For more than a decade, the University of Dayton has hosted Cinderella teams hoping for a last shot at the NCAA Division I men’s basketball tournament.

The University of Dayton pep band performs at the First Four block party on Sunday. ( Sharon Davis Howard, University of Dayton )

While the tournament can mean unprecedented exposure for lesser-known schools that go far in the Big Dance (just ask George Mason or Virginia Commonwealth universities), it also brings attention to the cities hosting games.

The games Tuesday night are expected to garner even more buzz than usual, as two world leaders plan to be in the University of Dayton Arena stands: President Obama and British Prime Minister David Cameron.

During the inaugural “First Four” series of games last year, the university was mentioned nearly 1,000 times in the top 100 media markets. That exposure has an advertising value of $1.2 million, according to data compiled by Cision, a media-tracking service. So far this year, the NCAA has issued 185 press passes for the two-day event.

In addition to the publicity, the city is expecting a jolt of at least $4 million to its local economy this week, as thousands are expected to attend the games and other events, according to the Dayton-Montgomery County Convention and Visitors Bureau.

Last year more than 20,200 fans showed up, and local leaders are hoping for a sell-out this year. The university has already been picked to host next year’s First Four, along with second- and third-round games.

This year also brought the inaugural “First Four Festival,” a day-long street party organized by the university, city, local businesses and the NCAA that attracted at least 15,000 people, according to a university spokesman. The free festival featured big-screen TVs broadcasting conference championship games, a basketball tournament with local players, live entertainment and a “First Four 4-Miler race.”

For on-the-court March Madness coverage this month, check out the Post’s sports section and The Early Lead blog. For off-the-court coverage, keep reading Campus Overload or follow me on Facebook and Twitter. And check out these articles:

Five myths about March Madness

BYU ‘mathletes’ film rap video ahead of March Madness

March Madness of graduation rates: U-Conn. loses, Notre Dame wins

Georgetown mascot Jack the Bulldog injured; surgery possible