your math is completely superficial by not including the number of other factors that actually make the balance, and therefore faulty, relative and in ultima linea biased.
It's a good thing then I didn't in fact proclaim to have a 100% accurate uber-mathematical model of the CoH2 game that takes literally everything into consideration. It's a forum post, not a scientific paper.
just a raw example: did you even think about how to take into account that your 3 hypothetical mediums 'are' or 'should be' in the fight from the considerable earlier timepoint, and all the theoretical DPS and vet they should've dealt and gained by the time the hypothetical heavy hits the field ? did it cross your mathematical mind that the THREE, fast, early units can be in the three different places at the same time - faster ! ..and theoretically and strategically utilize their role against EVERYTHING else that's in the game besides the "heavy" in terms of DPS, area denial, support, breakthrough and map control - far more effectively than one slow heavy unit - that's basically a steamroller and a scarecrow for allied spam of mediums ?
Alright, this is an actual argument. Finally something that can be refuted.
1) You MIGHT get a vet2 medium if you are lucky, by the time a heavy call-in hits the field. Vet1 is more often the case, and in the case of soviet mediums, vet1 is a laughable non-bonus. And so what? The mediums are much more prone to exploding and losing all the accumulated veterancy.
2) If mediums have such free reign, and are so effective, then why don't we see medium tank spam whined about so much in the forums, then? Why are games, and especially team games, usually decided by Axis heavies or Soviet super call-ins?
3) The mediums cannot counter everything else. A single AT gun and a few Schreck squads will chase off mediums faster than you can say Cheese. Also you propose using mediums in an aggressive role, which means they are much more likely to trigger a mine during their breakthroughs.
4) It's a victory point game and, ceteris paribus (oh look, Latin! It must make my argument look EXTRA SWEET), a heavy tank parked near a hotly contested victory point is a game decider. So the medium tanks can be everywhere on the map, except the places that will win them the game. And in case you want to say the mediums can harrass the 2 other VPs - you know, the heavy tank owning player still has 70+ popcap to defend at least another VP long enough for the cavalry to arrive.
5) You will note that three-to-one ratio that I used is completely unreal and just used for argument's sake. Popcap and cost-wise, ingame it's barely more than 2:1, approaching 2.3:1 in Tiger vs T34/76s. This further dilutes your argument of apparently roaming packs of mediums pwning the entire map while the poor heavy can do nothing as it is cumbersome and slow.
6) Heavy tanks are not that much slower than mediums, apart from JT. Maybe 20% slower than mediums.
your "calculation" should be considerably regarded as mathematical dilettantism.
What mathematical process except simple algebra did I utilize, and where did the math go wrong? Also, "considerably regarded"? Seriously? Normally I don't care about such things but if you want to go all high and mighty and Latin in your posts you should at least understand that big words and misplaced adverbs do not help your argument.