If someone picks this up, I would suggest a graphical output display. It would be a timeline starting at midnight user's time on the left and ending at midnight user's time on the right, the percent of turns taken per hour would be displayed in a bar chart.
I would also add another thing to the bottom: Average time to start turn. This would help to show if the graph is "accurate." If a user is just online 24 hours a day, his graph may be influenced by when other users take their turns rather than when he is online.
If you want to get really fancy, color code or indicate "dead time" which would be the periods where the user allows turns to sit for the longest period of time before taking them.
Note that the latter stuff is not nearly as useful as the first part. Freestyle games often have users waiting to be the LAST to take their turns. So if a user tries to be on from 1-3 PM every day, he may try to take the round's last turn at 2:30, knowing that it can sit around for 22 hours before he gets back on at 1 PM.