FARMINGDALE, N.Y. — The Tiger Woods of old entered every tournament expecting to win. An older, wiser Woods returned last year from his fourth back operation with tempered expectations.

As he explained Tuesday, “There’s more days I feel older than my age than I do younger.”

After Woods’s victory last month at the Masters, which he secured less than two years after undergoing a spinal fusion, the oddsmakers, and nearly everyone else, expected him to contend in his next start, the P.G.A. Championship at Bethpage Black, where he won the 2002 United States Open for one of his 15 major titles.

Instead, for the ninth time in his 76 major starts as a professional, Woods failed to advance to the weekend. He had won 10 major titles before missing a cut for the first time, at the 2006 United States Open about six weeks after the death of his father, Earl Woods.

Woods shot a three-over-par 73 on Friday to finish with a 36-hole total of five-over 145, one stroke above the cut line — and 17 strokes behind the leader, Brooks Koepka, with whom he was grouped.