The Washington Bullets averaged 11,408 fans last season; the Washington Capitals averaged 10,931. Yet a Washington Post survey of area sports fans shows that professional basketball is four times as popular as pro-hockey.

Why don't the Bullets draw crowds four times larger?

"We can't get that many people in Capital Centre," said Marc Splaver, the Bullets' public-relations expect.

That was a joke, yet in a way it revealed the Bullets' problem. The team must turn away fans for big games with Phidadelphia and Los Angeles, yet plays to as few as 6,000 when the opposition is less attractive.

"It's no suprise," said Bullet president Jerry Sachs. "Sometimes it become a question of economics, how often you can come to a game. Fans in the lower income brackets get some fulfillment out of watching the NBA on TV and most probably pick their spots. They come to see their favorite teams and favorite players. We have to build a base so high that we have less of a peaks-and-valleys situation."

The Post surveyed 1.017 persons in the District and in Montgomery, Prince George's, Arlington, and Fairfax counties and the city of Alexandria. Those participating were 16 or older and had attended at least one professional sports event in the last 10 years.

Of that group, 59.7 per cent considered pro basketball one of their three favorite sports, a ranking second only to football. Hockey placed fifth, with 16.7 per cent.

But in comparing basketball and hockey fans, by income, from among the overall survey, basketball drew a significantly higher proportion of its fans from those with annual family incomes of less than $10,000; hockey drew heavily from those with annual family incomes of more than $30,000.

Another factor is hockey's apparent success in persuading women to attend. Women made up 43 per cent of the survey but only 40 per cent of the basketball fans. The hockey figure was 46.5, and it was higher than 50 per cent in Northern Virginia and Prince George's County. Overall, 5.4 per cent of women called hockey their favorite sport, only 3.6 per cent of men.

"We are very conscious of the interest among suburban women and have figured a lot of our marketing work around it," said Capital president Peter O'Malley."

Despite the comparatively low rating for hockey in the survey, O'Malley said, "I'm very encouraged. That's a hell of a number for hockey, considering it's a new sport and few people around here were previously exposed to it. Kids grow up with footballs, baseballs and basketballs in their hands, but I think we're making inroads."

The survey was confined to the immediate area and O'Malley indicated the Capitals' appeal was strong in the outlying suburbs, with the circle of interest hitting Westminster, Baltimore and Richmond, and with significant group sales as far away as Pennsylvania, Norfolk, Harrisonburg, Va., and Shepherdstown, W. Va.

Although the Bullets attract groups of several hundred from Richmond for weekend games and draw about 3 per cent from Baltimore, their appeal seems more centralized.

Race is an obvious factor in the lure of the two sports. Blacks, especially young blacks, are fond of basketball in far greater numbers than their share of the population. Hockey draws its fans almost entirely from among whites.

"We do a considerable amount of promotion in the inner city," said Chip Reed, the Bullets' marketing specialist. "We solicit black businesses and social groups, and we sponsor clinics and bring in patrols and recreation department groups. We have D.C. high schools play preliminaries - the Maryland public schools are not allowed.

"We're not as successful as we want to be. I think public transportation is the big thing. If it ever gets out here, it will make a big difference."

Another interesting item is the revelation that 52 per cent of those listing hockey as a favorite sport are college graduates, a full 10 points over the proportion of college graduates in the general survey. That fits in with a Capitals demographic study that showed 81 per cent of hockey fans were in the professional-foreman categories, with 53 per cent college graduates.

Where hockey has benefited from women's interest, tennis also has mushroomed with female involvement. In the survey, 23 per cent of the men said they had attended a pro tennis match, while 27 per cent of the women said they had been to at least one.

Tennis ranked fourth among all sports, with interest highest in Northern Virginia and lowest in Prince George's. It is no accident that Northern Virginia has the most courts in the area and Prince George's the fewest.

The folks who fill the boxes at the Washington Star tournament - more than 100 are on a waiting list - give the impression that tennis is an upper-income sport.But the survey showed broad appeal among income groups, with surprising strength among those at the bottom of the ladder.

"We're trying to reach people just picking up tennis, because all you have to do is look at the courts and see the hundreds of hackers out there," said Sara Kleppinger, an associate of tennis impresario Donald Dell.

"We can tell a lot of people coming to the tournaments are new by some of the questions. They'll call up and ask, 'What game is tonight?' Or they'll call on Monday, when the tournament opens, and ask, 'Who plays Chris Evert in the finals?' The Chris Evert syndrome has taken tennis beyond its previous boundary of interest."

Among blacks, tennis ranked low in the District, but nigher in the suburbs, particularly Montgomery County.

Soccer ranked ninth among the 12 sports surveyed, with major interest shown in Montgomery County and Northern Virginia. Despite the large number of youth teams in Prince George's, soccer was rated guite low there, only 3.6 per cent of that county's respondents listing it among the top three.

Like hockey, golf is predominantly a white sports, whites accounting for 90 per cent of those who listed golf among their favorites. Golf also received below-average support from women and was rated low by those under 35, with interest increasing among older persons and reaching a peak among those 51 to 64.

Bowling interest was greatest among persons over 50, in lower income brackets and living in the District, a somewhat odd finding considering the District's limited facilities.

Auto racing rated highest among those 16 to 25, with women and those in upper income brackets showing little interest. However, it must be noted that most activity in the area is confined to drags and stocks, while sports cars are generally the lure of the wealthy, as witness the advertising that frequent, the sports-car magazines.