Caddie Steve Williams hands Tiger Woods a club under a tree off the 17th fairway during the third round of the Masters in April. (CHRIS O’MEARA/ASSOCIATED PRESS)

Steve Williams has carried Tiger Woods’s bag for 13 victories in major championships. If Williams’s 14th major title as a caddie comes this week at the U.S. Open, it will mean Adam Scott is the champion.

Williams, who has been on Woods’s bag since 1999, spent Saturday afternoon at Congressional Country Club working with Scott in a practice round, and he will caddie for Scott when the U.S. Open begins Thursday at the Bethesda course.

Mark Steinberg, Woods’s agent, said the pairing came about because Scott, an Australian, and Williams, who is from New Zealand, have a long-standing friendship off the course. Woods withdrew from the Open last Tuesday because of lingering injuries to his left knee and Achilles tendon.

Steinberg said Williams’s job with Scott doesn’t mean Woods is looking for a new caddie.

“Steve and Adam are friends,” Steinberg said by phone Saturday. “When Adam found out Tiger couldn’t play, Adam called Steve, and Steve called Tiger. As far as I’m concerned, it’s just for the U.S. Open.”

Scott and Williams, 47, completed an 18-hole practice round at Congressional at 5 p.m. Saturday, then rode a golf cart from the 18th green directly to a courtesy vehicle, leaving the course without comment.

“I don’t think there’s much for him to say,” Steinberg said of Williams. “Just like Tiger doesn’t want to miss any majors, I’m sure Stevie doesn’t want to miss any majors.”

Scott, 30, was once considered a talent who might challenge Woods regularly, and he modeled his swing and his game after that of the 14-time major champion. A decade ago, he even briefly hired Williams’s younger brother Phil as his caddie.

Scott tied for second at this year’s Masters, but he split with longtime caddie Tony Navarro last month.

Clark withdraws

South African Tim Clark withdrew Saturday because of a nagging elbow injury. Clark, 35, has played only twice since January, missing the cut at the Masters and withdrawing during the second round of last month’s Players Championship, where he was the defending champion, because of the elbow problem.

Clark was replaced by J.J. Henry, the first alternate from a sectional qualifying tournament in Columbus. . . .

When it announced tee times Friday, the U.S. Golf Association had to keep three spots in the field open for a pair of contingencies.

First, if any golfer who was not otherwise exempt moved into the top 50 of the Official World Golf Rankings over the weekend, he would gain an invitation. Rookie Gary Woodland moved to 41st in this week’s rankings and isn’t playing in the FedEx St. Jude Classic in Memphis, so he is solidly in the field. Only two others — Scott Verplank and Fairfax native Steve Marino — had the possibility of moving up, and both missed the cut in Memphis. Neither will qualify.

Second, if a player who was not otherwise exempt wins in Memphis, and it’s his second win on tour since the last U.S. Open, then he’ll earn an invitation. Rookie Keegan Bradley, who posted his first win two weeks ago at the Byron Nelson Championship, has an outside chance; he is tied for fifth after three rounds, five shots back of leader Robert Karlsson.

The spots will be filled by alternates from sectional qualifiers and will likely be announced Monday morning.