How do I know if I should replace the battery of my htc ville?

I have a htc one S (since 2012) with cyanogenmod and after 13 hours and 1.5 (!) hours of screen time, my phone is done for.
I already have bought a second battery and watched some youtube video on how to replace.
Still I do not know if I really should take the risk. Am i chasing ghosts and shadows or do I have a good chance of improving the power circle of my device?
Some betterbatterystats which seem to be fine (software-side) as far as i can judge:

Quote:

============ Battery Info ============ Level lost [%]: Bat.: -86%(99% to 13%) [6.6%/h] Voltage lost [mV]: (4001-3167) [63.6%/h] =========== Other Usage =========== Deep Sleep (): 10 h 10 m 52 s 77.6% Awake (): 2 h 56 m 22.4% Screen On (): 1 h 26 m 30 s 11.0% Phone On (): 17 s 0.0% Wifi On (): 3 h 58 m 11 s 30.3% Wifi Running (): 13 h 6 m 52 s 100.0% No Data Connection (): 3 h 38 m 33 s 27.8% No or Unknown Signal (): 3 h 38 m 33 s 27.8% Moderate Signal (): 5 m 45 s 0.7% Good Signal (): 8 h 12 m 62.5% Screen dark (): 59 m 13 s 7.5% Screen dimmed (): 11 s 0.0% Screen medium (): 13 s 0.0% Screen light (): 1 s 0.0% Screen bright (): 26 m 51 s 3.4%