Better battery life by factory reset? This is a bit odd. I thought I fairly well grokked how things worked, but this seems weird to me.

I have an original Moto X. I've had it for almost two years now. It started off with Android 4.2 (Jelly Bean) and, slowly but surely (because Verizon) got updated through to Android 5.1 (Lollipop). It has never been rooted.

I figured it's been getting a bit long in the tooth, and the battery life has reflected that. I could leave the house at 100% charge in the morning and, a two-hour train ride later, without ever touching the phone, would be down to about 60% battery. If I didn't charge at work, it would be dead by 2:00, with minimal usage. If I work at home, with reliable wifi all day, I can usually get to about 4:00 before having to charge. But, I figured, this is just what happens to a well-used phone toward the end of its life.

I finally got the Lollipop upgrade and had been using it for a couple of weeks. Things were okay, but not quite right. So I decided I had nothing to lose by doing a factory reset.

So, I did. I restored all the same apps back to the phone, with the exception of a couple that I finally realized I never use and some Verizon bloatware that I disabled.

But now, my battery life has improved tremendously. At home, with a fair amount of use, I never put it on the charger in the middle of the day and went to bed with 40% on the battery. I use an app that graphs my battery usage, and the slope is significantly shallower when I'm not using the phone than it used to be. I'm not using it any differently, but battery life is way up.

What could have happened? I used to check fairly frequently what was using my battery and there was never anything "weird" there. There also weren't any unaccounted for amounts. I am seeing the apparently irksome "Cell Standby" draining some, but even so the whole thing is lasting much longer than it used to.

I don't want to look a gift horse in the mouth, but I'm kind of wondering what I did by doing a factory reset.
You cleared Android's batterystats file by doing a factory reset, specifically the file /data/system/batterystats.bin was deleted and regenerated. This file holds a calibration for your battery. Before you did a factory reset, your batterystats was probably miscalibrated. It's a common practice, for rooted devices, to delete this file every now and then with a fully charged battery. This correctly recalibrates batterystats.