Although i must laud the Galaxy S4 Mini's battery. 13 hour video playback!! almost 10 hours web browsing (9:45 to be exact)!! Standby is not great but still Samsung getting such performance out of its 1900MaH battery. Even the Razr Maxx with 3300MaH battery couldn't catch up.
I am getting 11Hrs of videoplayback on my Sony tipo with 1500mAH.
Battery Backup mostly depends on CPU scheduler. To increase battery backup you can always remove battery draining apps. Use moli player it is a very efficient player and doesn't drain battery like other player in google market.