The Cincinnati Bengals threatened the unthinkable in 1995. Team owner Mike Brown vowed the team would move to Baltimore unless a new stadium was built.

Taxpayers in Hamilton County, Ohio, where Cincinnati is located, feared something greater than wounded civic pride if their football team left. They worried that the Bengals’ departure would spur an economic crisis throughout the region. A University of Cincinnati study released at the time estimated that the Bengals added $77 million to the local economy.

Hamilton County residents could avert disaster, however. All they needed to do was vote for a modest half-percent sales tax increase. The tax increase and municipal bonds would cover the estimated $287 million needed to build the Bengals’ new home.

Residents overwhelmingly approved the tax, and the Paul Brown Stadium for the Bengals opened in 2000 after cost overruns pushed the construction tab to nearly $450 million.

The Bengals’ worth has leapt from $423 million before the stadium to nearly $1.8 billion today, according to data from Forbes. The team is raking in cash from luxury boxes and other revenue streams the stadium has provided. The Bengals pay no rent, but they keep the income generated from advertising, tickets, luxury suites, concessions and most of the parking.

The deal hasn’t been as good for Hamilton County taxpayers, though. Revenue from the sales tax increase came in below projections for more than a decade, while the cost of maintaining the stadium has skyrocketed. Paul Brown Stadium is now estimated to cost taxpayers more than $1.1 billion by 2026.

Maintenance and upkeep — including $3 million to add Wi-Fi and $7 million for a new scoreboard — accounted for more than 16 percent of the county’s budget at one point. The county, also faced with state budget cuts, slashed social services, cut staffing and sold a hospital.

While the Bengals’ value grew, so did Hamilton County’s poverty rate, from 10.3 percent before the stadium was built to 18.6 percent in 2015, according to the Ohio Development Services Agency.

“We didn’t have money for things we needed, and it fell on deaf ears at the state Capitol,” said Hamilton County Commissioner Todd Portune. “They used the analogy that we bought a sports car when we couldn’t afford our mortgage.”

Municipalities across the country have funneled billions of dollars from taxpayers to wealthy NFL owners for stadiums. Those same venues now have taken center stage for the NFL players’ kneel-down protests of the national anthem. The players say they have a right to express their anger toward racism in the U.S.

Conservative politicians, however, view the protests as an insult to the taxpayers who finance these stadiums.

More broadly, the protests are sparking a conversation on the NFL itself and whether the public investment in teams pays off for communities that host them — and often serve as their cash machines.

In Congress, House Republicans have called for nixing the tax break that allows stadiums to finance using tax-free municipal bonds.

City, county and state officials are also vowing to take a new look at teams’ leases.

“We need to shine a light on all tax benefits for NFL teams, not just the Saints,” said Ken Havard, a Republican legislator in Louisiana, where billionaire Saints owner Tom Benson has the potential to receive nearly $400 million in taxpayer subsidies through 2025.

Pay to play

NFL teams’ pitches are generally the same: Pay for our new stadium because it will create economic growth and jobs. That will generate greater tax revenue, assuring the municipality will come out ahead.

Each NFL city receives an average economic bump of about $5 billion annually and 110,000 more jobs because of the league, according to a 2011 study paid for by the NFL Players Association.

But Edgeworth Economics, which produced the study, declined to make it authors available, and economists are skeptical of the findings.

Victor Matheson, a stadium financing analyst at the College of the Holy Cross, said whenever he sees a report by a team or boosters, he always moves the decimal point to the left and divides by 10 to get the actual number. That would bring the NFL’s financial impact to about $500 million.

Michael Leeds, chair of Temple University’s Economics Department, has studied the financial impact of Chicago’s five major sports teams. He concluded that if every Chicago team suddenly disappeared, the economic loss would be a fraction of 1 percent. The same study determined that a baseball team generates as much revenue for a city as a midsized department store.

“Scale that down to football, which plays only 8 regular home season games a year compared to baseball’s 81 games,” Mr. Leeds said. “Even if the most popular football team sold out every regular season and playoff game, it is going to draw less than half of what a below-average baseball team would draw.”

Boon or bane

Two University of Baltimore professors studied the economic impact of sports strikes on cities with professional teams. The study found that residents’ per capita income did not drop during the 1982 and 1987 NFL work stoppages.

The reason, economists say, is that stadiums do not increase spending. Instead, the stadium merely siphons money that would have been spent on other forms of entertainment in that city such as restaurant dining or theater shows.

“NFL games have a huge substitution effect,” Mr. Matheson said. “That means new money is not introduced into the economy but rather gets shifted around.”

The substitution effect is compounded by the hidden costs built into the life of a stadium’s lease. These expenses include replacing scoreboards and collecting trash on game days.

Judith Grant Long, a University of Michigan professor of urban planning, estimated that these costs increase the average public stadium subsidy to as much as 75 percent of the venue’s total value.

Mr. Leeds said stadiums and parking lots also take away land that could have been used for factories or office buildings that create more jobs and generate the property taxes that most stadiums are exempt from paying.

The NFL expects to take in roughly $14 billion in revenue this season, according to a league statement. That is over $900 million more than it made last year. The same statement noted that new stadiums in Atlanta and Minnesota contributed to the revenue gain.

Taylor Kielpinski-Rogers, an NFL spokeswoman, did not respond to multiple requests for comment.

Emily Parker, a spokeswoman for the Bengals, declined to comment. The team also denied a request to speak with Bob Bedinghaus, the county commissioner who pushed for the stadium deal and was hired by the Bengals shortly after losing his bid for re-election.

NFL spokesman Joe Lockhart told reporters that the league opposes efforts to eliminate pro sports teams’ use of tax-exempt municipal bonds because the benefits are “obvious in many of our communities.”

