Welcome to Android Central! Charge up to 100%, then let it drain to 20-30% with normal usage, without charging in between. Then show us:
1. The main Settings>Battery screen.
2. The fullscreen battery graph screen (which may show Awake time and Cell Signal Strength).
3. The Screen category (to see total Screen On time).
4. The Cell Standby category, if present (to see Time Without Signal).
In GSam, look for the battery graph, and show us what it looks like over the duration of a battery charge (i.e., from 100% down to about 20%). If it's mostly in the low to medium range, that's probably your main problem.
Has this happened suddenly or slowly over time?
A battery's charge capacity diminishes with age so even though it shows 100% it may be more like a 50% charge on a new battery in terms of amp/hours.
Best practice not to charge Li bats to 100%, it takes away hundreds even thousands of charge cycles!!!
Be mindful of this especially with a new battery. High temps and high level charges kill Li's prematurely.
Samsung Galaxy Labs has 2 useful apps Battery Guardian and Battery Tracker that can be useful. Very low power consumption.