Joffrey Baratheon has the ability to gain power, and quickly. For example, the plot Wildfire Assault could be used to kill your own Lords and Ladies and close out a game in one shot. Joff will stop at nothing to gain power, after all!
Otherwise, Joffrey Baratheon gains power gradually as the game goes on. He adds a reasonable boost to the blue icons of House Lannister- for best value, give him Widow’s Wail which is hideously efficient in Joff’s hands!