For times we don't know WHAT does Heroes' ability affects on damage spectrum: DPA or DPS. DPA is damage per attack. This is important as each troop has a different attacking speed. DPS is damage per second, mean rate of damage for 1 second. This is needed to be tested... Here is it:
Here is my video which proves that DPA is NOT rounded. The first cannon that attacked my level 5 Giant (670 HP) deals 15 DPS. As canons' attack speed is 0.8 seconds it has 12 DPA (no need to be rounded). It fired 21 hits toward the Giant before being destroyed by the Giant. The cannon in the upper section is both level 2 (11 DPS, either 8.8, 8, or 9 DPA, being tested). Now the giant is left with 670 - 252 = 418 HP. The number of total hits from both cannon to kill the giant corresponding to the DPA being suspected, is by dividing HP left with DPA and then round it up, and is equal to 48 (not rounded), 53 (round down), or 47 (rounded up). If you're not sure that it is 48 hits in this video there was a prove that wall breaker level 5 (42 HP) is not 1-hit by a Wizard Tower level 6 (41.6 DPA if not rounded), meaning that the damage is not rounded up.
Next is Hero ability's effect on damage (I stopped here temporarily):
My video that proved that the damage increased by Hero's ability is DPS. I dropped 2 Archers, 1 at a time so that the Town Hall is hurt by 5 arrows by each archer and the archer is dead. As it has 20 DPS, attack speed 1 second, and TH's HP is 1500 (level 1), it is now left with 1300 HP. Barking level 5's DPS is 129, attack speed 1.2 s, DPA 154.8. The Barbking first hit the Town Hall 7 times (1083.6 damage), leaving the TH with 216.4 HP. If the Barking's ability affects DPA then the TH is not destroyed at this point (154.8+56=201.8 while (129+56)*1.2=222). But after 7 times hitting TH and hit it 8th time in his ability, the TH is destroyed! This means that the ability affects DPS.