Same issue here
I have the same issue.
battery jumps up by at least 5 - 10 %
battery jumps down by 5%
battery stays at 1% for a very long time at the end of the day.
If there are no reboots involved then I would see sharp drops in the battery graph at the end of the day.
I looked into this issue and found out the battery circuit might be build poorly by LG for nexus 4.
I overcame this drain issue by:
- not looking at the graph often
- Installed custom kernel that allowed me to under clock to save battery.
If you are non-root then i would suggest letting the battery drain to the point where the phone turns off.
Then go to fastboot and let the phone drain more battery by leaving the screen ON. ( going to fastboot: 1) turn off the phone 2) press and hold the power and volume down button).