what about future prospects, like 07 kids? I'd say it's a pretty good way to get a kid on the radar that otherwise would have no interest or knowledge of how OSU could be a good fit for you.
A lot of the Ohio prospects get free tickets for unofficial visits, so most of the Ohio kids who matter have already seen at least one game at the 'Shoe.
As far as official visits for games, here is a complete list from the past four recruiting seasons:
2002 Recruits
Richard Washington (NC State[sup]1[/sup]) 10/05/01 (OSU vs. Northwestern)
Kwakou Robinson (Virginia) 10/12/01 (OSU vs. Wisconsin)
2003 Recruits
Dominique Brooks (Colorado) 09/27/02 (OSU vs. Indiana)
Tarrell Brown (Texas) 09/27/02 (OSU vs. Indiana)
DeMarcus Tyler (NC State) 11/01/02 (OSU vs. Minnesota)
Todd Boeckman (Ohio State[sup]2[/sup]) 11/22/02 (OSU vs. Michigan)
Dareus Hiley (Ohio State[sup]3[/sup]) 11/22/02 (OSU vs. Michigan)
Donte Whitner (Ohio State[sup]3[/sup]) 11/22/02 (OSU vs. Michigan)
Ashton Youbouty (Ohio State) 11/22/02 (OSU vs. Michigan)
Joel Holler (Penn State) 11/22/02 (OSU vs. Michigan)
Turk McBride (Tennessee) 11/22/02 (OSU vs. Michigan)
Mario Williams (NC State) 11/22/02 (OSU vs. Michigan)
2004 Recruits
Jeff Byers (USC) 08/29/03 (OSU vs. Washington)
Chris Pino (SDSU) 08/29/03 (OSU vs. Washington)
Brett Gallimore (Michigan) 09/05/03 (OSU vs. SDSU)
David Lonie (California) 11/07/03 (OSU vs. MSU)
DaJuan Morgan (NC State[sup]4[/sup]) 11/14/03 (OSU vs. Purdue)
2005 Recruits
Lawrence Wilson (Ohio State[sup]5[/sup]) 10/09/04 (OSU vs. Wisconsin)
Shawn Oatis (UCLA) 10/22/04 (OSU vs. Indiana)
Jason Gwaltney (West Virginia) 10/29/04 (OSU vs. PSU)
Elijah Hodge (Wisconsin) 11/19/04 (OSU vs. Michigan)
Maurice Wells (Ohio State[sup]3[/sup]) 11/19/04 (OSU vs. Michigan)
Ronnie Wilson (Florida) 11/19/04 (OSU vs. Michigan)
[sup]1[/sup]Washington committed to Ohio State on January 20, 2002, then signed with NC State two weeks later.
[sup]2[/sup]Boeckman committed to Ohio State on August 17, 2002, which was before his official visit to Ohio State.
[sup]3[/sup]Whitner, Hiley, and Wells were rumored to be "silent verbals" to Ohio State before their official visits.
[sup]4[/sup]Morgan committed to Ohio State during his official visit, and he specifically mentioned the game-day atmosphere as a major factor in his decision; Ohio State later rescinded his offer, and Morgan signed with NC State.
[sup]5[/sup]Wilson committed to Notre Dame on November 5, 2004, after his visit to Ohio State; Wilson later de-committed from Notre Dame and committed to Ohio State on Signing Day.
Out of the 23 official visits during the season over the last four years, Ohio State landed verbal commitments from only six prospects (Washington, Morgan, Wells, Hiley, Whitner, and Youbouty); Wilson verballed to Notre Dame after his OSU visit, and Boeckman was already an OSU verbal when he visited. Three of those six (Wells, Whitner, and Hiley) were most likely "silent verbals" when they visited, and a fourth (Washington) did not commit to OSU until long after his visit. Thus, only two of 23 prospects (Youbouty and Morgan) verballed to OSU during or in close proximity to their respective official visits, and of those two, only Youbouty actually signed with Ohio State. So, you could say that, in four years, Ohio State has signed only one player (Ashton Youbouty) who selected Ohio State based on his game-day official visit.