Creative Director's are paid a project fee + a percentage of the total project value. This represents the small amount of time that goes into the process, project set up and completions, although the time is only 3-4 hours, the payment is significant to represent the level of responsibility and success of Deep Work.
If the Creative Director is an expert on the sprint (e.g. a facilitator or designer), they are paid this rate on top. If the process is followed, you can expect the role to take little time. However, the payout represents that you are on hand for any mistakes or client issues, making sure you're available to drop anything and take full time, responsibility and energy to find a solution.