The Cavaliers’ muddled scenario at backup point guard became a little clearer Tuesday when the team claimed Shaun Livingston off waivers from the Washington Wizards and released Donald Sloan.

The Cavaliers, coincidentally, are in Washington tonight to face the Wizards.

Livingston, 27, is a combo guard who appeared in 17 games for the Wizards (four starts), averaging 3.7 points, 2.2 rebounds and 2.2 assists. The 6-foot-7, 175-pound guard was the fourth overall pick in the 2004 draft, but the Cavs will be the fifth team he has played for since the start of the 2008-09 season.

Sloan was signed out of the Development League in March and was averaging 4.1 points and 1.9 assists this season. He was playing on a non-guaranteed contract and knew he was vulnerable to be released at any point.

When the Cavaliers elected to carry three point guards out of training camp, coach Byron Scott said part of the reason was to prevent exposing Dion Waiters to the role. Scott thought he had enough to handle as a rookie without heaping point guard on top of it.

Yet 29 games into the season, Waiters is the primary backup to Kyrie Irving, while Jeremy Pargo and Sloan rotated for what few minutes remained.

Scott described his backup point guard scenario last week as “unsure” in part because the faces kept changing. Now Pargo is the only one who remains, but even his time lately has been sporadic.

Pargo went from starter while Irving was injured to inactive for last week’s loss to the Toronto Raptors. Then it was Sloan’s turn to sit and watch from the inactive list for the Cavs’ two most recent games. Part of the reason one of the two needed to be inactive was the injury to Anderson Varejao, which forced the Cavs to recall and activate Jon Leuer as an extra big.

Varejao is still out with a bruised right knee and did not travel with the team Tuesday night to Washington and has been ruled out of the game. It will mark the fourth consecutive game he will miss despite Scott hoping a week of rest would be enough to get him back on the court.

As for the point guard scenario, Scott last week called Pargo the “wild card” and thought Sloan was better served for close games because of his steady hand and consistency.

“I feel more comfortable with Donald when the game is close,” Scott said last week. “Donald doesn’t go in and make mistakes.”

Scott gave the example of the recent game against the New York Knicks, when the Cavs were hanging tough on the road. He had intended to use Pargo as the backup, but with the game tight, he changed his mind and went to Sloan. Yet Sloan isn’t as dynamic as Pargo, who averaged 14.5 points and 4.4 assists in 11 starts while Irving was sidelined with a fractured left index finger.

“If you’re down 10, J.P. is a guy you can throw in the game and get it tied quick,” Scott said. “Or you can go down 20. You just don’t know.”

Pargo played 13 minutes in Saturday’s win over the Milwaukee Bucks. He shot just 1-of-5, but he had two assists and didn’t turn the ball over. The spot minutes and inconsistent playing time can be challenging, but Sloan’s release may clear more minutes for Pargo.

“It’s a mental thing,” Pargo said. “Be focused and come out and do what you can every opportunity you get. I come out and try to do my job whenever I get the opportunity.”

The Wizards released Livingston on Sunday, giving the Cavaliers until 5 p.m. Tuesday to claim him and create a roster spot for him.

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