Each side is hoping for a perfect match.
Fredette joined the surging Bulls on Sunday after the team announced it had signed the sharp-shooting guard for the rest of the season. The 6-foot-2 Fredette then played the last three minutes of Chicago's 109-90 victory over the New York Knicks, drilling a long jumper for his first basket with his new team.
"These guys did a great job the whole game and got a big lead and I was able to get into the game," Fredette said. "I don't really know the plays or anything like that. Just knew a few simple things and ran those. But it felt good to get in there in front of the fans, and to have a great win like that was great for us."
Fredette, the 10th overall pick in the 2011 draft, was bought out by the Sacramento Kings on Thursday and cleared waivers on Saturday. He is averaging just 5.8 points and 11.1 minutes in his third season, but is shooting 49 percent from 3-point range.
The Bulls, who have won nine of 10, had been looking for more outside shooting since they lost Marco Belinelli in free agency last offseason, and then traded Luol Deng to Cleveland in January.
"Jimmer is going to be a hell of a player here," said teammate Jimmy Butler, who had 19 points against New York. "I hear he works incredibly hard, and we all know he can shoot the ball.
The knock on Fredette is his defensive ability and finding a way to get open for his accurate shot, but coach Tom Thibodeau said he wants to come to his own conclusions about what the former BYU star can do on the court.
"He's got to learn defensively what to do in terms of team defense and that's usually the biggest adjustment," Thibodeau said before the game. "But the fact that he can shoot the way that he can, I think it complements our primary scorers as well."
Fredette became a top NBA prospect when he led the nation in scoring at 28.5 points per game during his senior year with the Cougars, who made it to the final 16 in the NCAA tournament in his last season. He was The Associated Press player of the year, but he never lived up to his billing in Sacramento after the Kings acquired him in a draft-day trade with Milwaukee.
It was clear his time with the Kings was coming to an end when they decided not to pick up his option for 2014-15 before this season.
"I appreciate everything that happened in Sacramento," Fredette said. "It was character building for me continuing to go out and play hard. I feel like I progressed as a player. Even though sometimes you don't get the minutes you want to, you've just got to continue to work hard and know that if you keep playing hard and doing the right things then eventually things will turn your way."
One of the top attractions for Fredette with the Bulls is Thibodeau, who has a history of helping lower-tier free agents turn into valuable commodities. Belinelli and Nate Robinson flourished in Chicago last season, and D.J. Augustin has played well since he signed with the Bulls in December.
"This time of the year, I think you're always looking to get insurance for your team," Thibodeau said. "You like his makeup. I think he can grow. I think he'll get better. So we'll see how it unfolds. But you also have to remember you have to put the team first."
Jay Cohen can be reached at http://www.twitter.com/jcohenap