A question that is haunting me in my sleep:
If you give a unit double the hitpoints, does that make it twice as good?
"good" meaning here: value for the purpose it is made for, enough so to pay double the cost to have that unit, instead of 2x the same unit with the original hitpoints.
In other words this comes down to the question of quantity vs quality.
CASE 1: you got to choose between one onager with 200HP, or two onagers with 100HP. All other values are the same
CASE 2: you got to choose between one paladin with 300HP, or two paladins with 150HP. All other values are the same.
CASE 3: you got to choose between one siege-ram with 400HP, or two siege-rams with 200HP. All other values are the same.
lets think about it. [ warning: this paragraph contains hardcore theory, if you dont consider yourself a nerd or AOC die-hard, skip this one ]
HP-wise you have the same in total, and therefore you can reckon both options as equal.
But, with 2 smaller units, you have the risk of losing one unit as soon as you loose 50% of total HP. Death is irreversible. You will never see those HP back. With this unit you loose 50% of the attack force, while in the case of one strong unit, it keeps all its force until 100% of the total HP is lost.
HOWEVER... the attack power of the 2 lesser units was twice that of the one stronger unit, to begin with. So the death of one of them only brings its attack force to equal level. So, if you reckon over the total lifespan of those 2 units you end up with 1.5 times the attack power. 1x accumulated attack x 1 HP-lifespan + 1x accumulated attack x 2 HP-lifespan = 3 total attack potential << basically the surface of a triangle, because in masses the number of units decreases gradually over time, and with it its attack power.
The attack power of the 1 stronger unit will always be just 1x its (double) HP-lifespan. It can only deal 1x its attackforce. This is its achillesheel. And conversions. Once you loose the one unit, you loose it all. The total attack potential is just 2.
What am i saying in normal words?
Having 2 units with just half the HP, but with same attack and armour values, is more valuable then just 1 unit with double the HP. Because you can take advantage of the numbers: you have double attack power, until you lose one of them. A smart player can use 2 units more strategically: micro them with one attacking, the other luring away enemies attack. Therefore the chance for them to survive (at least partly) is much bigger then for the one unit with double HP. (conversions not taken into consideration yet)
Conclusion [If you assume that the HP of the units is in proportion with their lifespan]
if you just send them into death, ( no micro, healing, or converting taken into account ) having two units with half the HP but with same attack and armour is 1,5 times better then having 1 unit with 2 times the HP. This makes the two weaker units 0,75 x as good as the double HP unit, which in turn is 1,333x better then the others.
To make the one double unit 2 times better, it should have 2x HP + 1,5x attack, resulting in the same 3 total attack potential during its lifetime. Or some tweek into the armour value.
Biases
pro-quantity:
- micro-ing 2 units can greatly improve their total value
- one big unit is much more prone to damage by conversion. The damage counts double, because it will be used against you.
- every time a unit dies, there is some overkill capacity lost by the opponent. It is marginal, but larger your mass, the greater this margin will be.
- massed units have the advantage of spatial spread, which comes in handy at raiding or fighting trash. If you just have 1 very strong unit, it can only be at one place at the time, attack one unit at the time.
pro-quality:
- having big units has the advantage of being less sensitive to micro
- having big units give you more attack power overall when capped or housed
- big units have an advantage in non-open situations, narrow passes, tanking vs defensive builds
Reflection
I find these kinds of considerations very interesting, because if you develop these valuations, you can put a number on things, instead of just an experience feeling. How much better is the Celtic Ram(fu)? And what about the Mongol Ram(fu)? How do ETK(fu) and Elite Jaguar Warrior compare? How many should you need of each to balance them out?
How large is the influence of mass in ranged vs melee. Where lies the tipping point between them? For any unit composition.
Etc. I like to make graphs. Stats. Maybe in another life. I did start some kind of testing once. Statistical testing. But its a lot of work. And, its just theory. Maps have randomness. Games have luck-factor. Players have skills. In the end its all situational. **** happens. Life is a bitch. Where is my beverage.
