HOUSTON — The memories stalk Adrian Beltre, haunting and driving him. He has lived for nearly five years with the exquisite agony of that night in St. Louis when the Texas Rangers came so close to winning the World Series.

“It was twice,” Beltre said before a game this week. “It was twice that we were one strike away from celebrating. I was thinking about, at third base, how I was going to react. I don’t want to be too crazy; I don’t want to cry. I was thinking: Am I going to throw my glove up? Am I going to jump over the guys? I never got to experience any of that. We all know how that ended up.”

Beltre ended up with the ball in his glove with two outs in the ninth inning of Game 6 — but by then David Freese had slid safely into third, and the tying runs had scored. The Rangers grabbed the lead back and then lost it again in the 10th. The Cardinals won the game in the 11th and the World Series the next night. The Rangers have not been back.

But they have the best record in the American League, at 87-60 after an 8-4 loss to the Houston Astros on Wednesday night, as they close in on their second A.L. West title in a row. The national story line for October will be the Chicago Cubs’ quest for their first crown in 108 years. But the Rangers have been better for longer than the Cubs — this will be their fifth postseason trip in seven years — and have never won a championship.