Coyotes head coach Rick Tocchet talks to players after the team’s’ first practice of the season last week at the Gila River Arena.

GLENDALE – In many ways, Jay Varady is playing the role of proud father — ready to find out which of his progeny are equipped to take that proverbial next step.

But not unlike a prototypical parent, don’t ask Varady to pick a favorite, either; or, in this case, the second-year Tucson Roadrunners head coach hesitates to place odds on which recent Roadrunners might soon make the full-time National Hockey League jump.

“I’m cheering for all the guys,” Varady said with a slight smile.

“There are a lot of guys down there who did a lot of good things in Tucson last season, and this is their chance to show where they’re at … an opportunity for them to prove themselves.”

Varady is in Glendale for much of September, joining the Arizona Coyotes’ coaching staff, front office personnel and players — as well as nearly 20 forwards, defensemen and goaltenders who played significant time under him last season in Tucson — for the Coyotes’ 2019-20 NHL preseason training camp.

Camp opened Thursday with team meetings, media availability, photo shoots and equipment work. The nearly 50 players — the majority under contract with the Coyotes, including most of those 2018-19 Roadrunners, alongside a handful of special camp invitees — hit the ice for the first time together Friday.

Varady may not be far himself from being back in Tucson for the start of the new season. But, over these next couple of weeks, he’ll take up shop alongside Coyotes head coach Rick Tocchet and his NHL staff — observing, offering insight, preparing himself, to be sure, and ultimately readying to bring some familiar faces and a bevy of new prospects down to Tucson Arena for another 34 regular-season home games, as part of the Roadrunners’ 68-game American Hockey League slate.

The most obvious question, as it pertains to the Roadrunners, at least: which players will join Varady on the trek down Interstate 10? That all depends, of course, on the needs of the Coyotes, first.

While discussing the state of the NHL club Thursday after Arizona barely missed a Stanley Cup playoff berth last Spring, Tocchet at one point noted the contributions of players who spent a significant chunk of their 2018-19 seasons in Tucson.

“We stole a lot of players from Tucson,” Tocchet noted. “(The coaches) are teaching what we’re teaching up here. They sync really well with us (in Tucson) and that really helps. We probably wouldn’t have been in that position last year where we were that close if we didn’t have those four, five, six guys contribute the way they did.”

While forward Conor Garland managed 13 goals in 47 NHL games, he was a force while in Tucson last year, tallying more than a point a game (25 in 21) to go with 12 goals. Garland’s efforts earned him a new two-year contract from the NHL club last season, and all signs point to his time in Tucson being limited looking ahead.

But for players like goaltender Adin Hill, defensemen Kyle Capobianco and Robbie Russo, and forwards Michael Bunting, Hudson Fasching, Michael Chaput and Lane Pederson — among a host of others — the picture is hardly as clear.

Other than Garland, Bunting was the Roadrunners’ most efficient offensive force last season, with 19 goals and 41 points in 51 AHL games. Bunting also skated in five games with the Coyotes, but is still seeking his first significant NHL time.

Pederson had a breakout 2018-19 in becoming Tucson’s leading scorer with 23 goals and 47 points, but is still waiting for his first NHL call-up.

And Capobianco earned and AHL All-Star nod with Tucson last season and was recalled mid-year by the Coyotes, only to suffer a season-ending knee injury in just his second post-recall game. His recovery is ongoing.

Arguably the most curious roster situation for the Roadrunners involves Adin Hill, who certainly played the part of NHL goaltender during a number of opportunities with the Coyotes last year. But those only came after injuries to would-be Co-No.1 goaltenders Antti Raanta and Darcy Kuemper.

Both are healthy heading into 2019-20, and it wouldn’t be surprising for Hill to spend a large chunk of the season in Tucson.

“We hope (Hill) had a big summer and can come in and make a push,” Coyotes general manager John Chayka said Thursday. “He’s a good young goalie and we’ve got some guys coming in underneath as well. … You need to have that pipeline if you want to be a good organization for a long time.”

Once the Coyotes’ training camp nears its conclusion and players are assigned to their respective teams, Varady and the Roadrunners will conduct their own brief preseason camp prior to their season-opener on Oct. 4 at the Texas Stars.

Tucson then opens its home schedule at the Tucson Arena Oct. 18 against the San Antonio Rampage.