Ah, the mysteries of sports finances.

During the past several days, the top women tennis professionals have been hammering away at the Capital Centre, earning magnificent sums of money and generating reams of copy from some three dozen reporters on hand to chronicle the event. It is a publicist's dream come true.

But how would an accountant view the whole affair?

Typically, sports promoters don't like to discuss the crass realities of who makes what -- except to trumpet the payoff to be paid the winners. That, after all, is what helps turn a simple tennis match between two very fine players into a professional sporting event.

But if it is viewed strictly as a dollars-and-cents proposition, the Colgate Series Championships, which culminates tonight when two teenagers, Tracy Austin and Andrea Jaeger, meet, could not be described as a financial windfall for the business sponsors.

While the godfather of the tournament is the Colgate-Palmolive Co. in New York, a number of Washington concerns have pitched in to make the event work. At the head of the list of local sponsors is First American Bank, a subsidiary of the holding company, Financial General Bankshares, which peddled tickets to the five-day event at the holding company's 146 bank branches.

William Fitzgerald, Financial General's vice chairman, got his bank involved in sponsoring the second straight year. As it happened, this year Fitzgerald is also treasurer of the Reagan presidential inaugural, so during the past several weeks he has been splitting his time between this town's two big spectaculars.

Fitzgerald won't say how much his company contributed toward financing the matches, except to allow that it was a "modest amount." For Fitzgerald, himself a tennis addict, involvement in the event is a matter of the heart. The banker's other off-court activities include being treasurer of the National Tennis Foundation and a board member of the Tennis Hall of Fame in Newport, R.I.

Promoter Edythe A. McGoldrick, a vice president of Capital Sports Inc. in New York, came up with the idea of sponsoring a series of tennis tournaments with a cash-prize pool for the winners after a season's play. She brought the idea to Colgate, which already was heavily into women's sports. From 1976 through 1978, the tournament was played at Mission Hills, a Colgate-developed resort community in Palm Springs that the company used the tournament to promote.

According to McGoldrick, Mission Hills began to thrive, so the company decided to move the tournament to an eastern city to get maximum publicity. Washington was a logical choice, says attorney Raymond S. Benton, who with three of his law partners, including former circuit player Donald Dell, also operate a sports marketing firm here called ProServ Inc.

"The demographics of the serious tennis player is characterized by highly educated, upper-middle-class, aggressive people. And that profile certainly fits Washington," says Benton, who is tournament director of the Colgate championships.

Normally, the financial angel for a major tournament such as this can look to television to help defray expenses a bit. But unfortunately for Colgate, the timing of the event made it unsalable to network television. The pro-football playoffs took place yesterday, and the three major networks apparently were not interested in being involved at all in tennis during the play-off weekend. Indeed, there were no matches scheduled yesterday because tennis fans are probably footballs fans, too, and the huge Capital Centre would be left empty.

Without the networks, coverage of the event in the past two years has been left to cable TV, which pays only a modest amount to the tournament promoters.

By contrast, CBS will devote five hours to -- and pay handsomely for the right of -- televising the men's Volvo Grand Prix Masters tournament at Madison Square Garden next weekend, the pause between the playoffs and the Super Bowl. (Colgate was replaced by Volvo in 1980 as the chief sponsor of the men's Grand Prix and its climactic Masters tournament in New York.)

McGoldrick said that when the Women's Tennis Association meets here today the timing of the tournament is sure to be a main topic for discussion. "We've got to solve that somehow," says McGoldrick.

Another topic will be a reported bid by Toyota to assume sponsorship of the event when Colgate's contract runs out at the end of the 1981 season. Clearly, Colgate is not involved in the tournament for profit. But apparently the company thinks that financing women's tennis -- which gives it nine months of worldwide publicity -- is worthwhile, particularly since about 80 percent of the customers for its products are women.

As for the local sponsors, they seem to have been drawn in through a combination of self-promotion and civic pride.

"It means that we, as a store, are involved in what is today," says Bloomingdale's director of public relations Vicki McGugh. "It's to bring a whole new element to the city. We're reaching out."

Bloomingdale's plugged the tournament with bargains and brunch. Tickets were loss leaders at the store's sports clothes department, the Bloomingdale's Athletic Club, where customers got coupons exchangeable for two tickets for the price of one.

As part of the promotion deal with Bloomie's, tennis wunderkind Tracy Austin showed up for a brunch at the store for press and customers, while others were entertained by the store at the Capital Centre.

Drug Fair also offered coupons redeemable for tickets. In exchange, Drug Fair got advertising at the Capital Centre and box seats at the matches.

Pugeot supplied the cars to the tournament, and 7-Up, manufactured by sponsor Philip Morris Inc., was designated the "official drink." Players were lined up to give lessons to customers and friends of Xerox Corp., a sponsor.

Contestants, press, international tennis officials and others occupied 125 rooms at cut-rate prices at The Four Seasons hotel, one of Washington's poshest hostelries. And players could stroll up M Street to get their hair coiffed free of charge at the tournament's "official" hairdresser. CAPTION: Picture 1, Hana Mandikova, tennis' latest sensation, reaches for a volley during the Colgate championship at the Capital Centre.; Picture 2, Nineteen-year-old Hana Mandikova received $115,000 for finishing the 1980 season with the most points. Photos by Richard Darcey -- The Washington Post