Mark Rosentraub, the author of the book “Major League Losers,” said that many of the stadium deals included “revenue bombs,” with financial traps like balloon payments on debt in later years and sweeteners like the Hamilton County property tax rebate to win public support.

Image In 1996, voters approved a sales tax increase to build Paul Brown Stadium as part of a redevelopment project and to keep the Bengals in Cincinnati. Credit... Tom Uhlman for The New York Times

In many cases, the architects of the deals are long gone by the time the bill comes due.

“This is one of the effects of the economic tsunami sweeping through,” Rosentraub said of the deficits.

The 1996 proposal to build stadiums for the Bengals and the Reds had plenty of proponents. The economy was growing, Riverfront Stadium was outdated and the Bengals were hinting that they would move, as the Browns had done.

The plan went awry almost from the start. The football stadium exceeded its budget by $50 million, forcing the county to issue more bonds. Forecasts for growth in the sales tax turned out to be too rosy. The teams received sweetheart leases. In 2000, voters threw out the county commissioners who cut the deal.

That year the sales tax grew 1.8 percent, the first of many years below the 3 percent forecast. Both stadiums were originally expected to cost $500 million combined. Yet Paul Brown Stadium alone cost $455 million and the Great American Ballpark, the Reds’ home a few hundred yards down the Ohio River, cost $337 million by the time it opened in 2003.

The generous deal for the Bengals has been a sore spot. The team had to pay rent only through 2009 on its 26-year lease, and has to cover the cost of running the stadium only for game days. Starting in 2017, the county will reimburse the team for these costs, too. The county will pay $8.5 million this year to keep the stadium going.

The Bengals keep revenue from naming rights, advertising, tickets, suites and most parking. If the county wants to recoup money by taxing tickets, concessions or parking, it needs the team’s approval.