The spring signing period opens this week and, by Sean Miller’s count, there’s still three or four guys to get on board with the Arizona Wildcats.

But by flanking himself with two players at a news conference last week, the UA coach suggested something else is important this spring: the six guys he has coming back.

Allonzo Trier opted to return for his sophomore season and the player who joined him at last Wednesday’s news conference, Kadeem Allen, will become one of those valuable fifth-year seniors you don’t often see at the high-major level.

“My experience has always told me the value of returning players,” Miller said. “It’s not just those who aren’t here yet. Clearly, talent and depth are a big part of it. But it’s so much about those who have been in the tournament and lost early.”

With that, Miller noted how Villanova rebounded from two years of second-round losses NCAA tournament losses — as a No. 2 and a No. 1 seed — to become last season’s champs.

His players may have received that message.

While Miller and Trier both talked about how much Trier can improve his NBA stock and potential pro longevity by returning to school, Trier also acknowledged a lingering sour taste that came with a first-round loss to Wichita State.

“Of course,” Trier said. “If I didn’t want to win and come back to try to be a leader and try to bring this team to a Final Four, I wouldn’t be here.”

Leadership wasn’t Trier’s top priority last season. The Wildcats had four seniors and needed Trier, more than anything, to score and get to the free-throw line.

He delivered there. Trier was the Wildcats’ third-leading scorer behind seniors Ryan Anderson and Gabe York, averaging 14.8 points and 5.4 attempted free throws per game. He hit the free throws at a 79.3 percent rate, the highest on the team except for Mark Tollefsen (79.5), who averaged just 1.4 attempts per game.

But there was another number that could use some work: Trier had just 31 assists, an average of just 1.1 per game, and Miller said he expects that number to double this time.

It’s about “playing with others and learning do that even better. That really wasn’t his role this year, to have a lot of assists,” Miller said. “If you’re projecting him to leave Arizona as a 6-4, 6-5 combo guard, I think you want to see him be able to improve his passing and have a higher assist number, and make great plays at the end of the clock and the end of the game.

“That will be the role he will have. He’ll be more efficient in that role. And that bodes well for not only him but our team.”

Allen, who said he wants to work on his game and become more of a vocal leader, said Trier’s decision means a lot to the Wildcats.

“He’s a great player and a good guy to play with,” Allen said. “With Allonzo coming back, I feel we can push the guys and get better every day.”

Trier said he’s excited to come back to UA with a “little bit of a different role,” though not surprisingly, it was tempting to think about not coming back at all.

That’s just what guys do when they come up the five-star recruiting pipeline, make the McDonald’s All American Game and collect some gold medals with USA Basketball, as Trier did.

Draft Express.com wrote before the NCAA tournament that Trier “is likely to enter the 2016 NBA Draft,” and Trier didn’t deny the thought entered deeply into his mind.

“Of course, it was definitely something that you really look into and really think about,” Trier said. “You just discuss it with your family and your coaching staff. It’s hard because something you’ve worked so hard for, your dream is right here and it’s so close.

“But all it means is I’m coming back to Arizona to better myself as a player and a person, and we think that’s best for myself to have the best longevity for a pro career.”

Now it’s just a matter of who’s going to join Trier, Allen and Arizona’s four other returning scholarship players. UA has been chasing a mix of freshmen and transfers in a process that could go on late into the spring.

“The coaching staff keeps us well aware of who we’re recruiting and the guys coming in,” Trier said. “We’re excited to add new guys to the roster but as much as it is adding new guys, it’s about the guys who are returning who need to step up and get better. That can make this team go to new heights.”

Rim shots

  • Five-star forward
  • Josh Jackson
  • told USA Today he will announce his college choice Monday in his hometown of Detroit. Now attending Justin-Siena High School in Napa, Calif., Jackson has been considering Kansas, Arizona and Michigan State.
  • UA target
  • Terrance Ferguson
  • set a Hoop Summit record with seven three-pointers to lead USA Basketball to a 101-67 rout of the World team on Saturday in the annual international game held in Portland.

Sportswriter for the Arizona Daily Star covering Arizona Wildcats basketball