In fact, 13 of PU's 24 league titles occurred before WWII. When you base your school's superiority on things that happened before
the Germans bombed Pearl Harbor, you sound like a Michigan fan.