let us see after how many battles of 9 ogres vs 9 ogres will the shield upgrade have paid itself off.
first let's convert wood into gold. I do not have the numbers of wood and gold gathering speeds (at fortress phase of the game) therefore I cannot give exact factor - I used to have these numbers but I have lost my excel files. Let us go with an educated guess of factor of 2.2.
(900 + 500x2.2) / (550 + 70x2.2)
<=> (900 + 1100) / (550+154)
<=> 2000/704 = 2,840909090909091
So after 3 ogre battles of 9 vs 9 ogres your lvl 2 shield upgrade will have paid itself off.
Of course this is a very complicated topic and you need to balance your decisions in relation to every circumstance regarding your individual unique game (e.g.1: does your opponent have lvl 7 ogres or lvl 6 ogres, or e.g.2: can you yourself afford to get a temple of the damned plus 1-3 death knights plus the upgrades death and decay & haste).
Hey Sepi, I didn't look closely at your math to try to figure out your formula, but does it take in to account that every point of damage dealt above lethal damage is irreverent? I'm thinking that might be a key factor in how it might play out. The hp of an ogre and the average damage dealt might just work out to ogres generally killing each other with the same number of hits, and level 7 ogres just generally "overkill" level 6 ogres by a bit more.
If not, maybe it would be interesting to look at this as how many hits it takes a level 6 ogre to kill a level 7 ogre, vs a level 7 ogre to kill a level 6 ogre, figure out the distribution, and compute the gains/losses that way.
there are a lot of other factors, lvl attack, position, how many ogres will change target in fight(if ogre is changing his target, he will watch his "new" opponent and he is miss one hit, while ogre which didnt change opponent will hit him)
