Match play presents the extremes for those who watch professional golf. The experience can range from the very worst (think a 36-hole final between two obscure players that turns into a blowout) to the very best (an impossibly taut Sunday at the Ryder Cup).

The WGC-Dell Match Play Championship was much closer to the latter. The five days at Austin Country Club saw many hard-fought matches contested among the best players in golf on an interesting course. Most importantly, on the weekend, it had what match-play tournaments need most: showdowns among stars.

That was the simple formula of the original World Match Play at Wentworth near London, and why the event in its heyday was special. Sure, it had only eight contestants when it began in 1964. But all were big names, especially the original Big Three of Arnold Palmer, Jack Nicklaus and Gary Player. Palmer won the first inaugural event. Player won five of the next nine, twice beating Nicklaus (who won the event only once) in the final. Seve Ballesteros won five times , Ernie Els a record seven, and Palmer, Greg Norman, Nick Faldo and Hale Irwin were all multiple winners.

The inception of the WGC-Accenture Match Play Championship in 1999 eventually marginalized the Wentworth event, not to mention undermined the format itself. It seemed like a lose-lose when in three of the first four years of the 64-player WGC, the final matchs consisted of Jeff Maggert versus Andrew Magee, Steve Stricker versus Pierre Fulke, and Scott McCarron versus Kevin Sutherland.

A year ago, the WGC event was dramatically improved when, in order to avoid the one-and-done reality of single elimination and give the best players more opportunities to assert their superiority, round-robin pool play was established to whittle the field to 16. This year’s final day featured newly installed World No. 1 Jason Day beating No. 3 Rory McIlroy, 1 up, in a morning semifinal, followed by Day defeating Louis Oosthuizen, 5 and 4, for the finale.

It’s easy to give these showdowns too much significance. At the highest level of pro golf, it’s arguable that there are no upsets over 18 holes of match play. Still, close watching leaves strong impressions. In head-to-head contests, strengths and weaknesses seem more apparent, and intangibles, subjectively judged as they may be, take on more importance. Fairly or not, match play seems to make it easier to decide who is better.

Player, the winner of nine major championships, excelled at match play. In a phone call last week, the 80-year-old South African—described by Palmer as the fiercest competitor he ever encountered—fondly remembered his victories at Wentworth, especially an incredible comeback against Tony Lema in 1965 in which he was 7 down after 19 holes. “I wish I could have played more majors at match play,” Player said. “Match play is about key moments, and I had the ability to rise to the moment.”

Nicklaus agreed. “There was nothing really exceptional about Gary’s game except one thing—his desire to win,” Nicklaus told me several years ago. “I don’t think Gary was a great driver of the golf ball. I don’t think he was a great iron player. He was a good putter, not a great putter. But, when he really needed to be, he was a great driver, and a great iron player, and he made the putt when he needed to make it. Gary, as much as anyone I ever saw, had that thing inside him that champions have.”

Player unabashedly admitted he was driven by an inner desperation to succeed. “I am an animal when it comes to achievement. … I cannot attain enough,” he wrote in his autobiography. He seized pressure moments by using the “bleak awareness that nothing else but this precise shot would do.”

Tiger Woods, a three-time U.S. Junior, U.S. Amateur and WGC-Match Play champion, had the same capacity, perhaps even more than Player. Among the current Big Three, Jordan Spieth has most often demonstrated a special magic when he most needed it. The mercurial McIlroy seems less than manically driven, while Day, though a hard worker who has been seeking Woods’ counsel, can appear fragile. Certainly that seems to be the case physically—Day’s back was touch-and-go in Austin—but also mentally. In the oft-played Golf Channel teaser for the next episode of “Feherty,” the 28-year-old Australian said that in 2011 he was going to quit the game.

For McIlroy and Day, the WGC-Dell Match Play served as toughening tonic. Because of the finality of every hole—and some loose tee-to-green play—McIlroy in his early matches seemed to bear down harder than usual on putts inside eight feet and holed them with authority. It’s his too-frequent short misses in 72-hole events that undermines his ball-striking advantage and saps his competitive attitude. Although he had a bit of a relapse in his Sunday match with Day, McIlroy can go to the Masters more confident that he can handle the greens.

As for Day, his play in Austin established him as a short-game wizard and putter nearly on Spieth’s level, which when combined with his advantage in length over the Texan has made him the deserving his new spot atop the World Ranking. Going into the final against Oosthuizen, Day had gotten up-and-down from around Austin Country Club’s firm, undulating greens a remarkable 19 of 23 times. Perhaps his back wasn’t right, but like the truest champions, Day found a way.

Which might point to the best thing about match play for the world’s best: It amounts to a purifying trial by fire that can illuminate and ultimately burn away weaknesses. And watching that process is pretty great as well.