CLEVELAND — The billionaire owner of the Cleveland Cavaliers, Dan Gilbert, is a lucky man.

When LeBron James, his transcendent native son, left for Miami, the owner threw an impressive tantrum, going on about “cowardly betrayal.”

Despite that, James felt the tug of home and returned to Cleveland to revive Gilbert’s moribund franchise. In the NBA Finals, James resembled a Sherpa as he strapped a depleted team to his back and tried to drag it to the summit.

Gilbert made a splendid pile of cash off the Return. According to Sports Business Daily and Forbes, the Cavaliers’ revenue jumped by $67 million last season, while team salaries increased by just $15.2 million.

In the offseason, Gilbert dug his fingers into another pile of money, this one made up of taxpayer dollars. A year earlier, Gilbert and his fellow sports billionaires here — Larry Dolan, who owns the baseball Indians, and Jimmy Haslam, who owns the football Browns — had worked together to push through a referendum that extended a countywide “sin tax” on cigarettes, beer and liquor.

Over the next 20 years, taxpayers in Cleveland and Cuyahoga County will sluice $262 million into improvements for the city’s arenas and stadiums. This straitened city has already pumped $800 million into its sports stadiums.

Sweet deals for team owners are a distinguishing feature of pro sports capitalism. Costs are socialized, and profits remain private. Cleveland’s owners argue that this is only just: The stadium and the arena are publicly owned, and like any landlord, the city and the county should look after repairs and improvements.

Their logic does not apply more broadly. The team owners took control of the process of auctioning off naming rights for these public stadiums. The Browns sold their stadium’s rights for $100 million to FirstEnergy Corp.; the Indians will get $58 million over 16 years from Progressive Insurance; Gilbert’s home loan business paid a terrific sum to Gilbert’s team to name the place Quicken Loans Arena.

The owners shared not a penny with the hard-pressed city.

The Cleveland Indians have their hearts set on a new sound system. The Browns’ Haslam — whose truck-stop company, Pilot Flying J, just last year paid a $92 million fine to avoid a federal fraud prosecution — has compiled a list of improvements to be funded out of the public purse.

That sports teams have an umbilical tie to civic identity is not a fanciful notion. That this means that teams are drivers of economic progress, however, is a hallucination.

When James decided to return to Cleveland, city leaders and a few journalists retailed a narrative about L’Effect LeBron. They estimated that his return would pour many tens of millions of dollars into the city and speed the “Cleveland Renaissance.”

Cleveland has charming, leafy neighborhoods, fine museums and theaters and splendid lake views. More college-educated young adults are moving downtown. At the same time, in the last month for which figures are available, Cuyahoga County’s job growth rate was 0.0.

The city’s poverty rate hovers near 37 percent, and the infant mortality rate is 13.0 per 1,000 births, compared with about 4.0 in New York City, which has no shortage of poverty.

Public schools have absorbed cut after cut.

I called George Zeller, who has analyzed the economy here for decades. He declined to talk renaissance, saying no such animal existed.

“The theory that all of these sports teams are producing a gigantic boom is completely false,” he said.

Yet sin-tax dollars tumble into the hands of billionaires who employ millionaires.

The day after the end of the NBA Finals, I walked into the Cleveland office of Peter Pattakos. An ebullient lawyer, a sports fan and an Akron native, he helped lead the battle against the sin-tax extension. Ask a question, and he is off at a sprint.

“It’s outrageous that these are public entities and we let these billionaires derive untold profits,” he said. “They kept saying, ‘Keep Cleveland strong,’ with the implied threat that they’d leave town if we didn’t underwrite their stadiums.”

The anti-sin-tax campaign was a peasant crusade. Pattakos’ ragtag band suggested a $3 surcharge on sports tickets. The owners rolled their collective eyes.

“Proposing to punish Cuyahoga County families and sports fans by imposing a new, large ticket tax to pay for major repairs,” the owners complained in a news release, “is terribly flawed.”

A surcharge, they complained, would make it even more difficult for families to buy tickets. That argument has an out-of-body quality, as the owners set the prices. (The Cavaliers will raise ticket prices 15 percent next year.)

The teams’ owners and supporters outspent opponents, $3 million to $30,000. The vote to extend the sin tax, however, was not a blowout. Voters in the city of Cleveland rejected it; suburban voters carried the election.

In editorializing for the sin tax, The Cleveland Plain Dealer argued that the city had a landlord’s responsibility to pay for upkeep. Left unexplained was why the landlord had never tried to renegotiate terms with ever more wealthy teams.

(Note: The Indians offer a sort of exception. They rank next to last in the American League in attendance. The night I attended a game, the crowd had the feel of an extra-large backyard barbecue, and 25 percent of the fans seemed to be rooting for the visiting Chicago Cubs.)

Over the winter, the Cavaliers’ emissaries arrived with a new proposal. They wanted locals to split the cost — in addition to the sin-tax dollars — of overhauling their arena. Adam Silver, the NBA commissioner, added his voice, saying that the league would love to have the All-Star Game in Cleveland, if only its burghers would ante up again for the billionaire owner.

The Cavaliers’ chief executive says the overhaul would add to Cleveland’s “economic momentum.”

To be a wealthy sports owner is to feel no burn of embarrassment.