Thomas M. Arrasmith III claims not to be an avid football fan. He can't remember statistics. He can't even remember the name of a former Redskins place kicker who missed a point after touchdown, lost the game and caused him to punch his fist through the paneling of his Capitol Hill town house.

For Arrasmith, an IBM marketing representative, football is nothing more or less than the Redskins. He admits his agonizing love affair with Washington's NFL football franchise is absurd. Why, he asks, should he care about some "kid receiver who gets $175,000 a year--the salary of 10 English teachers?"

But after Washington beat Dallas last week, Arrasmith walked out of his living room and stood in the snow on North Carolina Avenue. He waved and hollered and felt close to hundreds of strangers.

"Washington becomes friendly and forthright and civilly uncivil," says Arrasmith. "This can be a very warm town when the Redskins win."

The Redskins weren't supposed to win this year. They were, for the most part, a team of unspectacular athletes. Their 11 victories came during a strike-marred season that angered and disenchanted millions of professional football fans.

That "unspectacular" team, however, plays today in the most prestigious and publicized of America's sporting events. By a magical transaction unique to sport, the Redskins have entitled the people of Washington to act like children: wear funny clothes, talk to strangers and unabashedly throw themselves into a make-believe world where the Big Game matters. By defeating the hateful Dallas Cowboys and moving on to Super Bowl XVII, the Redskins gave this status-conscious, often stodgy town a special week-long dispensation to wallow in silliness.

Thomas Hanlen, an electrical engineer, has invited a truckload of live hogs, along with 21 human beings, to watch the Super Bowl at his Dunkirk, Md., home. Montgomery County women flocked all week long to Over the Rainbow, a cosmetics boutique at the ritzy White Flint Mall, for burgundy and gold blusher. Students at Barbara Cokinos' fifth-grade class at Wayside Elementary in Rockville were given a Super Bowl math test. Every correct answer was a point for the Redskins, every mistake a point for the Miami Dolphins. "They just about all had 100 percent for the Redskins," said their teacher.

"I never close my store unless it is an emergency," says Charles Bowman, owner of Odds & Ends, a tiny beer and snack joint on Georgia Avenue NW. But Bowman is closing up at 5 p.m. today and going home to his television set. The Redskins, he says, "give me chills sometimes. I really get pumped up. I think I'm Coach Gibbs. I prance around the floor . . . . This game is an emergency."

"The only homework assignment this weekend," Larry Grove, principal of Walter Reed Elementary in Arlington, told his school Friday afternoon, "is be home Sunday night and cheer the Redskins to victory."

Looked at coldly, the phenomenon of a city losing its collective marbles over a professional football team makes little sense. The for-profit Redskins exist to take money from fans. The players, most of whom are newcomers to Washington, make far more money than most Americans are likely to ever make. The team's principal owner, Jack Kent Cooke, is a multimillionaire who can afford to charter a DC10 to fly 250 of his nearest and dearest to booze and schmooze in Pasadena.

In Washington, however, like in most cities with winning pro teams, it's bad form to look at the Redskins coldly. It is so much more natural and comforting to embrace them. Bill Veeck, who has owned baseball teams over four decades, has tried to explain the appeal of big-time sports:

"When you talk about [sports] you won't be rebuffed. The other person will know what you're talking about. Other than sports, the only other time people can freely converse is during disasters. I guess sports is like a hurricane."

At the Market Inn on E Street SW, where Redskin fans have been alternately whooping it up and crying in their beer for 25 seasons, owner Mike Kipp said the mood this last week has been a mirror image of the pervasive gloom that catastrophe brought to the city last year.

"It really is the reverse of the Air Florida crash," said Kipp. "Everyone has a reason to talk to everybody else. This time, though, everyone's up. We need it. Times are kind of hard."

Ubiquitous as Redskins fever may seem (and unrelenting media coverage makes it seem more prevalent than it is), it hasn't infected everyone.

Anita Beauchamp of Rockville, for example, remains fever free. The Hogs? "What are they?" she asked defiantly. John Riggins? "Never heard of him," she said proudly. For the evening's game, the Vienna-born woman has planned her regular antifootball ritual. When her husband James turns on the television set, she will go upstairs, play with her parakeet and sing.

"I'm just amazed at all the fuss made about this football thing," says a white-haired woman who, fearing a Redskins backlash, wants only to be identified as "one of the old ladies from Leisure World" in Silver Spring.

"Are these football players more important than the professionals who teach our young or heal our sick?" she asks. "And you wonder where we place our values nowadays. You can see these values by looking at the salaries we pay those football people. Of course, I'm being a wet blanket."

Since the 1960s, when professional football became a national obsession, sociologists and assorted thinkers have criticized the game as a dark celebration of society's sickness, and said things like: The violence is a vicarious release for sedentary, paper-pushing people. Frenzied fan response is a form of tribalism--a great, phony emotional fix. Emasculated men find reassurance in a spectacle where contestants "prove" their manhood. Football remakes human beings in the image of machines.

These claims, heard so often in recent years as to have become cliches, probably contain some truth, says Arrasmith, the man who punched his hand through the paneling of his house.

But in Washington, at least, Arrasmith believes pro football does something more for those who watch it.

"One of the things that a lot of us miss is personal accountability," says Arrasmith, who finds it difficult to explain precisely what he does with computers for IBM. "The Redskins, however, are accountable. They publicly take risks and chance failure. They are not ashamed when they lose. When they win, to a certain extent, it is my victory. You can be proud of a man from your town."