Washington Nationals fans celebrate after the Nationals clutched the National League East division title following a baseball game against the Philadelphia Phillies in Washington on Oct. 1. (Manuel Balce Ceneta/AP)

The District will spend as much as $76,000 per Nationals playoff game to provide extra police officers, taxicab inspectors, traffic-control officers and other city employees at the ballpark.

If the Nationals were to make it through the World Series, that could add up to about $836,000. But according to Mayor Vincent C. Gray, it’s a small price to pay for the city’s first baseball playoffs since 1933.

“The District will provide, as all major cities do in similar situations, additional security and traffic control around the stadium during the playoffs,” said Gray (D), who outlined the city’s plans at a news conference Wednesday. “This is an exciting time for the District, and we look forward to the national attention that the playoff games will bring.”

The city’s largest expense will come from the D.C. police department, which generally schedules 19 officers per game but would increase staffing to as many as 75. The extra deployment would cost more than $33,000 per game, according to estimates from the mayor’s office.

But Kris Baumann, chairman of the District’s Fraternal Order of Police chapter, said that the costs for officers could be much higher, pointing to an internal police memo indicating that as many as 400 officers should be deployed for a World Series game.

At the news conference, Paul A. Quander Jr., deputy mayor for public safety, said that the officers would be on hand for any disturbances or spontaneous celebrations. “They will be in place if we need them,” Quander said.

Baumann pointed to the costs to neighborhoods. “Those people are being removed from patrol. Violent crime’s up 8 percent right now,” he said. “I don’t know how we justify taking the police officers out of those neighborhoods to go downtown.

“They can massage it all they want,” he added. “This administration has discussed nothing with us.”

Gray said that he has confidence in Chief Cathy L. Lanier to deploy officers responsibly and that he could not understand the emphasis on costs. “Every city I know is ecstatic about something like this,” said Gray, an avid baseball fan. “I would just ask that we focus on what I see as phenomenal.”

Although the Gray administration tried to play down the costs, money recently became an issue after the District, Metro and the Nationals tangled over who would pay to extend Metrorail hours for playoff games that end late. In a game against the Atlanta Braves in August, many baseball fans had to leave before the game ended or were stranded at the stadium after a rain-delayed matchup stretched to 13 innings.

LivingSocial, a daily-deals company based in the District, stepped up to the plate last week and paid the $29,500 deposit Metro requires to extend service for an extra hour. (Tim O’Shaughnessy, co-founder and chief executive of LivingSocial, is a son-in-law of Washington Post Co. Chairman Donald E. Graham.)

Council member Jack Evans (D-Ward 2), chairman of the Committee on Finance and Revenue, estimated that each game could generate $500,000 in revenue, particularly through hotel and restaurant taxes. “I’m waiting to get a final fiscal-impact statement,” he said.

Mayoral spokesman Pedro Ribeiro said that the city would recoup the costs. “This is good for tourism,” he said. “This is good for the area around the ballpark. We’re very confident. When it’s all added up, the city’s going to come out on top.”

In addition to the police costs, more than $25,000 per game would be spent on deploying about 60 employees from the District Department of Transportation, most of them traffic-control officers.

City administrator Allen Y. Lew said that the city is looking at “various ways to exit” and “traffic flow.”

The city will also beef up its code-enforcement ranks, adding eight hack inspectors and eight vending-enforcement employees outside the stadium at a cost of about $5,000 per game.

Also Wednesday, the D.C. Taxicab Commission backtracked on its same-day announcement that riders would have to pay a $1 surcharge for each additional passenger on playoff days, beginning two hours before the game and lasting through 4 a.m. The commission reversed course after Gray learned of the surcharge through a news release and contacted Ron M. Linton, the commission’s chairman.

Meanwhile, the Nationals are offering Gray and D.C. Council Chairman Phil Mendelson (D) tickets to attend the games in their “official capacity,” said Chris Murphy, the mayor’s chief of staff.

Although the mayor and council get tickets to a box throughout the season, the stadium lease agreement does not extend the giveaway to the playoffs. “The Nationals have put out an offer,” Murphy said.

Murphy said the administration is trying to determine whether Gray and Mendelson can legally accept the tickets. In 2010, then-New York Gov. David Paterson (D) was fined more than $62,000 for soliciting and accepting 2009 World Series tickets from the New York Yankees.