First of all, it is interesting to note to that 20 states are NOT represented in the tournament, so just making it in is an accomplishment.
From my count, below are the best-represented states in the 2011 NCAA men's basketball tournament. Since there a lot of ties with states sending 4 or 5 teams, I decided to average the seeding of each state's teams and rank them by that criteria. I was also motivated to do it this way because I'm a Hoosier...
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State (No. of teams) -> Avg. Seed
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Indiana (4) -> 6.75
Ohio (4) -> 7.00
California (4) -> 8.75
Pennsylvania (5) -> 9.60
Tennessee (4) -> 9.75
Virginia (5) -> 11.20
*Feel free to check my work*
As can be seen, Pennsylvania and Virginia are sending the most teams, but these teams are not of the highest average quality. Regardless, these six states represent a very large portion of the current College Basketball market.
North Carolina has 4 teams in the 2015 NCAA basketball tournament with an average seed of 5.75
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North Carolina sent 5 teams to the 2012 NCAA Mens Basketball Tournament. NC State, UNC, Duke, Davidson, and UNC Asheville. I'm pretty sure this was the more than any other state. Virginia had a good showing as well. I'm not sure if Georgetown is in Virginia or Washington D.C.
The reocrd is North Carolina with 6 in 2002 with UNC, Duke, NC State, Wake Forrest, Davidson, UNC-Charlotte, and UNC-Wilmington.