NAUCALPAN DE JUÁREZ, Mexico — Golfers build their professional careers on the conceit that they are better than everyone else. But since 1986, only 20 players in the men’s game have been able to say, conclusively, that they are No. 1. The brainchild of the game’s first mega agent, Mark McCormack, the official world golf rankings were conceived as a promotional vehicle and have grown to become — what, exactly?
The sixth-longest reign at the world No. 1 spot belongs to Luke Donald, who has never won a major. Phil Mickelson has five major victories but has never been the world No. 1. The ranking, for so long prefixed to Tiger Woods’s name like a royal title, has become much more democratic in recent years.
From 1999 to 2010, Woods twice spent five-year reigns at No. 1. Since Rory McIlroy rose to No. 1 for the first time five years ago this weekend, the top ranking has exchanged hands 19 times among seven players, including Woods.
“I think for a lot of guys, it’s an ego thing,” said McIlroy, who is lurking at No. 3. He can knock off Dustin Johnson on Sunday if he wins the World Golf Championships event at Club de Golf Chapultepec and Johnson finishes outside the top four.
 “It’s not as if I earn more money because I’m the world No. 1 or 39,” McIlroy said, “but it’s just nice to be able to say that you’re the best in the world at what you do.”
Johnson was asked last week if he agreed with McIlroy that the No. 1 ranking was mainly a boost to the ego.
“Yeah, I mean, I guess,” he said.
For Johnson, the world No. 1 ranking is akin to the Grammy’s Lifetime Achievement Award or the Honorary Award at the Oscars. It is earned for one’s body of work. For that reason, Johnson considers it a taller mountain to scale than a victory in one of the majors.
“You’ve got to play very well for a long period of time,” said Johnson, the reigning United States Open champion. “Winning a major is unbelievably difficult, too, but you only have to play well for four days.”
The world-ranking points for each player are accumulated over a two-year rolling period, with an emphasis on recent performances. Johnson, 31, won the Genesis Open in Los Angeles last month to overtake Jason Day, who had been No. 1 for a total of 51 weeks.
The world No. 4, Hideki Matsuyama, who has yet to win a major, also had a chance to supplant Day with a victory in Los Angeles, but he missed the cut. Matsuyama said that the top ranking wasn’t a focal point and that he was not stressing about it, but his results would suggest otherwise. In his first four PGA Tour starts of 2017, he was a cumulative 51 under par. Since he first moved within range of the No. 1 ranking, Matsuyama has played five rounds, over two starts, and is five over.
To become No. 1 would be historic for Matsuyama, who would be the first player from Japan to reach the men’s summit, much as McIlroy was the first to plant Northern Ireland’s flag at the top. For Americans used to sharing the sports firmament with a constellation of compatriots, it can be hard to grasp the intensity
 of the spotlight that the No. 1 ranking attracts in sport-crazed countries where worldbeaters are farther and fewer between.
When Day possessed the title, it also possessed him. The public acclamation became a personal albatross that blurred his identity, with his obligations as the public face of the sport bleeding into his time as a husband and father.
“It’s very, very difficult,” said Day, who became the third men’s No. 1 from Australia, after Greg Norman and Adam Scott. “It’s tough to be at the top of a sport and trying to deal with new things and trying to compete and handle certain parts of your life and be able to put them in boxes.”
As his reign came to a close, Day sounded worn out. He is the only player in the world top 50 not competing this weekend, having withdrawn because of a double ear infection.
“Oh, man, being No. 1 in the world is tough,” Day said before the Genesis Open, adding, “I wouldn’t trade it for the world, even though it is mentally and sometimes physically demanding.”
Yes, well, consider what it was like competing in Woods’s heyday, when he dominated golf the way the University of Connecticut has ruled women’s basketball. For Scott, who joined the PGA Tour in 2003, the road to No. 1 started out as a dead end. “At least the first half of my career, it was just a nonevent,” Scott said. “It was just Tiger by double the points.”
Mickelson could not overtake Woods despite 32 worldwide victories, including four majors, from 1999 to 2010. In the same period, Woods had 74 worldwide titles, including 13 majors. Mickelson had opportunities to reach No. 1 in 2010 but wasn’t able to seize them.
Scott did reach the top spot in May 2014, but his stay was short — less than three months. “I think I probably relaxed when I got there,” he said. “Maybe I should have treated it a bit differently, and I might have stayed there a bit longer. I was just — the sense of accomplishment was great, and I was obviously playing well, so I
didn’t really try and put more pressure on myself to play better or perform like a No. 1.”
The seventh-ranked Scott said one of his “big missions” this season is to join the scrum of players angling for No. 1 “before it’s too far gone for me.”
The 23rd-ranked Mickelson has let go of that ghost. Inducted into the World Golf Hall of Fame in 2012, Mickelson, 46, aspires to join a more elite club than the group of 20 who have graced the top of the men’s rankings since 1986. His goal is to match Gene Sarazen, Ben Hogan, Gary Player, Jack Nicklaus and Woods — the only men who have won the career Grand Slam.
“Winning the four majors over the course of your career is the greatest example of a complete player,” said Mickelson, who is missing the United States Open crown. He added: “If you get hot for a stretch, you have the ability to be the No. 1 player in the world. But to play those four major championships that offer such varied challenges would be the greatest example of an overall complete player.”