Once again, Redskins Coach Mike Shanahan was proven wrong. His failure in picking quarterbacks this season is now complete.

In changing quarterbacks again before Sunday’s 20-9 loss to the Miami Dolphins here — the Redskins’ fifth consecutive defeat — Shanahan reinforced two points: No one should waste time listening to him, and the Redskins are a wreck at quarterback.

After saying ineffective quarterback John Beck would start against Miami, Shanahan informed the team Saturday he planned to bench Beck for ineffective quarterback Rex Grossman, whose four-interception performancein Week 6 led to Beck becoming the starter.

Shanahan, who has acknowledged that he sometimes lies publicly about major issues facing the Redskins, has shown we shouldn’t put too much stock in what he says nor trust him to make sound decisions about the game’s most important position. His ability to restore the Redskins to greatness — which owner Daniel Snyder hired him to do — is very much in doubt.

Grossman had two more interceptions against the Dolphins, though one occurred after Redskins wide receiver Leonard Hankerson slipped running his route. Grossman’s inexplicable, momentum-changing interception in the fourth quarter was all on him.

To some degree, all coaches manipulate the media, and the truth, especially about quarterback issues. They misdirect in hopes of surprising opponents. The goal is to gain a competitive advantage. It’s part of the coaching gig.

Shanahan risked losing the locker room if he didn’t turn back to the turnover-prone Grossman. Privately, some players were strongly opposed to the initial quarterback change. Beck’s performance only strengthened their opinion.

Problem is, Shanahan has made a complete mess of Washington’s quarterback situation.

Following the loss to Miami, which had only one victory before Sunday’s game, Shanahan was asked to explain his reasoning for the switch.

Predictably, he essentially avoided the question. He alluded to the team’s injuries, and specifically the loss of right tackle Jammal Brown, in determining that “Rex gave us the best chance to win. . . . With the game that Jammal went down, [that] put John in a situation where we had a number of players go down.

“With his experience, I thought it was [in] our best interests to go with the guy that I felt gave us the best chance to win the game. That was Rex.”

Beck took over for Grossman during a game in which two starting offensive linemen were injured, including one for the season. He retained the position after veteran wide receiver Santana Moss went down.

Now, we’re supposed to be believe that Beck, much more athletic and mobile than Grossman, is out because the team’s struggling right tackle is sidelined?

Surely, Beck’s 0-7 career mark as a starter — including 0-3 this season — and his teammates’ lack of confidence in him had nothing to do with the move.

At least Shanahan is consistent.

Mike and Kyle Shanahan, Washington’s offensive coordinator, were the only two NFL people who believed that Beck was capable of being more than a backup. Mike Shanahan compounded his error, saying he would stake his reputation, in large part, on Beck, who has wasted an opportunity no other team would give him since he started four games for Miami back in 2007.

At the time of his benching, Grossman, unfortunately the Redskins’ best option at quarterback, was tied for the league lead with nine interceptions. He had 11 turnovers. In nine starts for Washington, Grossman has 19 turnovers.

Shanahan actually believed Beck, whose vision seemed to extend no more than 10 yards downfield, was better than any quarterback he could have selected in the April draft, Redskins people say.

Really, that’s all you need to know.

The Redskins never had a chance this season because Shanahan, the guy who picks the players, relied on Grossman and Beck. Those were the Redskins’ options. Obviously, they weren’t good ones.

This season is over. It doesn’t matter who plays quarterback for the final seven games. Washington’s starter could change weekly. Shanahan’s arrogance has sabotaged the Redskins. He believed his system and his coaching would be enough to elevate the play of two guys who just aren’t very good. He was very wrong.

Washington’s defense isn’t bad. For the most part, the front seven has provided reason for long-term optimism. There’s nothing on coordinator Jim Haslett’s play sheet, however, that could help the defense overcome Washington’s offense.

With each three-and-out, pressure increases. Put in bad positions over and over again, the defense wears down. It happened again in the final quarter against Miami.

Trailing, 13-9, with a little more than 12 minutes to play, the Redskins had first and 10 on the Dolphins 10-yard line.

Then Grossman had one of his signature turnover moments, throwing the ball to Miami linebacker Karlos Dansby, who caught it at the 5 and returned it to the 19. The Dolphins put the game away with an 81-yard drive, getting an 18-yard touchdown run from Reggie Bush through the right side of the defense.

Neither Rex nor Beck is good enough to provide a bridge to Washington’s quarterback of the future, and the Redskins’ wasted 2011 season will likely be remembered for Shanahan’s quarterback flip-flopping.

Shanahan’s act played better in Denver, while he was riding John Elway’s coattails to consecutive Super Bowl championships in the late 1990s. But that was a long, long time ago. After winning only one playoff game in the 10 years that followed Elway’s retirement, and missing the postseason his final three seasons with the Broncos and six overall during that span, Shanahan was ousted. Since taking control of the Redskins, Shanahan’s record is 9-16. Former head coach Jim Zorn was 11-14 in his first 25 games.

At this point, Shanahan has shown no signs of being able to return the Redskins to .500, let alone elite status. He has done little to justify the millions Snyder is paying him. He’s simply a guy still chasing Zorn. And that’s no lie.