Fortunately, Fraser does have a midfielder who recently made a very big difference, scoring the goal that gave Chivas its first victory of the Major League Soccer season and Fraser his first win as an MLS head coach.
That would be Mariano Trujillo, the Mexican midfielder who last weekend bundled home the rebound of a shot by teammate Justin Braun as Chivas upended the San Jose Earthquakes, 2-1.
It wasn't the prettiest of goals, as Fraser admitted ahead of Saturday night's match against New England in Carson.
"Absolutely," he said, "but if he doesn't make the run to get there then he doesn't score it. So, to be honest, it was the type of goal that I would envision him scoring because it's an unselfish goal."
Braun's shot from the right side of the net was palmed away by diving San Jose goalkeeper Jon Busch, and the ball fell kindly for Trujillo, who was trailing the play on the left.
"I was defending on the left side and I was just following, following," Trujillo said. "I saw that Justin was running through the defenders, and I was waiting for the deflection. I was ready. Fortunately for me, the ball came straight to me and I was able to kick it in."
Not really. It was more a case of the ball bouncing off Trujillo's shin and into the net, but the details were unimportant. It was the victory that mattered.
"It was great," Trujillo said. "We've been working so hard during the week and not being able to get a result on the weekend. It was kind of frustrating. When we got the victory, in the locker room it was kind of like a party, something like that."
Trujillo said Chivas is gradually coming together as a team and the fact that it was unbeaten in four consecutive games coming into Saturday's match supported that view.
"In the beginning, it was a new process," he said, "new coach, new players. I think finally after six games we've found ourselves in a good spot to play as a team. I think we're on the right path."
Fraser said Trujillo's play in the midfield, where he is more at home than in the defensive right back spot he occupied last season, has helped.
"Mariano came in and did well against San Jose," Fraser said. "I thought he really provided some energy" as a second-half replacement for starter Ben Zemanski.
"He had some good possession and then some good attacking forays, which obviously ended up with him scoring the game-winner.
"What a great thing where a guy just makes a hard, unselfish run to the back post — no idea if he's going to get it or not — but he makes a run to be an option and Justin does the right thing, hits it low and far post, and Busch makes a save and it spills right to his feet.
"I was so happy for him because he's such a good professional and such an unselfish person."
It was Trujillo's first goal in MLS in his third season in the league.
New England, meanwhile, promised to provide as much of a challenge as any Chivas has faced this year, with Joseph, the 32-year-old Grenada international playmaker being the main threat.
"It's been amazing over the years," Fraser said. "When they've had good teams, he's been great. When they've have bad teams, he's been great. He's just the type of player who changes games.
"For so many years now, more than I can actually pinpoint, I feel like Shalrie has come up with a key play for them week in and week out, when they needed it the most.
"At the end of the day, you've got to think it's about Shalrie."