After several months of statistical analysis of raid and AW fighting, here is my conclusion.

The damage can be estimated from the attack / defense ratio with a power function.

EDIT : After the post of RedPython, it made me think and I redid my calculations …

And finally, everything is clearer! all my previous calculations are merged into one formula, so I modified the original message. Again thank you @RedPython!

** Damage ≈ 100 x ( θ x Att / Def ) ^ 1.35 **

Tile damage is divided by three

The defense of the team managed by the AI is increased by 20% (certainly only concerns PvP fights)

θ is a random parameter between exp(-.5)=0.606 and exp(.5)=1.649.

I have no way of being sure of the formula used by the game algorithm, but these estimates are reliable for the 1047 cases studied. They allow us to deduce interesting things.

As long as the attack is inferior to the defense, the damage is ‘compressed’ between 1 and 33 for the tiles and 1 and 100 for the special skills and attacks of the defenders.

On the other hand, once the attack is superior to the defense, the damage can fly away with no known maximum.

(This also explains the impression of ‘levels’ felt on the map and against the titans. Once our heroes have evolved so that their attack is superior to the opposing defense, everything becomes easier!)

Having several heroes of the same color only increases tile damage. They are calculated by adding the attacks of these heroes

Lowering the enemy defense is more effective than increasing the attack.

Combining defense penalties and attack bonuses has a devastating effect.

I hope they will not change the calculation right away …