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The comments about Evil4Zerggin's graph made me want to do a bit of checking. I wrote down some values for attack, defense, and probability from the game, plugged them into open office, and drew a scatter plot. Don't have enough points to make anything pretty, but here are my conclusions:
Despite what the opening post in this thread says, 1:2 attack:defense is not some inverse of 2:1 attack:defense. 1:2 gives 0/0/75/25 probabilities (the floor, 0.38 avg dmg) while 2:1 gives 20/80/0/0 probabilities (the ceiling, 1.1 avg dmg).
Rampant rounding errors in EL lead to an imperfect graph.
The general shape shown by Evil4Zerggin's graph is about right. Neither probabilities nor avg dmg rise linearly with ratio of attack:defense. The shapes of curvature is the same in my plot as in E4Z's graph.
The probabilities displayed in game are not the same as displayed in E4Z's graph, and neither is the average damage, at least according to my calculations.
The ceiling is definitely not at 2:1 attack:defense, but somewhere before that. 1.82:1 gives the ceiling.
Don't have data proving the floor is not at 1:2, but the shape of the graph suggests that it occurs before that point-- E4Z's 0.68:1 could be right.
Within the domain of 1:2 to 2:1, the slope less than 1. For a fourfold increase in attack, damage increases by less than threefold. However, if E3Z's floor and ceilings are correct, we have a three fold increase in damage over a 2.2 times increase in domain.
Average damage has the steepest slope at the lowest, unfloored values of attack:defense, meaning that increasing attack benefits most at the lowest unfloored values and increasing defense at the highest.
Average damage, of course, has a flat slope while attack:defense is floored or ceilinged.
Variance/standard deviation is lowest when attack:defense is very large or very small, and highest when attack:defense is 1:1
If I was to design this system, I would probably make it very differently: linear, 1:1 continuous relationship to average damage, with variance increasing with attack:defense ratio
natev wrote: If I was to design this system, I would probably make it very differently: linear, 1:1 continuous relationship to average damage, with variance increasing with attack:defense ratio
This system came in very late in development and there was a lot of debate on this.
The problem is the "0" Damage fumble (which everyone liked). In order to even this out (mathematically) the Critical (currently 150% Damage) had to be bigger or more frequent, which felt too strong.
Also, the Designers wanted to avoid weird calculations. When damage values like "Zero", "Half", "100%", "150%" and "Double" are easy for players to figure out. When you see a number pop up that's 38% of your damage stat, it's hard to understand what is going on.
Thanks, I can see how it can be an artifact of the design process.
Even though I think that, given equal improvements, damage trumps attack, a lot of people disagree with me-- and disagreement on how to most strongly play a game is a good thing. It demonstrates that the mechanics aren't just mathematical equations to solve. So maybe I'll take it back and say, "Hey, Amplitude, good job "
I´m not able to extract any form of real, applicable knowledge from all the math. The graphs are fun to look at, but they can´t possibly include all the variables present in a real match, or even in a real battle. Drawing conclusions, in my opinion, based on numbers instead of actual gameplay is bound to cause frustration. I´m not saying any plot is wrong, I´m saying that it could be completely right and still fail to provide any insight of how actual games play out.
I'm still thinking about this. The fact that the curve is asymmetrical-- that increasing defense gives accelerating returns while increasing attack gives decreasing returns-- seems to mean that high base attack units are less effective than high base defense units. This jives with my experience, as well, where armies that rely on attack like the Ardent Mages tend to be weaker than armies that rely on defense like the Broken Lords.
I have this huge issue with amount of times I see dust bishops with ~30 attack dealing full damage more often than half damage against 150+ defenses. I don´t see it happen with any other unit, it usually goes as I´d expect, so I´m betting on a skewed perception from my part. I do find it very very disturbing though.
BPrado wrote: I have this huge issue with amount of times I see dust bishops with ~30 attack dealing full damage more often than half damage against 150+ defenses. I don´t see it happen with any other unit, it usually goes as I´d expect, so I´m betting on a skewed perception from my part. I do find it very very disturbing though.
If you're describing it accurately, it can't be just your perception, because 30 attack vs 150 defense should never deal full damage. It should deal half damage 75% of the time and no damage 25% of the time.
In practice, Dust Bishops tend to have higher morale than any other unit, because there is such a strong incentive to get them adjacent to as many units as possible. If you're ignoring morale effects, I could easily see how Dust Bishops would seem especially capable.
I'm interested in a counter-аttack. Question: does damage of the counter-attack depend from defense of target and attack of attacker Or from attack of the target and defence of the attacker?
MetallEater wrote: I'm interested in a counter-аttack. Question: does damage of the counter-attack depend from defense of target and attack of attacker Or from attack of the target and defence of the attacker?
If I read your question correctly, it.s the latter.
When counter-atracking, the roles are inverted accordingly.
Given that some questions seem to remain, I'll try to explain by way of example:
A Necrophage Necrodrone attacks a Drakken Drakkenling.
Two rolls are made to determine the quality of the hit (miss, partial, full, or critical).
The roll for the damage taken by the Drakkenling (i.e. the defender) depends on the Necrodrone's Attack compared to the Drakkenling's Defense
The roll for damage taken by the Necrodrone (i.e. the attacker) depends on the Drakkenling's attack and the Necrodrone's Defense.
Forests boost the Defense value, high ground boosts the attack value. As far as I know, this is updated just before the attack is performed, though I'm not completely sure about that.
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Having played through once, and read this thread I cannot expect my ideas to carry any authority. I hope you find some of these valuable.
Failed attacks should reduce initiative the following round.
I like that it is possible for attacks to fail, but every action should have consequences.
Initiative is an all or nothing trait. If it can be reduced in battle, then being overpowered still gives an advantage. This sort of thing is valuable for players who don't want to sweat the system.
It gives units that are pinned in melee the opportunity to retreat, which makes the battle more dynamic.
Attack and Defence become more useful traits. I would like to see more special effects depend on the attack roll so that these traits get their proper respect.
Actually that is it. I thought I had more, but it is easy to blame your own bad tactics on the system. This at least addresses some of the issues other people have raised.
Unilever wrote: I would like to see more special effects depend on the attack roll so that these traits get their proper respect.
I've been considering special effects that depend on landing a critical for a mod, but I am yet to test if they can be implemented reasonably easily and without lending too much weight to RNG.
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