Firstly to clarify - your calculations are slightly off - you aren't compensating for when a player runs out of armor before running out of health. This means a soldier actually dies in 6 hits rather than 10.
To explain it simpler, the armor strength ratio simply alters how much armor / health to take off for any given damage.
For example, taking 10 damage as soldier = -2 hp and -8 armor. if you have 0 armor available, you take -10 hp.
A much simpler way to calculate shotgun shots is to add health and armor values together and divide by the damage per shot.
So real figures, assuming a super shotgun does 54 damage
Scout: 125 = 3 shots
Sniper: 140 = 3 shots
Soldier: 300 = 6 shots
Demoman: 210 = 4 shots
Medic: 190 = 4 shots
HWGuy: 400 = 8 shots
Pyro: 250 = 5 shots
Spy: 190 = 4 shots
Engineer: 130 = 3 shots
Quote:
So 80% damage reduction, and a 145 damage grenade would be 29 damage.
100 - 29 = 71 health. 71 : 10,8 = 6,5. So that's 7 hits with the shotgun. That's still pretty high. I know I'm a newbie, but It just doesn't seem right to me.
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Indeed, thats not right.
300 total hp/armor - 145 = 155 which is 3 shotgun shots to kill after a full grenade.
Balancing
However, I am guessing your post is more about "feel" than hard numbers.
What you're experiencing is likely a pub vs competitive play problem. In particular, several pub maps remove secondary grenades, and a large portion of the medics power comes from his secondary grenade (concussion grenades). On maps like Dustbowl and Napoli, which remove secondary grenades, medics will feel underpowered, because they don't have access to their primary power source.
Maybe there is something we can do to give medics more of a role in those maps, without giving them concussion grenades.