I've got wiser again these 15 minutes. GL HF
If you give a unit double the hitpoints, does that make it twice as good?
"good" meaning here: value for the purpose it is made for, enough so to pay double the cost to have that unit, instead of 2x the same unit with the original hitpoints.
In other words this comes down to the question of quantity vs quality.
CASE 1: you got to choose between one onager with 200HP, or two onagers with 100HP. All other values are the same
CASE 2: you got to choose between one paladin with 300HP, or two paladins with 150HP. All other values are the same.
CASE 3: you got to choose between one siege-ram with 400HP, or two siege-rams with 200HP. All other values are the same.
lets think about it. [ warning: this paragraph contains hardcore theory, if you dont consider yourself a nerd or AOC die-hard, skip this one ]
HP-wise you have the same in total, and therefore you can reckon both options as equal.
But, with 2 smaller units, you have the risk of losing one unit as soon as you loose 50% of total HP. Death is irreversible. You will never see those HP back. With this unit you loose 50% of the attack force, while in the case of one strong unit, it keeps all its force until 100% of the total HP is lost.
HOWEVER... the attack power of the 2 lesser units was twice that of the one stronger unit, to begin with. So the death of one of them only brings its attack force to equal level. So, if you reckon over the total lifespan of those 2 units you end up with 1.5 times the attack power. 1x accumulated attack x 1 HP-lifespan + 1x accumulated attack x 2 HP-lifespan = 3 total attack potential << basically the surface of a triangle, because in masses the number of units decreases gradually over time, and with it its attack power.
The attack power of the 1 stronger unit will always be just 1x its (double) HP-lifespan. It can only deal 1x its attackforce. This is its achillesheel. And conversions. Once you loose the one unit, you loose it all. The total attack potential is just 2.
What am i saying in normal words?
Having 2 units with just half the HP, but with same attack and armour values, is more valuable then just 1 unit with double the HP. Because you can take advantage of the numbers: you have double attack power, until you lose one of them. A smart player can use 2 units more strategically: micro them with one attacking, the other luring away enemies attack. Therefore the chance for them to survive (at least partly) is much bigger then for the one unit with double HP. (conversions not taken into consideration yet)
Conclusion [If you assume that the HP of the units is in proportion with their lifespan]
if you just send them into death, ( no micro, healing, or converting taken into account ) having two units with half the HP but with same attack and armour is 1,5 times better then having 1 unit with 2 times the HP. This makes the two weaker units 0,75 x as good as the double HP unit, which in turn is 1,333x better then the others.
To make the one double unit 2 times better, it should have 2x HP + 1,5x attack, resulting in the same 3 total attack potential during its lifetime. Or some tweek into the armour value.
Biases
pro-quantity:
- micro-ing 2 units can greatly improve their total value
- one big unit is much more prone to damage by conversion. The damage counts double, because it will be used against you.
- every time a unit dies, there is some overkill capacity lost by the opponent. It is marginal, but larger your mass, the greater this margin will be.
- massed units have the advantage of spatial spread, which comes in handy at raiding or fighting trash. If you just have 1 very strong unit, it can only be at one place at the time, attack one unit at the time.
pro-quality:
- having big units has the advantage of being less sensitive to micro
- having big units give you more attack power overall when capped or housed
- big units have an advantage in non-open situations, narrow passes, tanking vs defensive builds
Reflection
I find these kinds of considerations very interesting, because if you develop these valuations, you can put a number on things, instead of just an experience feeling. How much better is the Celtic Ram(fu)? And what about the Mongol Ram(fu)? How do ETK(fu) and Elite Jaguar Warrior compare? How many should you need of each to balance them out?
How large is the influence of mass in ranged vs melee. Where lies the tipping point between them? For any unit composition.
Etc. I like to make graphs. Stats. Maybe in another life. I did start some kind of testing once. Statistical testing. But its a lot of work. And, its just theory. Maps have randomness. Games have luck-factor. Players have skills. In the end its all situational. **** happens. Life is a bitch. Where is my beverage.
I've got wiser again these 15 minutes. GL HF