I think you missed a few points.
You can't join the Ohio State Alumni Association unless you are an Ohio State graduate.
Ohio State leads the nation in active fans and in dues-paying alumni. The margins are roughly 2 to 1 and 15 to 1 over Alabama, respectively.
The original point was that Alabama would travel better than Ohio State. Given these much larger numbers and the large numbers of Buckeyes in the South, especially retirees, I think we've refuted that argument and we can move on, don't you?
irrelevant.
My point was, the alumni base itself. There's 500,000 dues paying alumni. With 50,000+ graduating every 4 years, you can figure out how many don't pay dues.
It's obvious you two have not been following what the alumni association has been doing. The alumni association no longer collects dues. In order to encourage the alumni to give back to the university, they switched to a gift based model. Prior to 2012, the alumni association had two levels, dues paying members and lifetime members. In 2012, the structure was changed to the following:
Basic members: All graduates of OSU. No dues, no paperwork, just automatically members. There are some benefits such as access to online alumni magazine, online library access, and affiliation discounts.
Sustaining members: Instead of dues, members give at least a $75 tax deductible gift to an OSU fund of their choice. These include gifts to sustaining funds for colleges and programs, scholarships, the medical center, the Spielman fund, and even athletics. This level comes with more benefits such as in person library access, golf course membership eligibility, and the football ticket lottery.
Lifetime members: Phased out, but those alumni who were already lifetime members are allowed to keep it.
The numbers you are comparing are not really equivalent. The over 500,000 you reference are all graduates of Ohio State (basic members). The 34,000 for Alabama are members giving gifts to their alumni association. I would guess the OSU has more sustaining members than that (couldn't find the number), but they are also able to designate where their money goes. It's possible that Alabama has just as many alumni donating to their university, just not to the alumni association. Also, Alabama does not have a football ticket lottery which would likely increase their membership.