“You can look around the country and see the economic development that’s generated from some of these stadiums,” he said, according to Reuters.

The consensus among sports economists, though, is that publicly financed stadiums are sinkholes.

The $750 million in public funds Nevada will use to build a new stadium for the Raiders could have provided a year’s worth of education to nearly 100,000 public school students or funded all state highway rehabilitation costs for the next 6.5 years, economist Michael Farren wrote in a recent article.

In Indianapolis, the $619 million in taxpayer money used to build the $719.6 million Lucas Oil Stadium would be enough to give $730 to every man, woman and child in the city, according to the Taxpayers Protection Alliance.

“The biggest hole you can throw your money into is an NFL stadium,” said Neil deMause, editor of Field of Schemes, a blog that tracks stadium financing. “An arena can house a team or two, host concerts and you can get about 200 nights out of the year where stuff is going on. But with football stadiums there is a huge opportunity cost in terms of wasted space because you could put pretty much anything else there and it would be a better neighbor in terms of promoting and developing the surrounding area.”

Then there are the truly hidden costs such as crime.

NFL home games are associated with a 2.6 percent increase in local crime rates, said David Kalist and Daniel Lee, who are economists at Shippensburg University. Using crime statistics for certain NFL cities from 2004 to 2006, the two researchers say an increase in economically motivated crimes such as motor vehicle theft, robbery and larceny increase on game days, costing cities an average of $86,000 per game.

Costs linger

St. Louis learned that an NFL team can be a drain even after it’s gone.

The city lured the Rams from Los Angeles in 1995 with promises of a new stadium and a better economic market. The city and county of St. Louis, along with the state of Missouri, raised $280 million — $440 million in 2017 dollars — to build the Edward Jones Dome.

St. Louis was so desperate for team that it agreed to a lease that allowed the Rams to leave town if Edward Jones lost its status as a “first-tier stadium.” As modern stadiums eclipsed the dome, team owner Stan Kroenke invoked that clause to return his team to Los Angeles last year, where a $2.6 billion stadium is being built.

St. Louis and Missouri, though, still owe $78 million on bonds for Edward Jones, which they will be paying through 2022 — seven years after the Rams’ departure. Combined with maintenance costs, the nearly empty stadium will cost taxpayers a total of $144 million over the next five years. St. Louis will now have to make those payments without the $500,000 in rent the Rams paid to the city each year.

Darlene Green, St. Louis comptroller, said it has become a black mark on the city’s borrowing sheet.

“Debt service without increasing revenue is a burden on the city’s credit,” she said.

Yet stadiums are still being built.

King Banaian, a former member of the Minnesota House of Representatives, said he lost his re-election bid because he opposed using roughly $500 million of public funds to build the Vikings’ $1.1 billion new home, U.S. Bank Stadium. The Republican said that during the 2012 campaign, doors were slammed in his face and he was called “the jerk who opposed the stadium.”

“Think about the kind of things we could have done with the money we spent on U.S. Bank Stadium,” he said. “We could have improved our schools or roads or parks. There are all kinds of things we could have done with that money, but since the trade-off cost is something you can’t see, it’s a very hard argument to make.”

Mr. Banaian has vowed to never set foot in the Vikings’ new home, which will cost taxpayers $1.3 billion, when adjusted for inflation, over the next 30 years.

The Vikings contributed about $477 million toward the stadium, including $100 million passed on to the fans in the form of personal seat licenses. State officials touting the project say the stadium will generate more than $1 billion in economic activity in downtown Minneapolis.

Some Minnesota politicians remain skeptical, however.

“I haven’t seen anything that suggests the money that has been taken away from taxpayers and given to a billionaire owner has provided some inherit economic benefit to Minnesota,” said Steve Drazkowski, a Republican member of the Minnesota House. “But I have seen taxpayers and businesses struggling for sure.”

In Louisiana, the state agreed to pay $85 million to renovate the Superdome in New Orleans in 2009.

As part of the deal, Mr. Benson, the Saints’ owner, paid $42 million for an office building, shopping mall and parking garage near the stadium and leased it back to the state. Mr. Benson agreed to spend about $22 million to renovate and upgrade the office tower, which had sat vacant for three years.

Louisiana is now renting the space at $24 per square foot, according to a report in The Times-Picayune newspaper. Downtown class-A office space in the city leases for about $18.60 per square foot.

Greg Bensel, a spokesman for the Saints, said the deal was a win for the state and that Mr. Benson has invested more than $100 million in the building.

“The dilapidated building was not only an eyesore, but a hindrance to recovery in that area,” Mr. Bensel said. “Its reintroduction into commerce has been credited with spurring hundreds of millions of dollars of investment in that area.”

Mr. Havard, though, called the deal a drain on the state’s finances. He noted that the state is paying rent for floors that are unoccupied.

“The state is leasing property that we are not even using at an inflated rate to send money back to the Saints,” he said. “That’s on top of the state funding we used to renovate the dome.”

Some clauses in the Saints’ lease open unique revenue streams for the team. For example, the state is required the pay the Saints $5 million every time the team hosts the Super Bowl. Another amendment forces the state to pay the Saints up to $6 million each year if the team fails to generate $12 million in revenue attributable to the renovations.

Mr. Bensel said the Saints are entitled to that $12 million revenue because it has taken the risk of trying to generate revenue from the Superdome. He noted that the Saints have never collected the $6 million payment.

“We are about to raise taxes in Louisiana to pay for services that were less than when I got here six years ago, because we cut funding,” Mr. Havard said. “We used to have a charity hospital in Louisiana that cost the state $300 million. There are numerous things we can’t fund in this state, and most of it could be funded for less than what we give Tom Benson.”

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