Below is a table showing the multipliers used when calculating hero damage. For example, if you want to calculate damage from a basic attack for Augustus, you can take the 49.5% and multiply that by the Attack value on Augustus to give you the average damage he will do for a basic attack. There is also a random +/- 10% adjustment to the damage amount, so you will see a range of damage around the average calculation.
Same process for special abilities. Kozar's Home Run ability does damage equal to 95% of his attack value. Note that the base damage amount visible in the Tool Tip on the Hero ability tab in game is based on unadjusted Attack value. So, if you wanted to calculate that number, you would have to go into the stat tab of the hero, press and hold down on the Attack stat and make note of the unadjusted Attack amount. If you multiply that Attack amount by the multipliers in the table, you can recompute the amounts you see in the Hero ability tab tool tip.
Some interesting things to note: Most basic attack multipliers are 49.5%, except for heroes with epic weapons, which are increased to 50% for some reason. The exceptions to that exception are: Bauble, Grog Nog, Selwyn and Pontifex. These four all have a 50% multiplier for their basic attack, but don't have epic weapons. Selwyn had been 49.5% for a long time and just recently changed to 50% -- maybe we will see a Selwyn epic soon? Pontifex has actually been at 50% for a long time, so not sure why he is different. Other exceptions to the 49.5% rule are heroes that have AOE basic attacks or some other special basic attack ability along with just damage. For example, The Furnace has a basic attack multiplier of only 17.5%, because his basic is an AOE that hits all opponents. Aria's basic attack multiplier is 35%, possibly because it has the Provoke feature to it. Interestingly, Grog Nog is a bit overpowered with is basic attack, because he gets the full 50% multiplier, but has a double attack for his basic. I'm guessing this was intentional, but does seem a bit unfair in comparison with all other heroes.
In terms of multiplier MVPs, General Krexx takes the prize of the largest single target multiplier at a whopping 210% for his first special (Tail Strike). And who is the king of AOE? Hands down it is Grog Nog, who is significantly ahead of the pack with a 130% multiplier on his Strike ability. Grog Nog seems to have been given an abundance of AOE blessings, as his second ability (Snow Day), comes powered and is at a respectable 115%. Even his 3rd ability (Frost Breath) becomes an AOE if a Snow Day buff is active. And let's not forget Grog's basic attack is also a 2 person AOE.