Clippers prepare to open training camp with big questions, like ‘who fits?’

The NBA’s offseason ended for Doc Rivers in the middle of the night last week.

Following a restful summer in which he became a grandfather, the Clippers coach could no longer sleep.

“I bought a Fitbit and it has a sleep monitor,” he said, raising his left wrist to show his new activity tracker. “I’m trying stuff, and it’s driving me nuts.”

Rivers, who is entering his 20th season coaching in the NBA, understands sleepless nights are hardly unique among his peers in a high-stress, high-visibility profession. Yet it couldn’t have helped to know that, unlike the star-driven teams he inherited after arriving in Los Angeles in 2013, the roster he’s opening camp with Monday is largely an unknown quantity.

“I like this team,” he said. “I don’t know this team yet.”

Rivers predicted it will take longer than the four weeks allotted for the preseason to do so, and for good reason. Assimilating rookie guards Shai Gilgeous-Alexander and Jerome Robinson as well as offseason additions Marcin Gortat, Mike Scott and Luc Mbah a Moute would take time even under normal circumstances, let alone blending them into a rotation barely given the opportunity to build a foundation last season.

Injuries led the Clippers to use a league-high 37 starting lineups, mine its G-League affiliate for depth and cost the chance to play three key players together.

Small forward Danilo Gallinari (hand and glute injuries), point guard Patrick Beverley (right knee) and guard Avery Bradley (abdominal muscles) played 38 games combined, but none together. They first shared a court during summer pickup games. Their play — and health — is critical to keeping the Clippers afloat during the regular season’s opening stretch in which 12 of the first 13 opponents are playoff teams from last season.

“They know each other because they were around each other in the locker room in street clothes all year last year but they’ve really never played together,” Rivers said. “That is so strange for a team. These guys were together for most of the whole year last year, yet as far as the amount of game time on the floor, it’s zero.”

Bradley and Beverley create arguably the league’s top defensive backcourt and the 6-foot-8 Mbah a Moute, who played for the Clippers from 2015-17, has the length and intelligence to guard all five positions.

“If you’re up one at the end of a game and you throw Avery, Luc and Pat on the floor, you’re thinking, ‘Good luck scoring on that group,’” Rivers said.

Identifying two others able to close out games defensively isn’t as obvious. Forward Tobias Harris, acquired alongside Bradley in a mid-season trade from Detroit that offloaded Blake Griffin, proved to be an excellent scorer in his 25 games after the trade, averaging 19.3 points, but never mastered his new team’s defensive rotations to limit corner three-pointers, in particular, Rivers said. The extra time Harris has spent this summer with the Clippers is expected to produce significant improvement.

“Defensively I know we can close,” Rivers said. “Offensively we’ll find out if we can close. If we can do that we’re going to be really good.”

Gallinari is a key to both. He worked with Clippers assistants in Italy before returning early for offseason workouts at the team facility, where he is “dominating,” Rivers said. There is little dispute about his offensive skill, and Rivers called Gallinari underrated defensively, but he has played in more than 70 games once in his last seven seasons.

“He was really disappointed with all the injuries last year,” said Lawrence Frank, the president of basketball operations. “I think you kind of see just someone who is very, very determined.”

The team opens camp Monday in Playa Vista before training in Honolulu for the next six days. Seventeen players under contract are competing for 15 spots, all while talk of Minnesota All-Star guard Jimmy Butler’s trade demand, and reported preference to land with the Clippers, persists in the background.

Jet lag might not be the only thing keeping Rivers awake while in Hawaii.

“Can we function together? Who fits, and not only this team but in the future?” said Rivers, when asked what he hopes to learn during the preseason. “Who fits us in the long run? We’re going to find out a lot about our young guys, too, and I think that’s very important. There’s a lot going into the year that we don’t know, that we need to know.”

andrew.greif@latimes.com

Twitter: @andrewgreif