It's not about lowering the rig, it's about eliminating the min day and going to purely an average day. The average day and the rigs will ensure the efficiency, but a min calendar day or duty period minimum over 4 hours will make it impossible for the pairing generator to spit out commutable pairings on a consistent basis. Your point-to-point network actually makes it easier for the pairing generator to create efficient trips that are commutable, but you're artificially constraining it with the min day. The job of the pairing generator is to spit out a solution that saves the company the most money while still complying with all of the constraints. So when you plug in a 5 hour min calendar day or min duty period, it will do everything in its power to make all of the pairings have no duty periods or days with less than that amount, commutability be damned.
In reality, the average day is what really matters. A 26 hour 4-day pays the same 26 hours whether it's spread out over the 4 days or crammed mostly into the middle 2 days. If I can have a trip that puts 8 hours into each of the middle 2 days, that leaves only 4 hours on the beginning and ending day, making it far more likely that they'll be commutable. But if the pairing generator is running a solution, and it has a trip with 26 hours, but the beginning and ending days have only 4.5 hours on them, and you've got a 5 hour min day, guess what the generator is going to do? It's going to tack on another short out-and-back to make sure that the company doesn't pay you 0.5 hours each of those days for flying that you didn't do.
Scheduling constraints are a double edged sword. You want to make sure that you design them so that the company doesn't make your schedules inefficient, but you don't want to make them so constraining that the pairing generator screws you over. Obviously, for the greedy f-cks who don't care about spending time at home, none of this matters. But for the people who do, how you design scheduling rules is of the utmost importance.
