With a new single-elimination format replacing the controversial round robin of past years, the 13th Volvo Grand Prix Masters tennis tournament opens Tuesday night at Madison Square Garden. The tournament officially concludes the 1982 Grand Prix tour.

Jimmy Connors, the '82 Wimbledon and U.S. Open champion, is seeded No. 1, having accumulated 3,355 points. Guillermo Vilas amassed 2,495 points on the tour and is second. Ivan Lendl and John McEnroe, with 2,313 and 2,305 points, respectively, are third and fourth. These four players will each receive first-round byes in this new 12-man format.

The winner of the singles will receive $100,000 from the Masters' total purse of $400,000.

The Men's International Professional Tennis Council, which sanctioned this event, has sought from its inception to make this event a playoff for the 81-event, year-long tour. The public thirst for a competitive vehicle to determine who's No. 1 has led to record crowds at previous Masters events.

I played in the first Masters, in Tokyo in 1970. Professional tennis was just 2 years old then and the temptation to emulate the other professional sports was overwhelming. Former Wimbledon and U.S. champion, Jack Kramer, who conceived of the Grand Prix format, constantly asked, "What's the use of connecting all these worldwide events if we don't wind it up with a shoot-out by the best players?"

Now with Volvo as only its fourth sponsor in 14 years, the Masters enjoys the third-highest television ratings for tennis events. The previous winners include some of the sport's greatest players: 1970, Stan Smith; 1971-2-3-5, Ilie Nastase; 1974, Vilas; 1976, Manuel Orantes; 1977, Connors; 1978, McEnroe; 1979-80, Bjorn Borg; 1981, Lendl.

Connors is pumped up. "Hey, I love New York City," he says, "they're my kind of crowd. New Yorkers always come to sports events cheering for one side or the other. They're not wishy-washy. I like that."

Connors' competition is formidable and there is little room for error with this revised format. He opens Friday against the winner of the Steve Denton/Johann Kriek match, after which he would meet Lendl, who plays the winner of the Vitas Gerulaitis/Yannick Noah match.

In the bottom half of the draw, Vilas plays the winner of the Jose Higueras/Andres Gomez match and McEnroe plays the winner of the Mats Wilander/Jose Luis Clerc match.

In previous years, a round-robin format was used. This caused many problems, the most serious being that some players appeared to tank matches they considered unimportant or even disadvantageous to win. In a controversial 1980 match, Lendl lost to Connors when a win would have meant a semifinal meeting with Borg.

I remember Connors casually talking to me in the players' lounge just before that Lendl match. It was around 11:30 p.m. and he rhetorically said, "What do I do? If I beat the guy, I play Borg in the semis. If I lose to him I play Vilas."

"You have no choice," I told him. "Your fans here would crucify you if you threw a match. That's not your image. Even though you play Borg if you beat Lendl, you, Jimmy Connors, must play to win."

And he did. Connors defeated Lendl, 7-6, 6-1, and then lost to Borg in the semis. His fans stayed on 'til 1 a.m. and booed Lendl as he left the court.

There were other fiascos. Borg once had a straight-set apathetic loss to Gene Mayer. And last year, McEnroe went to a late-night rock concert after he was erroneously assured he had already won his round-robin group. He hadn't.

(Incidentally, Mayer had a place in the Masters but didn't want to play an extra tournament to protect his spot. So he wound up 14th.)

The prize money has always been a controversial subject. The Grand Prix bonus pool of $3 million is apportioned among 32 singles players and 16 doubles teams; $2.4 million is allocated to singles and $600,000 to doubles.

The top players have claimed for years that they are underpaid, some saying that the distributions are skewed too much toward the bottom. Conversely, the middle and lower-ranked players snicker at such complaints. Journeyman players talk of under-the-table payments received by almost all top players from tournament organizers around the world plus the enormous sums derived from endorsements.

Connors and Vilas alone will share $1 million in bonus money--a third of the total. During the Masters, Bjorn Alstrom, the president of Volvo USA, will hand Connors a check for $600,000 for finishing first in the bonus pool. Vilas' check is $400,000 for second place.

The Grand Prix tournament directors are primarily concerned with three things: the rival WCT, television coverage and exhibitions. "Let's face it," says Ray Benton, the Masters director, "a big first-place check attracts the big names and big names attract TV."

No singles player is seriously affected by injury. Connors claims he is ready, although his bad back will cause him to shorten his 1983 schedule. McEnroe has learned to live with his suspect left ankle. Higueras' hand blisters are healed and he has recovered from hepatitis, which sidelined him for most of 1981.

Lendl, last year's winner, says in a matter-of-fact tone, "I'm ready to play."

I'm picking Connors to win because he's got a good draw, he's in shape, he's got a winning record against Lendl and he loves New York. Lendl is my second choice because he just beat Connors in a tune-up event in Chicago.

And McEnroe? "No rock concerts, that's for sure."