BTW you had me laughing out loud with your comments and the exchange with CP. It was as if you two had orchistrated a straight man funny man act. Good fun. I was L-ingOL (or is it LOL_ing?) over your convolutions.
IN the two graphs the dots are what we actually did and the curves are the models.
The only goal we had each day was 12 hours of travelling, although we did go more than 12 and less than 12, of course.
The points climb more steeply at the end because with a lighter pack we could go further, both faster and longer -- that was UL backpacking at its best.
Of course the terrain did matter -- swimmimg rivers and snowy passes slowed us down. So did bear detours and tussocks. But the big picture shows a consistent, but somewhat weak, trend of going farther, faster as the trip progressed, not just becasue we were stronger, smarter, more driven (because we also had less chocolate, more difficult travelling, and more sore feet) at the end, but because we could move more easily -- hence farther each day with the same amount of overall effort.
If you were to go on a long hike and record the distance walked each day and plot the distance from the start, your curve would likely look similar. Your initial distance per day may be less, so your average distances per day would also be less, but the slightly upward curve to the data points would be there for you, too, I reckon.
Anyway, thanks for indulging me!
Some like to tinker with gear, I like to tinker with the relationship between my body and Earth's landscapes and to interpret them in a variety of ways -- analytical as well as emotional.