My Moto X is working fine going on 5 yrs. with the original battery. Is that unusual?
It’s not unheard of, I would not expect lots of them that’s been used since the first launched in late fall of 2013 to still have great battery life, I would say you got lucky [as the phone expected battery life is 2-4 years and you are at 4.5+]
Many factors affect battery lifespan.
Usage habits of the phone it self, how often u charge, ambient temperature during use and charging, use of OEM or 3rd party chargers and cables, the quality of raw power going in to the charger, the manufacture quality of the battery it self.
I have had many phones over the years, even identical models, and sometimes the battery is still very good 3 yrs later, but often they are much weaker around 2 yrs. Most phone batteries, in my experience, have noticeable lower life just after 1yr.
I can say for certain, that todays newer phones and batteries are far worse lifespan than older made devices. I still have some old 3G smartphones, and even some older bar and flip phones. Their batteries are still good and even have held its charge and the phone power up over a year later of just siting in a drawer unused.