SAN JOSE, CALIF. – He had already lost the tale of the tape, by but A.J. Greer still wanted to drop ’em with the biggest guy on the ice Monday night. That says it all about the Colorado Avalanche prospect, who might as well have “No Fear” as his new nickname.

Kyle Wood, a former defenseman Avalanche prospect now with the Arizona Coyotes, stands nearly 6-foot-6 and goes about 220 pounds. Greer, though, tried to get the hulking Wood to drop the gloves and address a skirmish between the two, that happened right before, with their bare fists. Wood declined. It was probably a smart choice.

Greer plays a hell-on-wheels kind of game, always barreling toward the net, always getting dirty in a scrum, always itching to stick his nose into an opposing player’s business. His future as a true agitator already seems secure.

Here’s the rub though: The Avalanche need him to put some points on the board in his career. He’s a second-round pick, No. 39 overall, from the 2015 draft. He’s one of two good young offensive prospects the Avs attained in the big Ryan O’Reilly deal with Buffalo, and he had a very solid first season of pro hockey in 2016-17. He was good enough, in fact, to be named an all-star in the American Hockey League with San Antonio and he played five games with the Avs too.

Can Greer make the transition from a pretty regular scorer at the AHL level to something similar in the NHL? Or, is he going to fall into something of that agitator-type of role that some players often just get pigeonholed into because the offensive talent just isn’t quite there?

It’ll be up to Greer one way or another, but what the Avalanche doesn’t have to worry about with Greer is a burning desire to do whatever it takes to make it at hockey’s highest level.

“The bar is set high, and I want to reach that bar,” said Greer, after scoring a goal in the Avalanche’s 4-3 overtime loss to the Arizona Coyotes in a “Prospect Showcase” game at Sharks Ice. “I don’t think I want to give an opportunity to anyone else to make this team, but at the same time I can only do my best and hope that the best happens.”

Greer finished with four shots on net, and his tip of a Tyson Jost shot tied the game 3-3 with 2.9 seconds left in the second period. He was a minus-2, however, one of only two Avs players to finish in minus territory.

With the Avs having more depth at left wing than on the right side, the normally left-wing Greer might have more of an opportunity to make the club playing on the opposite side. Is he OK with that, he was asked?

The questioner was quickly made to feel silly.

“I’ll do whatever the coaches want me to do. I’ll play forward, defense and goalie if I have to,” Greer said.

Greer skated on the left side in this game, on a line with Tyson Jost at center and Shawn St. Amant on the right. He wasn’t happy, it seemed with his minus-2 number, but a rough start by goalie Petr Kvaca (who settled down to play well after that) didn’t help anyone’s plus-minus.

“You always want to compete and win, whether it’s practice or a game. For me, it’s always trying to be the best, and beat the best,” he said. “Everyone wants to prove they can play on this level. I had some plays I regret and wish I could turn the (clock) back on, but it’s all part of the process. I just have to move forward and get better.”

Rampage coach Eric Veilleux, who manned the bench again Monday, said “Training camp will dictate what’s going to happen to him this year, and I’m not here to talk about that, but I think he’s had two pretty solid games so far. He’s proven he can be physical. He’s a good presence on the power play and in front of the net. He did that all year last year. All he needs to do, I think, is keep playing the same way he has so far. I think he’s very well prepared to make that (Avalanche) club. What’s going to happen? I don’t know.”

NOTEBOOK: The Avalanche outshot the Coyotes 38-30 and carried the play territorially for long stretches at times. Who stood out in a good way? Probably defenseman Chris Bigras is near the top of that list. Bigras nearly won the game late in regulation with a dazzling rush down the right side, and he moved the puck effectively again on the power play, with a couple of big slap shots thrown in. Bigras is clearly doing the right things so far in his attempt to make the club out of camp. … Jost had another strong game, with several dazzling sequences. Alex Kerfoot notched two more assists as well. … Defenseman Sergei Boikov, a sixth-round pick in 2015, scored a nice goal to get the Avs on the board in the second period. He blasted a shot from the left circle past Coyotes goalie Hunter Miska. … It was another quiet day on the Matt Duchene front. His agent, Pat Brisson, was asked again by BSN Denver whether his client would show up for camp Thursday, when veterans are due to report, but Brisson declined to answer one way or the other. Avs GM Joe Sakic told BSN Denver Saturday, “He’s under contract, and I expect him to be here Thursday.”

The Avs’ box score from Monday: