The afternoon that Bjorn Borg stomped all over Jimmy Connors in the semifinals at Wimbledon this summer, Washington sports attorney Donald Dell -- a former U.S. Davis Cup captain and frequent television commentator on tennis -- expressed an interesting opinion. "I think the first time Connors hears people referring to him as 'one of the best half-dozen players in the world,' " Dell said, "will be the day he quits the game."

Of the 128 men entered in singles in the U.S. Open tennis championships, which will begin Tuesday in New York, probably none has a more desperate psychological need to win than the defending champion, Connors.

Defeat here would destroy his personal grand illusion that he, rather than Borg, is the best player of the decade -- a notion Connors has clung to and peddled with the fervor of a snake oil salesman long since it ceased to be realistic.

James Scott Connors will celebrate his 27th birthday during the Open, on Sept. 2, and will undoubtedly look back on his 26th year with mixed emotions.

Personally, he appears to be happier than ever before. He secretly married former Playmate-of-the-year Pattie McGuire last fall and became a father on Aug. 1. Friends say he has been walking on a cloud since the arrival of David Brett Connors -- "a cute little guy, a champ," according to the proud papa. At the rate Connors has been passing out snapshots of his boy to buddies, casual acquaintances and strangers, you might want to consider running out and investing in Fotomat.

But professionally, Connors seems as inwardly distraught as he is outwardly swaggering. He does not want to acknowledge what the world already knows: that his arch-rival Borg has established clear superiority over him, and that ascending John McEnroe could shortly relegate "Jimbo" to third place on the totem pole at the pinnacle of the tennis world.

Connors was undeniably brilliant -- a paragon of internal combustion and controlled aggression -- in winning last year's Open. He clobbered McEnroe and a subpar Borg (blistered thumb) in the final two rounds in six straight, devastating sets.

But since then, both rivals have gotten revenge and made Connors look like a man condemned to running up a down escalator.

McEnroe beat an injured Connors en route to the Grand Prix masters title in January, and whipped both Connors and Borg to win the World Championship Tennis title in Dallas in May, confirming his coming of age.

Borg won his fourth French Open on clay in June and his fourth consecutive Wimbledon singles title on grass in July. He has won his last 22 matches, including the recent Canadian Open final over McEnroe. He also has beaten Connors in seven of their last 10 meetings, including all three this year -- on clay in Florida, cement in Las Vegas, and grass at Wimbledon. Connors has yet to get more than three games in any set against Borg in 1979.

After McEnroe beat him in Dallas, Connors promptly chartered a private jet and flew off in a huff. When Victor Pecci upset him in the semifinals of the French, the world's premier clay court championship, he was more civil. But after Borg walloped him at Wimbledon he was gone within 10 minutes, the latest in a series of profane and graceless exits for which he is notorious.

Connors played well against Borg at Wimbledon and still got drubbed, 6-3, 6-2, 6-2. This prompted many observers, including some top players, to wonder whether he will ever again beat the Swede in a match of consequence.

Connors, not surprisingly, claims he is a new man now that he has "three mouths to feed." It is telling that he said, within days of his son's birth, "I have to win now so that he'll be proud of me."

Connors has played on a hungry high in his two tournaments since fatherhood, winning the U.S. Clay Courts at Indianapolis over Guillermo Vilas and a second-level Grand Prix tournament at Stowe, Vt., on the same surface (an asphalt-based hard court called Deco Turf) on which the U.S. Open will be played at the National Tennis Center in Flushing Meadows, Queens.

Connors recently has tended to attribute his losses at Paris and Wimbledon to the impending arrival of his first born."My game has been a little rocky because I had other things on my mind. . . . I wasn't really with it the last few months," he said at Indianapolis. There have been similar variations on the theme.

This plea-copping is very much in character, for Connors historically has been an expert at explaining away failure. This is one of his least appealing traits -- along with a proclivity for using crude language and gestures -- and has contributed to his reputation as one of the all-time bad losers.

Connors never, never gives an opponent credit for beating him. To hear Jimmy tell it later, either he was injured, or his mind elsewhere, or his "serve took a vacation." His ego seems incapable of coping with the idea that the man on the other side of the net simply played too well. It is an unbecoming blind spot.

Now we are back to the U.S. Open, the tournament that has done the most for 'connors' psyche over the years. He has been in the final five years in a row. The last man to do that was Big Bill Tilden in the 1920s. Connors has won three times, in 1974-76-78. Curiously, he has never won in an odd year.

Connors has an astonishing record in U.S. national championships. Last year he swept the U.S. Indoors, Clay Courts and Open. This year he already has defended the Indoor and Clay Court crowns, bringing his total of national titles to 16. He likes to boast that he owns any championship with the letters "U.S." in front of it.

The pace and bounce of the courts at Flushing Meadows favor Connors. He polished his incomparably physical game on hard courts as a teen-ager, while Borg still finds them somewhat foreign.

But Borg is on a crusade. He has practiced on hard courts and geared his whole summer toward winning his first U.S. Open, the third leg of a possible French-Wimbledon-U.S.-Australian Grand Slam. In his only tournament since Wimbledon, the Canadian Open this week before last, he did not lose a set and thrashed McEncore, 6-3, 6-3, in the final.

The fact is that Borg is unquestionably the best player in the world right now, on any surface. While Connors' game has remained at the same level or even stagnated in recent years, Borg's has improved markedly.

Borg wins many points outright on his serve now, which Connors has never been able to do. Borg is steadier and more punishing from the back court than any other player alive, and he has systematically eliminated the weaknesses from his game. Connors, meanwhile, has not. He remains vulnerable on the forehand, especially when he has to generate his own pace.

Connors, of course, steadfastly refuses to admit any of this. To him, it is unthinkable. Like a Muhammad Ali with a racket, he goes on proclaiming himself The Greatest. He truly thinks he is. When the truth becomes so obvious that he can no longer delude himself, he might well decide to hang up his sneakers.

That is why this U.S. Open is so vitally important to him.