Nexus 6 Battery Issues

Hi there, I just purchased new a Nexus 6, love the phone, seems that all new phones all looking like a Samsung or iPhone which is not good.

The phone just purchased is new out of the box from eBay and shipped over from Hong Kong.

When the phone is idle I get a good day out of it buy when in use I can see the banner count dropping very quickly, if I had to use it for an hour on the phone I would guess that the banner would drain to 0. If I play around with the phone I would assume that it wont last more than 2 hours at the most.

Is this a common issue with the phone or should I assume that the phone has been sitting in a warehouse for the past 4 years with no use causing an issue with the banner to deplete so quickly.

I was also wondering if it is was worth replacing the battery or is it an issue with the phone?

A few days ago I noticed the phone shutting down when at 15%, since then I re-booted the phone in safe mode, worked with it for a few hours, then back to normal mode and it seems that it now drains to 0.

Any help appreciated.