My battery is draining fast as well without any OS update. Have you tried wiping the cache partition? Often that will fix battery problems. With the phone off, touch the Volume Up, Power, and Home keys at the same time. The phone will go into recovery mode. Use the Volume Down key to highlight Yes to the Wipe Cache Partition. Click the Power key to execute the action. After partition wipe is complete, select Reboot and press Power to execute the reboot. Hopefully, this will help.