Sorry for taking so long to post.
You didn't specify how much you actually use your battery, and if, as I suspect, your usage pattern is similar to mine - I virtually never use my battery. - you ought to read
this thread.
The issue of battery non-use hasn't been addressed anywhere that I've been able to find in a number of years, so I've asked several AppleCare techs and Geniuses what to do and invariably been told to run my battery down once a month. (The last AC tech I spoke to was shocked to hear that there isn't an Apple doc that addresses the issue, and said that he was going to request that advice to run unused batteries down once a month be added to Apple's database, but the issue still hasn't been addressed.
)
...your turn to call AppleCare if your issue is the same as mine.
As for running your battery down to 20%, I've always allowed my deuced Mac(hina)s to run until they shut down, but newer Macs, yours included, I imagine, don't actually shut down even though it looks like they have; they start up on their own - no need to hit the power button - a moment after you reconnect the MagSafe, i.e. it looks like current batteries are designed so they may be run down with no resultant damage.
To complete the picture, I'll say that I've had two batteries go bad on me over the years, but "Why?" is anybody's guess.
By the way, since your old MBP is about to become a seldom-used backup machine, I'll mention that there's advice on the matter in
Batteries - Maximizing Performance (to which joemike has already linked and which you may have already read) and more in
How to store Apple notebook computers and their batteries.