I like your statistic method, Master Hopwood: good enough for meaningful analysis but not obsessively precise. My anecdote doesn't relate to a Rohloff, because I got my Rohloff at the changeover to a different kind of bike, tyres, wheel type, brakes, everything, so the comparison was always dicey in a statistical sense, too dependent on opinion.
But earlier I changed from a Gazelle Toulouse, fitted with a manually controlled Shimano Nexus hub gearbox, to a Trek Navigator Smover, a very similar sort of bike, with a Di2 fully automatic gearbox (basically the same Nexus with a stepper motor rather than a gear cable), electronically operated. The only important different thing was that the suspension was also electronically operated on the Trek. At first I was slowed down a bit by trying to operate the gearbox in the manual mode. But the minute I got the hang of just pedaling up to my predetermined heart rate and letting the electronics take care of everything else, I soon started building extra speed. My median results over hundreds of rides over the same circuit that I rode almost daily, was around the 7-10% mark faster than before, which isn't as important to me as nailing my heart rate somewhere around 78% of max and holding it there, which I did much more consistently and, crucially, faster on each ride, so that the beneficial exercise in fact lasted longer even if the ride was shortened by greater speed.
It took me a couple of months to settle down to that stage, and I emphasize, I wasn't making a huge change like you did, just going from a manual to an automatic gear change.
By the way, I find that my version of heavier wheels, which come with low pressure 60mm Big Apple Liteskins (790gr each!), leaves everyone on road bikes behind on the downhills. They have to ride round the potholes on their their narrow tyres. I just ride right through them, and the roughness of the road, which throws them everywhere so that they have to slow or lose control, I just steamroller flat, hardly noticing the road surface. So not all heavy wheels slow you on the downhills.
Before my medical problems, I was a bit faster on my Rohloff-equipped bike overall than on the theoretically lighter, faster bikes. (By then I didn't bother with keeping records: smiles before miles, as has been said in this thread already.) The reason is again my bad roads and the difference the huge 60mm low pressure tyres make: on the Marathon Plus and workalikes I had before on the (theoretically) faster bikes, I had to slow down for the road, which on my Rohloff-equipped big balloon bike I generally pay zero attention to, except when I run out of it because I'm going too fast, and am painfully reminded of it. (I keep meaning to write up "An Anatomy of Bicycle Incident" -- we old racers never, never, ever, use the word *cc*d*nt -- but running out of time.)
