Someone explain the math of attacking a city?

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I'm trying to figure out how results like in the picture below happen. I can see that my strength is about half the cities strength so I can understand that my attack should do half the damage that the city returns upon me. Instead however, the city does 4 times the damage to me as I can do to it. This isn't a great picture as the conquistadors are admittedly a little past their prime, as industrialization/etc have been teched and it is an attack upon a capital.. that being said, I was experiencing very similar results while still in tech parity attacking a city of population 2! with Just War and GG. I've come to accept that melee attacks are pretty pointless against cities, but I'm still curious to know how exactly this math is calculated to create these situations in the first place. It's such a vast difference from Vanilla where conquistadors could easily take cities, while in G&K attacking a population 2 city with Just War you can throw them at the city and suffer half your health bar while taking off just the smallest fraction of the citys health bar.
 

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There is that Tradition policy that increase damage by cities with a garrison by 100%. And a pantheon that adds 30%. These modifiers are not really reflected in the shield defense either (ie someone with a 50 defense city will do more damage with the policy/pantheon than another civ with the same 50 defense without the policy/pantheon.)

I'd also imagine the equation is not a linear one.
 
There is that Tradition policy that increase damage by cities with a garrison by 100%. And a pantheon that adds 30%. These modifiers are not really reflected in the shield defense either (ie someone with a 50 defense city will do more damage with the policy/pantheon than another civ with the same 50 defense without the policy/pantheon.)

I'd also imagine the equation is not a linear one.

isn't the tradition policy just a 50% increase to ranged attack strength, which with the goddess of protection pantheon would also just be reflected if the city were the one doing the attacking, as opposed to my attacking the city? maybe the city has walls/castle and this isn't showing up, but is upping the defensive strength.. strange anyhow. i think what bugs me is that while i can live with *my* attack doing minimal damage, I don't understand why the damage done to me is so enormous - over half my health bar! im just trying to figure out what exactly caused this to change from vanilla to G&K. I'm considering toying with things to balance things out better, I'm getting really really bored of wars in which siege/range are about the only units necessary, it's beginning to remind me of age of empires, where people would build armies composed entirely of catapults.

from that picture you can see i would require about 13 conquistadors to have a chance of taking that city out (assuming no other attackers). each conquistador suffering about 70% of their health bar to perform the attack.
 
Maybe I am missing something, but I didn't notice any mention in this thread of cavalry doing less damage when attacking cities- this is the case for all cavalry, isn't it? Probably what the downward pointing triangle in the Conquistador's bonuses indicates. I don't know for sure but I think that has always been the case for cavalry in Civ 5. Are you sure you used to use cavalry for city taking to good effect before G&K?
 
It is tied to a defense rating i beleive. Don't know in which exact proportion though.
 
Maybe I am missing something, but I didn't notice any mention in this thread of cavalry doing less damage when attacking cities- this is the case for all cavalry, isn't it? Probably what the downward pointing triangle in the Conquistador's bonuses indicates. I don't know for sure but I think that has always been the case for cavalry in Civ 5. Are you sure you used to use cavalry for city taking to good effect before G&K?

conquistadors don't have the penalty vs cities.. part of what makes them a unique unit. the same for mandekalu cavalry. in vanilla i could take out capitals with about 5 conquistadors in a couple of turns, cycling them in and out, suffering a normal 33% or so damage to myself while attacking.
 
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