Republican John C. Cook won the Fairfax County supervisor position Tuesday by 372 votes in the closely watched Braddock District, edging out Democratic challenger Janet S. Oleszek. (Tracy A. Woodward/THE WASHINGTON POST)

If there’s a reason Fairfax County Supervisor John C. Cook won by a gnat’s eyelash in Tuesday’s election, it might have to do with a big hole in the ground.

Democrats and Republicans both say that Cook, a Republican who eked out victory over Democratic challenger Janet S. Oleszek by 372 votes in the closely watched Braddock District, had a record of dealing with hyper-local problems.

And perhaps no such problem was as vexing as what to do about the abandoned eyesore that once was the Kings Park West Swim Club.

After the community pool, faced with declining membership and growing maintenance bills, closed several years ago, the site became a magnet for graffiti artists and other troublemakers. It also was a safety hazard. Neighbors explored putting a day-care center or homes there. But nothing came of such ideas.

So Cook worked with the county’s Department of Public Works and Environmental Services and the Fairfax County Park Authority on a plan to transform the site into a storm-water retention basin and parkland.

Oleszek’s campaign chairman, Benjamin A. Tribbett, thought of the defunct pool on election night when returns showed the usually Democrat-friendly Robinson precinct, where the pool is located, went for Cook by 55 votes.

“The reality is that there’s just nothing you could say to a hardened Democrat that was living on that street — they’re going to vote for the guy who fixed it,” said Tribbett, who writes the Not Larry Sabato blog.

In other words, constituent services trumped ideology, as often happens in local races. And who better to help constituents than the people who are already in office?

All of which may explain why Tuesday’s back-to-the-future vote gave Board of Supervisors Chairman Sharon Bulova (D) and every other board member another four years in office.

Going forward, the board’s most pressing piece of business will be replacing County Executive Anthony H. Griffin. Griffin, who has overseen the day-to-day workings of the government since 2000, announced his plans to retire in the spring.

The board also hopes to find common ground with a new school board, whose biggest priority will be finding a replacement for Superintendent Jack Dale, who has announced he is stepping down in 2013.

Democrats said Tuesday’s vote was proof that Bulova’s middle-of-the-road approach and emphasis on consensus might be short on drama but is high on results. Redistricting, too, may have played a role: Some challengers, uncertain of what their district might look like, launched their campaigns much later than usual.

The election offered some other lessons, too. As recently as summer, Republicans had sensed a wave election breaking their way in Virginia. But by Tuesday night, they had to resign themselves to the status quo, perhaps because Democrats phoned and knocked on doors to get out the vote more aggressively than the GOP did.

Bulova, the top vote-getter in Fairfax, lost only 13 precincts in the county and picked up more total votes than her predecessor, Gerald E. Connolly, while spending about half the $1.2 million he spent. The Democrats’ political action committee, Fairfax Victory 2011, oversaw a coordinated get-out-the-vote effort that involved 26 candidates, including some, such as Sen. George L. Barker, whose districts extend outside the county. Jason Tipton, the PAC’s director said, said the Democrats called 75,000 voters 10 times each.

“Some people were complaining about the number of phone calls they were getting,” Bulova said.

Some Republicans acknowledged that their field of county candidates was uneven, perhaps because the GOP focused most of its energy on trying to seize outright control of Virginia’s Senate and, locally, the school board.

Still, Republicans were pleased that Cook held on in a swing district that had belonged to Bulova for more than 20 years before she became board chairman in 2009. Her predecessor was Audrey Moore, also a Democrat. In the waning days of the campaign, Democratic contributors, especially labor unions, poured thousands of dollars into the Braddock race. Oleszek, who received nearly $64,000 in October, spent nearly $123,000 her bid, while Cook spent nearly $153,000, according to reports compiled by the Virginia Public Access Project.

“Job number one for the Democrats was to knock Cook out. They put a lot of resources in it,” said Anthony Bedell, chairman of the Fairfax County Republican Committee.

Cook, like his predecessor, knew that his job security relied on handling the mundane stuff that constituents call about almost every day: potholes, cracked sidewalks, downed tree branches, traffic signals, and speeding.

“From day one, I said to my staff that’s going to be our priority — to deal with these problems and fix them,” Cook said. “That’s the part of the job that crosses party lines. Especially for supervisors, someone in local office, they want someone out there in the community.”