Wizards shooting guard Jordan Crawford (15) tosses the ball after disagreeing with a call during a game against the Milwaukee Bucks on April 2. (Evan Vucci/AP)

The Washington Wizards have 13 games left on another agonizing season that has yielded a coaching change, some roster upheaval and several more reasons to have doubt in the rebuilding plan of the past two years.

The Wizards (12-41) were eliminated from playoff contention before the final month of the season for the fourth year in a row but may find a reward on the other side, as they currently have the second-best odds to win the May 30 NBA lottery and earn the right to draft national college basketball player of the year and NCAA tournament most outstanding player Anthony Davis.

Before they can look ahead to some lucky bounces and air gusts on select Ping-Pong balls — the method the NBA uses to select its draft lottery order — the Wizards are now staring squarely at some unsettling history. They need to win at least three more games to avoid setting a new franchise mark for futility in a season.

“I don’t care about that,” guard John Wall said when asked about the record. “I’m just playing basketball. Things ain’t been going our way the whole year. We got 13 games left. That’s enough time to get those wins, if that’s what everybody is worried about.”

The 1961-62 Chicago Packers, who ultimately became the Baltimore Bullets, went 18-62 and won 22.5 percent of their games. The 2008-09 and 2000-01 Wizards squads are tied with the fewest wins in an 82-game season with just 19, and won 23.2.

At their current pace for a winning percentage of 22.6, the Wizards would finish with 15 victories, which would keep them — barely — from finishing with the worst winning percentage in franchise history.

“Well, I want to get to 20 wins. That’s what I want to do,” guard Jordan Crawford said. “I mean, you know, we eight away. Thirteen games, you go 8-5 to end up. That’s pretty good.”

Considering the Wizards needed to play 36 games to reach their first eight victories, that goal will also be pretty difficult to accomplish. The Wizards will play their next set of three games in three nights starting Wednesday, when they host the Indiana Pacers. They are uncertain about when starters Nene and Trevor Booker will return, after both players were forced to miss the past two games — both losses — with heel spurs.

The Wizards have gone 10-26 since Randy Wittman replaced Flip Saunders as head coach on Jan. 24. Wittman has encouraged his players to make the most of these final games and build on their improved play since the team traded JaVale McGee, Nick Young and Ronny Turiaf at the trade deadline to get Nene.

“We’re a different team than what we started at the beginning of the year and we want the wins to show that in the end,” veteran Roger Mason Jr. said.

Though they are just 3-9 since the deal, the Wizards have held 10 of their past 12 opponents to fewer than 100 points, including a streak of nine consecutive games that matched the longest stretch of sustained defensive effort in nearly 10 years.

“Keep going out the way we’ve been playing. That’s how we want to go out. Let the chips fall where they may,” Wittman said. “You want to go out with that competitive play that we’ve had. That’s what we’re trying to stress with them. Especially for young guys, rookies, second-year players. That leads to better things to come next year.”

The Wizards seem perpetually in search for better days. And, for a franchise that has finished with a winning record in just 18 of its 51 seasons of existence, the past four seasons have actually amounted to the worst run ever for the organization.

Since making their last playoff appearance in 2008, the Wizards have compiled a record of 80-219 and failed to win more than 26 games in any season. Finishing with the lowest winning percentage for a season would mark a significant regression in the rebuilding efforts.

“If that happens, that happens, but we’re not looking at that. We just have to get better as a team,” forward Chris Singleton said. “We just got to build chemistry and look forward to next year and look forward to ending in a positive way. We knew it was going to be a tough season, but we’ve got to fight, keep playing and we get three, four months off.”

Six opponents on the Wizards’ schedule are currently among the top eight teams in the Eastern Conference race — Indiana, New York, Orlando, Chicago and Miami (twice). Milwaukee, which has won three games against the Wizards this season, is in ninth place and battling with the Knicks for the final spot.

The Wizards also have seven games on the road, where they have gone just 5-21 this season. That’s actually an improvement from last season, when the team won just three of its 41 road games.

“You always want to play hard. You always want to give your best effort when you’re playing basketball, period. This is once a lifetime, to reach your goal, and you never know when it’s going to be over,” Wall said. “Some of these teams are fighting for playoff spots, trying to get seedings, so we have to go out and give a fight. . . . We know we’re not making the playoffs, so we just want to finish this season strong, to give ourselves motivation for next year.”