Hits to kill
Below data is hits to kill per unit to wipe out the opposing force, the left number is without +10% the right number is with +10%, all cases not displayed yield more hits required per unit gold.
16 Wisp vs 18 Sandstinger 15.0 14.625
16 Wisp vs 2 Apocalyte 1.6666666666666667 1.625
16 Sandstinger vs 2 Percognitor 0.8888888888888888 0.875
16 Sandstinger vs 18 Sandstinger 7.0 6.75
16 Sandstinger vs 2 Apocalyte 0.7777777777777778 0.75
3 DevilkinDervish vs 3 GroveTender 2.25 2.0
3 DevilkinDervish vs 4 Quadrapus 3.0 2.6666666666666665
3 DevilkinDervish vs 3 Frostcaller 2.25 2.0
3 DevilkinDervish vs 12 Raptor 9.0 8.0
3 DevilkinDervish vs 4 Ignitor 3.0 2.6666666666666665
8 Scuttleguard vs 18 Wisp 14.0 13.5
8 Scuttleguard vs 4 Purifier 6.666666666666667 6.5
8 Scuttleguard vs 18 Sandstinger 16.0 15.75
8 Scuttleguard vs 2 Apocalyte 1.7777777777777777 1.75
8 GlacialRanger vs 3 GroveTender 2.6666666666666665 2.625
8 GlacialRanger vs 18 Wisp 12.0 11.25
8 GlacialRanger vs 2 Percognitor 1.7777777777777777 1.75
8 GlacialRanger vs 4 Quadrapus 3.5555555555555554 3.5
8 GlacialRanger vs 3 Frostcaller 2.6666666666666665 2.625
8 GlacialRanger vs 12 Raptor 10.666666666666666 10.5
8 GlacialRanger vs 4 Ignitor 3.5555555555555554 3.5
I have run all of the numbers for vanilla units vs the damage +1 upgrade this is the 10% boost, as was noted by Day[9] and I agree a number that we should also be looking at is the number of hits to kill. I look at two cases across all combinations of all units, we look at the minimum case, which is 1 attacking unit with a +10% damage upgrade, and we look at the maximum case, this is the attacking units at cap. We then take the gold count of both situations and max out the defending units. In this way we have 4 cases. We have 1 attacking unit against x defending units where the attacking unit has +1 attack. We have N attacking units and x defending units where the attacking units have no attack upgrades. We have maxed out attacking units against x defending units, where x cannot exceed the defending units cap, and we have N attacking units vs x defending units where N is the maximum number of units that will fit into our gold cap after the upgrade.
We only care about situations where the upgrade has yielded a smaller number of attacks per attacking unit to eliminate the opposing force. To find this, we take the number of attacks required for one attacker to kill on defender, multiply it against the number of defenders and divide that by the number of attackers. This gives us the number of attacks required per attacking unit to destroy all enemy units. Note that I am not taking into consideration many variables, and that this is only a first pass, but it gives us a rough idea of how much that +10% upgrade helps us. Please note that there are no cases where one unit with 10% additional attack is beneficial, this makes sense, but also means that I might need to look into small numbers of units, or fixed gold points...
Above are the only situations I have found that the +10% damage upgrade is useful. I plan to expand this to the +25% upgrade soon.
I would be interested to see what you guys think, I have the source code for this if anyone wants to take a look... I would also be curious if you guys agree with my math, perhaps there is a better way to do this that I am missing?