I have three batteries used in succession and all new. The problem is the same. I supect apps are in use when not needed I've replaced my damaged battery with a new one in my Samsung Galaxy Note 2, but it drains too quickly.

After fully charging the battery, when I leave the phone without using it (the screen is totally off &amp; no apps running background), the battery level gradually reduces to 87% with in 20 to 30 minutes. 

Below 87% to 36%, the battery performance is petty good, but when it is below 36%, the battery drains too fast. It falls to 0% within 5 to 10 minutes, and if I play any game when battery level is around 30%, it shuts down without informing me the battery low information.

I changed the battery twice from the shop that I bought it from, but the same thing occurs.

Why is my phone draining my battery so quickly (and inconsistently)? Is it a battery/software/hardware problem?
Please check is there any application having more number of services. Setting-> Application -> Running.

If there is more number of services it will eat your battery.

The main thing is your display will drain your battery. So that the android OS recommend that the following

http://www.wikihow.com/Save-Battery-Power-on-an-Android

http://www.pcmag.com/article2/0,2817,2367542,00.asp