Ask most everyone in the Leverage team, and they'll say Sophie is the resident actress of the group. Sure, her acting's hammy and overdramatic when she's on stage, but she's a master grifter. But there's another actress on the team, and the whole world's her stage: Parker.
Parker functions like any other member of the team. She plays her part in the team's cons when she needs to. But the persona the team thinks she has? It's all an act.
Jumping from foster home to foster home, from parent to parent, hurt Parker as a child. She started to question whether she was actually loved or not. She soon discovered the best way to get attention, good or bad, was from doing unpredictable things. Parker created her own portable theater through the act of being spontaneous. Sometimes it worked. Most of the time it didn't.
As she learned how to become a thief, Parker discovered the theater of unpredictability worked in her advantage. It heighted all the stunts she pulled in order to pull off her heists. It made her that much more dangerous. There were also advantages and disadvantages to her theater. Over time, Parker developed a legend for her persona and her heists. This led her to the Leverage team. But her persona also caused her to be arrested by Nate Ford before the Leverage team was formed. And after the Leverage team was formed, she couldn't switch off the persona in front of her teammates.
Sometimes Parker wonders if she'll tell the team she's not as mad as she appears. It would be closing time on her act, and her legend of being unpredictable would fade away. But after she thinks this, she decides she'd rather let the team think she's crazy instead. She doesn't want to lose the family she has over one little white lie.