They have the worst record in the league, one of the shoddiest playing fields in professional baseball and a certain hometown following that would like to run them out of town.

The Alexandria Dukes, who open their home season tonight against Kinston at 7:30, enjoy less than a full share of the American public's reverence for the grand old game. In fact, this Class A minor league baseball team of major league dreamers has lost almost as many games off the field as on.

Since the team was formed in Alexandria four years ago, returning professional baseball to an area that had mourned the passing of the Senators for seven years, the Dukes have been involved in more civic spats than Charlie Finley.

Last spring, the city school board voted to evict the team from its public school playing field (the expulsion order was overruled by the city council). The local civic association distributed pamphlets that called the Dukes "a cancer that is eating away at out tax monies." And just two months ago the mayor of Alexandria, Charles Beatley, told a reporter the team had been "a loser for the city."

"Baseball is the American game everywhere else except in Alexandria, where we're all of a sudden detrimental," says Rick Holt, the exasperated general manager of the team. The Dukes have lost $129,000 during the first three seasons of the franchise. But the Dukes recently signed a three-year contract affiliating the club with the Pittsburgh Pirates. "We've literally had to fight and claw every inch of the way."

Loyal Duke supporters, and there are hundreds in Alexandria, including former mayor Frank Mann, blame political intrigue for the Dukes' problems. The school board, they argue, used the Dukes to continue a long-running fued with the city council. Mayor Beatley, say Duke fans, is against the team because it was fathered by former mayor Mann, Beatley's political nemesis.

"The whole thing has been political static," claims Mann, who persuaded the city council in 1978 to appropriate $120,000 to improve the playing field next to Cora Kelly Elementary School. "The people against the Dukes are the same bunch of people who complain about anything, are never in favor of anything and always try and knock something down."

George Pope, a former president of the Lynhaven Civic Association, which represents the predominantly black neighborhood surrounding Cora Kelly, admits that politics played a part in his opposition to the team.

"The mayor (Mann) dumped the team at Cora Kelly because it was less of a political problem for them. They figured in a predominantly black community there wouldn't be as much political awareness of what was happening," said Pope. At a public hearing in 1978, Pope and other neighborhood residents argued that the money to improve the baseball field, which now totals $280,000, would be better spent on tennis courts and soccer fields.

"The team represents nothing more than a payoff from the mayor to his backers who like baseball," said Pope.

Supporters of the Dukes counter that the money has not been spent just for the Dukes. American Legion teams, city recreation leagues and T.C. Williams High School use the field. The Dukes have also spent approximately $50,000 of their own money for improvements that will remain if the team moves.

"Being against the Dukes is like being against the U.S. Marines," said Frank Higdon, a certified public accountant in Alexandria and the team treasurer. Higdon is one of 10 members of the Dukes' board of directors and one of 300 supporters who have purchased at least $100 worth of stock in the team. Other board members include a past president of the American Medical Association, a former Alexandria city council member, a drug store executive and the owner of a concrete business. None of the directors receives any pay for his work. And none of the stockholders has yet to see a dividend.

"You wouldn't want to put your rent money on the Alexandria Dukes," said Higdon.

It is ironic that the Dukes, who have fought desperately to keep the Alexandria field, would gladly trade it in for a better model. The playing field is almost within throwing distance of Alexandria's railroad tracks and is lost in one of the city's less-polished neighborhoods. Because of its location next to a school, beer cannot be sold and that, say team officials, probably cuts home attendance by 100 per game.Last year, the Dukes' average attendance at home was 500.

Then there is the field itself. The outfield is an impossible combination of ruts, mounds and rocks. One player in the team's first year claimed to have built a 1954 Chevrolet from parts he stumbled over chasing balls.

"The auto parts are gone now," joked General Manager Holt. "But they left behind a giant oil slick."

For the past two years, the team, along with its stockholders and friends in Alexandria's Chamber of Commerce have been trying to persuade the city council to build a stadium on a Cameron Valley site near the Beltway where a new park is planned. But last September, the Northern Virginia Regional Park Authority voted unanimously not to develop the park if a baseball stadium was included.

While the Dukes have been suffering on the field (they opened this season with five straight losses), there have been some victories off it. In December, the city school board appropriated $25,000 to convert an unused corner of Cora Kelly Elementary into locker facilities for both the Dukes and T.C. Williams.

A greater coup was the recent agreement by the Pittsburgh Pirates to adopt the Dukes as a minor league franchise for the next three years. Under that agreement, the Pirates will pay salaries for the players and coaches a well as part of the team's travel expenses. Duke officials figure that agreement is worth approximately $100,000 a year.

"Things are a long way from ideal," said Timothy Sweet, an Alexandria insurance salesman and the team's vice president. "But if we win some baseball games, I think this will be an entirely different year."