Mandi,
Yes, some randomness is needed in this case. Your idea of 2.5 day long shifts does look like a move in the correct direction. The PagerDuty schedule editor does allow 60 hour shifts, corresponding to 2.5 day shifts. However, that specific value, 2.5 days, isn’t perfect. That schedule repeats every five weeks. A little better than repeating every two weeks.
The math of finding the repeat is multiplying the number of people times the shift length, then determining how many times that needs to be multiplied to get a multiple of 7. Finding a value other than 2.5 is “an exercise for the reader.”
What we actually did was shift the rotation order. e.g. If seven folks are ABCDEFG, we went ABCDEFG, then moved A to end yielding, BCDEFGA, then B yielding CDEFGAB. The result was a little better, though we found shifting two folks would yield an even better result.
The mechanics of implementing a shift in the rotation order in PD were adequate, though tedious. The only way we found to enforce a new rotation order was to start a schedule with one person in the rotation as of the date they are “on.” Then another schedule with the second person, etc.
thanks for considering the problem and sharing your experience,
Peter