Delonte West injured his right thumb in a very typical way during his rookie season with the Celtics in 2004-05.

He sprained the thumb during an in-practice fight for a loose ball, and was later spotted by then-coach Doc Rivers actually talking to his hand.

“He said it listens to him — it’s going to heal that way,” Rivers, a personal fan of the combo guard right from the start, said with amusement that day.

Two qualities were immediately established. West would continue to get hurt because he sacrificed his body whenever necessary, and he had an infectious sense of humor. Later on, especially after he moved on to the Cleveland Cavaliers and LeBron James, West’s lifelong battle with a bipolar disorder became dominant.

He soon had trouble staying in the league because of his fears and mood swings, spiked by his 2009 arraignment on weapons charges and his subsequent house arrest. But West never stopped hitting the floor for the next opportunity, be it a return to the Celtics in 2010-11 or a run with the Mavericks the following season.

The Mavericks also cut him in the fall of 2012 for argumentative behavior, and in the minds of many, that was it for West’s NBA chances.

But Rivers, who had never fallen out of touch with West, got a call from the guard this month on the eve of the NBA Summer League in Las Vegas. After several months with the Texas Legends of the NBA D-League and an assignment many American players have found to be sheer purgatory — a season in the Chinese Basketball Association — West was ready for another chance.

“No strings attached,” West said to the now-Clippers coach while making a pitch for a spot on Rivers’ summer league team.

OK, Rivers decided. Summer league doesn’t require any commitment.

“He just wanted a shot — he just wanted a chance with no commitments to try and make it,” Rivers said last week.

Rivers said the Clippers made the necessary inquiries about West’s time in China and the NBADL, and decided offering him a summer league slot was relatively risk-free.

“You check all of that out — no doubt,” Rivers said of West’s behavior. “I got calls from several people in the D-League and in China who said he’s ready for this. He has a baby and a fiancee now. A lot of things have been going right for him.

“I just think he’s far more mature now,” he said. “He’s given up a lot in his life, and he wants to do well. He still has a disease that he has to fight every day. I know he’s doing everything he can to get back into the league, and it’s nice to see him here.