There are a lot of different things that can cause this, but a "miscalibrated battery" is not one of them. Android does not store battery information through a reboot.
There are 2 apps you can download to help understand what is using battery on your phone and slow down apps' energy usage. I do not represent either of the developers, I've just used them for years with a lot of success.
- GSam Battery Monitor- this is a replacement for the built in battery monitor which, on my device, is about as accurate as if you asked a 3 years old how much battery my phone is using. It takes far more accurate measurements that the default monitor.
- Greenify- this app is an interesting type of task-killer. It uses the phone's accessibility system to force quit apps for you when they no longer need to be running, such as the insane amount of background battery drain from Facebook. Apps that are "Greenified" are shut down for you if you are rooted, or with a tap of a shortcut on the home launder if you are not. Be careful what you use this on though. Anything that you need notifications from or needs to be running in the background (like any messaging services) should not be killed.
There are some other little things you can do in the settings too. Wifi is normally a very large drain on the battery because of Google's wifi scanning for geolocation. This can be turned off in the location setting's advanced menu. In the wifi advanced settings, there is also an option to return wifi off while asleep. This saves more power than you'd think it would.
Finally, if your battery is removable, you have the advantage of being able to replace the battery at a fairly low cost.