Even if he wins The Barclays and collects 1,485 Ryder Cup points to move up from 23rd in the standings, Ryan Moore will fall just short of being in the top eight when qualifying closes after this tournament. But with his stellar match-play background and as one of the hotter players on the PGA Tour, you would think he might be one of four captain’s picks by Davis Love III.

“Honestly, that’s probably the farthest thing from my mind,” Moore said Friday after a 3-under-par 68 at Bethpage Black that put him in fourth place at 5-under 137 after two rounds. “I’m just trying to play good golf and win golf tournaments, and I’m trying to get to the Tour Championship.”

Moore won the John Deere Classic two weeks ago, and many consider him a fit for the Ryder Cup match-play format after winning two U.S. Public Links titles and the 2004 U.S. Amateur as well as twice reaching the quarterfinals of the World Match Play event on the PGA Tour.

But when he finished 11th in the Ryder Cup standings two years ago, he was snubbed by captain Tom Watson, and Moore has no reason to believe anything has changed. “It’s something I would love, and I do enjoy match play and team events,” he said. “But the reality is I have to play my way on. It’s been made very clear to me that’s what needs to happen.”

Black is green for Barnes

If there is a horse for the Black Course, it might be Ricky Barnes, who played in the 2002 U.S. Open, tied for second in the 2009 U.S. Open, tied for 24th in the 2012 Barclays and Friday shot 4-under 67 to tie for 10th at 139 at the halfway point. “I’ve probably played it as much as any player has, making the cut in three of the four,” he said. “I’ve always enjoyed the USGA events and courses, the Oakmonts, the Bethpages, the Pebbles.”

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Putter switch helps Kokrak

Jason Kokrak, who was paired with Barnes the first two rounds, tied with Jamie Lovemark for the low second round at 66, but it took a 41-foot bomb of a par-saving putt at the 18th.

“I switched putters back to an old one I hadn’t used for awhile, and there was some good mojo with that,” Kokrak said. “Any time you can make a putt like that when you finish on 18 to save anything, it’s a big momentum saver. It keeps it going for the next day.”

Na helps others, hurts self

When Kevin Na bogeyed No. 17, it moved the cut line up to 3-over 145 to keep Bubba Watson and Brooks Koepka, among others, around for the weekend. When Na double-bogeyed No. 18, he finished at 5 over. On his way off the green, Na deposited a putter bent into an “U” shape in a trash receptacle . . . Prominent players who missed the cut include new PGA champion Jimmy Walker (5 over), who is safely on the U.S. Ryder Cup team, Bill Haas (6 over), who began the week on the bubble at No. 14 in Ryder Cup points, Northern Ireland’s Graeme McDowell (6 over) and South African Branden Grace (8 over).