Joe Carrico, the outgoing president of the United States Tennis Association, called me into his office just under the stadium court at the National Tennis Center. "Tony (Trabert) has decided he's had enough as captain of the (U.S. Davis Cup) team," Carrico said. "The executive committee has thought about it and all of us want you as our next captain."

The proposition, Sept. 4, caught me by surprise. I hadn't had any inkling until two days earlier that Trabert planned to resign. He had been captain for five years, and we had won the cup twice (1978, '79) in that time. Our players are favored to win any Davis Cup against any nation on any surface. But a history of the annual competition reads otherwise.

Our problems since the early 1970s involve getting those top players to play.

The primary difficulty is the lower priority accorded the competition by the likes of Jimmy Connors, Vitas Gerulaitis, Roscoe Tanner, Harold Solomon and Eddie Dibbs (but not John McEnroe, who loves playing Davis Cup).

It's not that these players don't want to participate at all. T's just not at the top of their lists of "musts," like it was in the years before open tennis. The world outdoor attendance record for tennis still is the U.S.-Australia Davis Cup match in Sydney in 1954. It drew 25,000 frenzied Aussies in their 3-2 loss to the Americans. Trabert himself played that match, and notes, "it was wild."

Money is one obvious reason for the U.S. players' lessened interest. Jimmy Connors can make $30,000 a day playing an exhibition. But the players who are finally named to the official four-man Davis Cup squad get $10,000 for each match, and that's for an entire week. All expenses incurred are paid by the USTA, under whose aegis the U.S. team is formed. But, as you can see, for some players, $10,000 a week is pocket money. That may change, however, with the anouncement that the winning nation will earn $200,000 thanks to a $1 million prize donation from a Japanese electronics firm, NEC.

Another formidable problem until recently was the time involved for the Davis Cup campaign. It used to be at least a five- to seven-week commitment, 12 months in advance. The Davis Cup matches are played during vacant weeks on the Volvo Grand Prix schedule. Most players don't like committing themselves that far in advance. Something better might pop up.

Three months ago, at the annual meeting of the Davis Cup nations in Vienna, a new format was approved, to take effect, in next year's competition. vThe top 16 nations will meet in a single-elimination playoff in just four selected weeks of the year (those nations not good enough to make the last 16 will play in regional competitions for a spot in 1982). The fourth and final weeks would be a mutually agreed upon date, so as to allow for geographical considerations (summer in Argentina is winter in the United States).

Initial player reaction to the new plan ranged from "It's about time" (McEnroe) to "It's a step in the right direction". (Stan Smith).

My chief problem as the new captain will be moving the Davis Cup quest up on every player's priority list. This new format and a possible raise from the $10,000 fee per match should help.

Stickler still is the problem of resolving differences the players have with the USTA and among themselves. Remember, professional tennis players are not too fond of linesmen, much less someone telling them where to place their serves.

The draw for the 1981 competition shows that we have our work cut out for us. If we get past Mexico, the Czechs with Ivan Lendl await us. After that, Sweden and Bjorn Borg or France with Yannick Noah appear likely. I would feel very strange indeed as captain of the U.S. team playing against Noah, who also is black. Now that would be a first. But I know his weaknesses.

Argentina should get past West Germany and Romania should lose to Brazil, because Ilie Nastase is suspended for 18 months from Davis Cup play. Italy should get by Britain and New Zealand looks a sure winner over Korea.

We have a choice of ground (better known as the home-court advantage) in our first three encounters, no matter who the opponent happens to be. All of our best players excel on fast, hard courts -- except Solomon, who prefers a clay surface. We have an outstanding record at home.

One former captain, Dennis Ralston, mockingly offered me his condolences upon hearing of my appointment.

"it's a lot of fun, but it's a lot of headaches, too," he said. "if you win, it's because you had great players. If you lose, it's your fault."

We'll see. The Mexico match is March 6-8. First things first.