At their best, Pete Sampras and Andre Agassi were largely regarded as peers in the talent department.

So what explains Sampras having nearly twice as many majors as Agassi and leading their head-to-head series 20-14, including 6-3 in the majors? The edge in the majors was largely due to Sampras’ steadiness and Agassi’s more unpredictable qualities; in his autobiography, Agassi described it as his rival’s enviable “dullness,” his lesser need for inspiration to win majors.

Their head-to-head record may have had to do with a unique aspect of the Sampras game: With his huge first and second serves, he could count on winning his service games more reliably than most players, and this allowed him to take chances on the opponent’s service games.

This was evident in the matches he won against Agassi in 1999; knowing that no one could defeat Double-A by out-rallying him, Sampras either chipped or floated his backhand, forcing his rival to generate his own pace.

When he got a ball to the forehand wing, or had time to really swing at a backhand, Sampras went for winners. This made for more errors from The Pistol but caused huge headaches for baseliners, who usually need to hit a lot of balls to really start playing their best. Agassi would later say that Sampras could play really well against him and win 7-6, 7-5. He then added that Sampras could also play rather poorly, and win 7-6, 7-5.

This type of opponent was not unbeatable, certainly not against a player of Agassi’s caliber, but required perfect execution. Perfection, of course, is not easy, especially since Sampras didn’t allow Agassi to do what he did best, which was to work the opponent’s legs over and then finish him off.

Going into the Australian Open 2000, Agassi had just finished a career-best year, capping a return from a ranking of 140 in 1997 to win Roland Garros and complete a career Grand Slam. He’d been runner-up at Wimbledon, won the US Open, and finished the year at No. 1 for the first time.

However, he’d lost to The Pistol in three of four meetings, and a straight-set loss to Sampras in the finals of the World Tour Championship was not a fitting way to end his best year.

But at least it gave him motivation. In the first half of the new decade, the now 30-something Agassi took better advantage of tennis’ brief offseason than any other player, getting into his best shape with the help of trainer Gil Reyes. Not worn down by the matches, the traveling, and setbacks that come with life on tour, his stock was highest Down Under.

Plus, with his unrivaled ability to make an opponent run, Agassi thrived in the hottest temperatures on the ATP calendar.

Sampras had tied Roy Emerson’s Grand Slam record of 12 titles in London and needed one more to set a new mark. Still, hampered by an injured back, Sampras’ 1999 campaign was shortened, leaving him at No. 3 despite his Wimbledon and Tour Championship wins, as well as his positive head-to-head record with Double-A.

This put them in the same half of the draw, and meant that fans were likely to get the championship match they wanted, but a couple of days early.

Agassi was playing the best tennis of anyone in Australia prior to their semifinal encounter; he’d dropped only one set, and that was to the huge-serving Mark Philippoussis, a threat for the title himself. Sampras had seen a few more struggles, dropping a set to the underpowered Slava Dosedel and having to rally down two sets to the undersized Wayne Black.

Not that this mattered; Agassi had been crushing opponents going into the Wimbledon and World Tour Championship finals, but in both cases having the Las Vegan across the net had galvanized Sampras, allowing him to turn in peak performances.

He did start off slower than Agassi that night in Melbourne, though, with Agassi grabbing a break and winning the first set 6-4. In the second, he turned the match around, getting a break of his own which, typically, was all he needed to win the set. In the third, the two played as equals for 12 games, with neither one able to put a dent in the other’s serve.

At least not until the tiebreak. Here, Sampras came alive, opening with an acutely angled running forehand to win the minibreak, liberating him to hit out on every shot. Agassi committed no unforced errors and yet lost 7-0; the announcers described it as “complete destruction.”

Agassi went back to work in the fourth set, hoping to take care of his service games, extend the match and give his fitness edge a chance come into play later. To do that, though, he’d have to find a way to win the fourth. To do that, he’d have to win one of the all-time great tiebreaks.

What is it about fourth-set ‘breakers between great rivals at majors? Borg-McEnroe 1980 can’t be topped for its mounting, seemingly endless tension, and Federer-Nadal 2008 can’t be beat for its spectacular conclusion.

But in terms of shots, and only shots, Sampras-Agassi 2000 may be the best tiebreak ever played. Its virtues really have to be witnessed (and you can do so here ) to be appreciated, but here are the basics:

Over those 12 points, Pete Sampras committed no unforced errors, finished two points off at the net, and hit one running forehand pass seemingly from the top of his Nikes. He also hit two aces, which may not seem like a major feat from him, until you consider that both came on second serves. All this, and he lost the fourth set.

Andre Agassi committed no unforced errors, no forced errors, and missed not one first serve: Every ball he could get a racket on he put back into play. His serving forced three misses from Sampras, and a thoroughly crushed backhand caused Sampras to miss one volley.

Agassi also hit one backhand winner and two off the forehand wing, one of which came on set point. Upon winning it by a score of 7-5, Agassi celebrated with more enthusiasm than he would upon claiming championship point that weekend.

The fifth set was only a coda; Sampras had strained a muscle in his hip early in the match and had very little left. Despite hitting 37 aces on the night, Sampras would go home the loser, his quest for Grand Slam No. 13 postponed.

World No. 1 Agassi faced No. 2 Yevgeny Kafelnikov in the final, in a match whose highlights are worth watching just because of the strokes: The two cleanest hitters in the top 10 facing off, producing an untold amount of forehand and backhand winners.

Still, though Agassi started slow on championship Sunday, the outcome of that match was rarely in doubt. Double-A had stamina enough to play all day, and as well as Kafelnikov could pound the Penn, the 10 Commandments of tennis tell us, “Thou shalt have no other ball-strikers before Andre.” He won in four sets to capture his sixth major, and second Down Under.

Even before that, though, he’d created a memory fans would savor. Sampras would get the best of Agassi in most of their major meetings; but the one where he didn’t was their best match of all.