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Dunleavy obviously won't be starting over Luol Deng or Jimmy Butler at the wing positions, but he can be used to give the Bulls a spark on offense if they're struggling to score.
According to Hoops Stats, the Bulls were 23rd in the league in bench scoring in the 2012-13 season, but a huge portion of that is credited to Nate Robinson, who became a starter during the playoffs.
Furthermore, it's unlikely that the Bulls could cough up enough money to re-sign Robinson to a long-term contract.
Dunleavy won't provide the same level of playmaking and intensity, but he's still an effective contributor in limited minutes off of the bench.
For the past two seasons with the Milwaukee Bucks, Dunleavy has averaged 26.1 minutes per game, but only started in six out of 130 games. He still managed to average 11.2 PPG on 45.7 percent shooting from the field and 41.6 percent from beyond the arc.