But Davis often comes back. And his latest comeback from just such a scare spooked the Clippers more than anyone else Tuesday night.
Davis shook off the rib contusion that caused him to leave the game late in the first half to score 31 second-half points. He finished with a game-high 41 points to go with 13 rebounds and helped the Pelicans to a 121-116 victory.
"He is just playing on a really high level and nothing seems to affect him," said New Orleans head coach Alvin Gentry. "That is a really tough injury right there. It feels like somebody is sticking an ice pick in your side when you are trying to breath with those bruised ribs and stuff like that. But he played through it and did a great job."
The win was the ninth in a row for the Pelicans, who are holding on to fourth place in a crowded Western Conference playoff race.
Davis had 10 points when he exited in the second quarter after struggling to box out Clippers center DeAndre Jordan. The Pelicans were initially unfazed by Davis' injury, closing out the final 3 minutes, 4 seconds of the quarter on a 13-1 run without him to lead at halftime 67-52.
"I didn't see it, I didn't look at the film," Davis said of his injury. "I am not sure what exactly happened. I know what I felt and then came and got it checked out. They said I was fine, and I went back out."
Davis came out with the team to warm up for the second half, declaring himself good to go after adding some protection for his ribcage.
He then splintered the Clippers for 19 third-quarter points, capped off with a buzzer-beating 3-pointer -- his fourth 3 of the period. New Orleans led by as many as 20 points in the third quarter, the largest lead of the contest.
Davis said he received inspiration during halftime from teammate DeMarcus Cousins, who has been sidelined with an Achilles tendon injury suffered in January.
"DeMarcus told me at halftime, 'If you won't go back in, let me get your Achilles,'" Davis said. "I wanted to go out there and do whatever I can to help the team."
Gentry, Davis' head coach for three seasons, knows that Davis' ambitious efforts occasionally land him in the locker room early, but it's the toughness of the sixth-year veteran that allows him to return from short-term injury to perform.
"Well, I think he -- you gotta understand, guys, he's willing to sacrifice his body to make a play here and there," Gentry explained. "You know, we wish he weren't that way, but you know, he really is. He's a guy that's going to do everything he can to help us win games. So, when he goes to the locker room, if there's any chance that he can play, he's going to come back out and play."
And Davis has full trust in his teammates when he does get nicked up.
"They're fine. They're fine. When I went out, they actually went on a little tear," he said of the Pelicans' work against the Clippers during his absence at the end of second quarter. "So, they've played without me before and won games. You know, they're fine. Everybody in here's a professional. No matter who's on the floor, we're going to go out there and compete."
The Clippers, however, stormed all the way back in the fourth quarter. Bolstered by NBA Sixth Man of the Year favorite Lou Williams, who scored 14 of his team-high 27 points in the final period, they flipped that 20-point third quarter deficit into a 113-109 lead with 2:05 left to play in the game.
"We got a little complacent and started to try to one-pass shot, one-pass shot, but then we got ourselves back organized again," Gentry said. "They have a great scorer in Lou. I mean he is a professional scorer, and I will say this, I think that it is a shame that that kid wasn't on the All-Star team. Everything that he has done and this is a career year for him. A guy in his thirties, I think it is a shame that he didn't make the All-Star team. I know that we voted for him, because we felt like when you are doing what he is doing at this stage in your career, it may be your only opportunity to be an All-Star, then he deserves it -- and you can see why if you watched the game today."
But then Davis took over down the stretch. The Pelicans finished the game on a 12-3 run in the final 1 minute, 56 seconds, and it was all Davis offensively: a running layup; a driving bank shot to tie the game with 1:35 left; and a go-ahead turnaround jumper with 31 seconds left that represented the game's final lead change.
"I always want to take the big shots; make or miss, we are going to live with it," Davis said. "But I think that having other guys going earlier in the game, like Jrue [Holiday] and [Rajon] Rondo hit some shots, E'Twuan [Moore] and Darius [Miller], so that was able to open up the floor a little bit for me, so I can create."
Holiday overcame a poor shooting night (7 of 22 field goals) to finish with 19 points, a career-high 17 assists (with only two turnovers) and a game-saving steal while guarding Williams down the stretch. But Holiday was deferential to Davis after the game.
"Do I have to thank Anthony again? That is why he is here, to make the big shots, especially down the stretch," Holiday said. "That is why he is an All-Star player and the leader of our team. He calls for it. He wants it, especially down the stretch. We are just lucky to have him on our team."
The Pelicans finished with 39 assists and only eight turnovers. It was the most assists by any team this season in a game in which the team also had fewer than 10 turnovers.
Clippers coach Doc Rivers offered his assessment of the outcome.
"I just didn't think we executed throughout the game. I really thought that if we won the game, it would have been a robbery," said Rivers, whose team is now 35-30 and a half-game behind the Denver Nuggets for the eighth and final playoff spot in the Western Conference. "We didn't play with the right spirit, and it happens, but I don't know why it happened."
New Orleans will attempt to extend its winning streak to 10 games when it visits the Sacramento Kings on Wednesday night.
When Davis was asked if he would be good to go against the Kings, he was coy.
"We'll find out at 7 o'clock," Davis told ESPN.