Nam Y. Huh / AP

Tiger Woods lines up his putt on the 18th green during the final round of the BMW Championship. Woods finished 22-under.

And for those who question his ability off the tee, he missed only two fairways the entire weekend at Cog Hill. Asked the last time he had struck the ball that well, Woods mentioned Southern Hills, noting that the PGA fairways were more narrow.

Memories can be short.

Justin Rose has played with the world’s No. 1 player on big stages like Muirfield and Carnoustie. But this was the first time in a final round, and he noticed a difference.

“He’s so intense, but he’s also incredibly relaxed,” Rose said. “You can see he lets his round build. He starts off very relaxed, very calm, doesn’t let anything bother him. And then as the round gets on and he gets more into it, he gets more and more focused.”

That’s what coach Butch Harmon was trying to share with Phil Mickelson about his former client.

When Mickelson won the Deutsche Bank Championship last week outside Boston while playing three rounds with Woods, he made it sound as though Harmon had shared some secrets.

In fact, Harmon said the tips were the same thing Rose discovered.

“One of the things he (Mickelson) can learn from Tiger is he doesn’t let anything bother him,” Harmon said in a telephone interview last week. “Tiger’s greatest strength is what you can’t see — his mind, his heart, his desire. I explained things I learned in my 10 years being around Tiger, and it was geared toward making Phil more comfortable in that environment.”

Along with reaching his 60th tour victory, the timing could not have been any better for the PGA Tour.

The FedEx Cup now has the No. 1 player atop the standings going into the Tour Championship, with Stricker and Mickelson right behind and both capable of winning the $10 million prize. Woods winning the cup would lend some measure of credibility for the skeptics. Stricker or Mickelson as the FedEx Cup champion would mean they won two of the four playoff events. There’s nothing wrong with that, either.

Having those three among the top contenders will help take some attention away from the greens at East Lake, which are in bad enough shape that practice rounds effectively have been banned.

Woods helped promote the FedEx Cup by doing TV spots for the tour, the first time he had done a commercial for free. He is among players who wonder about the shelf life of these PGA Tour Playoffs. But if there’s a trophy on the line, he wants it.