But mostly, Crawford, like anybody who followed Jones growing up in North Vancouver, remembers the winning. All that winning, from atom to pee-wee to bantam to midget to the Western Hockey League to the American Hockey League, and now to the NHL.
"Martin doesn't know anything but winning," said Crawford, the former NHL coach who watched Jones grow up playing with his son, Dylan, in Vancouver's North Shore Winter Club. "All this kid does is win."
Jones is winning with the San Jose Sharks now, and they're thrilled.
"He's been great," left wing Patrick Marleau said.
"People will start to pay more attention to him now," defenseman Paul Martin said.
Jones, 25, was undrafted and is getting his first chance to be a No. 1 goalie after two seasons behind Jonathan Quick with the Los Angeles Kings (16 wins and a Stanley Cup championship to show for it). He is 4-0-0 with a .982 save percentage and 0.49 goals-against average. He has allowed two goals on 110 shots and already has set the Sharks' shutout streak record (234:33).
The Sharks play the New York Rangers at Madison Square Garden on Monday (7 p.m. ET; NHLN, TVA Sports, SN1, CSN-CA, MSG). Jones is expected to start after getting the night off in a 6-3 loss to the New York Islanders on Saturday.
"I played against [Jones] in the minor leagues, and he was one guy we could never beat," Sharks forward Tommy Wingels said. "We'd have 45 or 50 shots, and he'd get a win in the bank. Guys are very confident in him, and he's very confident in his skill set. He's a big goalie, very technical. I think there were question marks for a guy who doesn't have experience, but he's proving he belongs in the elite goaltending category."
Crawford, now coaching in Switzerland, had no doubts. He said he was amazed that Jones went through the 2008 NHL Draft without being picked, mainly because he thought the Vancouver Canucks would take him in the seventh round when they were looking for a goalie.
Jones' dad, Harvey, is in charge of operations at Rogers Arena, where the Canucks play their home games. Vancouver instead selected Morgan Clark, son of their goaltending coach at the time, Ian Clark, who now works for the Columbus Blue Jackets.
"One way or another, there was going to be some nepotism, but Marty went through," Crawford said.
Crawford said prior to the 2008 draft, when he was still coaching the Kings, he tried to convince L.A.'s scouting staff to get to know Jones. They listened and signed Jones on Oct. 2, 2008, after inviting him to training camp.
"They saw him in training camp and they were like, 'Wow, he is that good,'" Crawford said.
Jones was named the top goalie in the WHL in 2010. He won 84 games in three-plus seasons with the Manchester, which was L.A.'s AHL affiliate at the time.
Jones went 12-6-0 with a 1.81 GAA and .934 save percentage with the Kings in 2013-14, including a stretch of eight straight wins with three shutouts and eight goals allowed from Dec. 3-21, 2013, when Quick was out with an injury.
The Kings have Milan Lucic because they traded Jones in a package to the Boston Bruins on June 26 for the power forward. The Sharks got Jones from the Bruins four days later for a first-round pick in the 2016 NHL Draft and prospect Sean Kuraly.
San Jose signed Jones to a three-year contract reportedly worth $9 million, giving him the opportunity to be a No. 1 goalie in the NHL seven years after he went undrafted.
"I wanted to work for it and earn my ice time," Jones said. "I didn't want to be handed anything. I want to continue to earn it."
Jones is trying to be realistic, not satisfied, about his start to the season.
"I don't want to get too far ahead of myself; it's four games," he said. "Part of being a starting goaltender is doing it over the course of 82 games. I just want to make sure we continue with the focus we've had here."
Sharks coach Peter DeBoer admitted there was a curiosity factor to Jones when he got to San Jose because he had never been a No. 1 goalie in the NHL. DeBoer, though, said the reports he got on Jones reminded him of the reports he got on Cory Schneider when he was coach of the New Jersey Devils.
"It was situational, just like Cory," DeBoer said. "It wasn't the fact that he wasn't ready to play."
Schneider had some success with the Canucks but was in Roberto Luongo's shadow before the Devils acquired him for a first-round pick in the 2013 NHL Draft (Bo Horvat).
Schneider has become one of the better No. 1 goalies in the NHL. Jones might be on his way.
"Composure," DeBoer said when asked what sticks out about Jones. "He really has a calming sense. I think good goalies have that. Marty [Brodeur] had that. Cory [Schneider] has that quality. They don't get rattled. They don't get too high or too low. Your team reads off of that, so it's a nice feeling."
Crawford saw that 12 years ago, when Jones helped the North Vancouver team to the championship at the esteemed Quebec International Peewee Hockey Tournament.
"They had about five or six kids playing in the NHL now, including Evander Kane, Patrick Wiercioch and Stefan Elliott, which means they had a lot of really good players, but [Jones] was outstanding," Crawford said. "I watched the tape of it two or three years ago and I'm looking at it going, 'Holy, was Marty ever good.' So often that was the case."
And that has still been the case with the Sharks, albeit only through four games. His fifth comes Monday at MSG. Crawford can't think of a reason why it will go any differently than the previous four.
"The goalie has to win games for you, and he's learned how to do that from a young age," Crawford said. "I've very rarely seen him have bad outings. When he does have one, he'll follow it up with a real quality start. That's character, but it's also having the quality of knowing what your game is all about. That's why I think he'll continue to be real good in the NHL."