Just to be sure that we're on the same page, do you have a 2016 with Sport mode, and have you tried it at least 5+ times?
I was thinking about putting a camera below the seat recording the pedal, and another recording the dash/speedometer, but then I don't know exactly yet how to show the difference. I guess I'll have to try a few times going on the same uphill ramp with and without Sport mode to know how to describe it. Mazda probably has some internal charts showing the difference, but for now it seems to me that it's like a car's handling, you have to drive a Mazda to know how it's different from a Toyota.
If you've tried Sport mode, do you notice that you just have to tip-in slightly, and it doesn't rev as loud as when you floor it, yet it stills get the power to accelerate quickly? That could be the difference I felt between normal and Sport mode when not pushing the engine to its max.
At least in term of feeling, both my daughter and I can tell the acceleration in Sport mode pushing us against the seats, that feeling can hardly be felt in normal mode.