When Gary Williams left American University to become basketball coach at Boston College, one of the perquisites making the job attractive was a three-year contract with New Balance, a Boston-based maker of running shoes that was entering the basketball market.

Other coaches and officials of other shoe companies say Williams is receiving $30,000 annually from New Balance as a consultant to the company. Williams says $30,000 is too high, but declined to say what he is receiving.

Other perks include endorsements, summer camps, television shows and courtesy cars, but shoe contracts are the most visible perquisites associated with major coaching jobs. You can tell the company paying the coach by the brand of shoes his team wears; because of those deals, companies also will provide free equipment for the team.

Last week, in fact, Georgetown was told that center Patrick Ewing could not wear a T-shirt with the Nike logo on the sleeves under his game jersey because it violated an NCAA rule: that shirt was not available to the general public.

The general public can buy the same Nikes that Patrick Ewing and his teammates wear, however, and that visibility sells.

Five years ago, when Nike started paying 17 college coaches to be consultants, including Maryland's Lefty Driesell, the company's total sales were $71 million, about 10 percent of which came from basketball shoes. In the most recent fiscal year, Nike sales were $693.5 million and basketball shoes accounted for $146 million, or more than 20 percent, according to a company spokesman.

Nike has driven to surpass Converse Rubber Co. as the dominant name in basketball shoes. In 1978, Converse had total sales of $150 million, of which $105 million, or 70 percent, came from basketball shoes; last year, Converse's total sales were $205 million, with $150 million in basketball shoes.

Converse now signs coaches to contracts, the same as Nike, Puma, Pony, Pro Keds and Adidas, the other leading brands of basketball shoes. According to the companies, Nike has 75 Division I coaches under contract and Converse has 170; there are 277 colleges and universities in Division I.

Now, according to industry sources, some top coaches receive as much as $50,000 annually; according to one source, the top coaches signed by Nike also are offered the opportunity to purchase 300 shares of Nike stock at a price below current market value. Nike declined comment about the stock options.

Digger Phelps of Notre Dame, under contract to Pony, is said by industry sources to be the highest-paid consultant, at about $50,000. Driesell and Georgetown's John Thompson, both with Nike, reportedly earn $25,000 from the company, the same range as other highly regarded coaches under contract to the shoe companies.

Nike's success--and what makes the cash payments more palatable to universities--also can be attributed to giving the schools $8,000 to $12,000 worth of equipment annually.

When Driesell was among the original group signing with Nike in 1978, he received about $8,000 annually, one of the top amounts paid coaches at that time. Now $8,000 is the average payment to the 75 coaches under contract to Nike, according to Tim Renn, a Nike spokesman.

Joe B. Hall, the coach at Kentucky, reportedly turned down a $40,000 annual offer from Nike and remained with Converse, as has North Carolina's Dean Smith, according to industry sources. Each of them reportedly receives $25,000 annually from Converse, according to the same sources.

Nike has been very aggressive on the East Coast, and especially in the Big East Conference. Converse is strong in the Southeastern, Southwest and Big Eight conferences.

Seven of the nine Big East schools use Nike; the two that don't are Boston College and Pittsburgh.

Locally, Maryland, Georgetown and George Mason use Nike; George Washington and American use Pony; Navy uses Converse, and Howard uses Adidas. Howard Coach A.B. Williamson is the only local Division I coach not under contract to a shoe company; he says coaches at Howard are not allowed.

"I wouldn't turn down anything I could get," Williamson said. "But I don't get the opportunity to get involved. Some coaches travel all over the country in the summer, even to Hawaii, for the shoe companies. I stay in Washington."

When coaches first started getting contracts from the shoe companies, the board of the National Association of Basketball Coaches discussed the matter thoroughly, said Smith, one of the leaders of the NABC hierarchy.

"I talked to my chancellor and athletic director," Smith said. "It's like a member of the medical faculty or business school being a consultant to firms. We (the NABC) decided it was ethical. The average time a Division I coach is at a school is three years . . . You have to treat it accordingly."

"It's time somebody did something about giving coaches some kind of security," said Dale Brown, Louisiana State's coach. "How many athletic directors, how many assistant athletic directors, how many sports information directors, how many sportswriters are at the same job they were 15 years ago?"