Why Upping Attack Values Won't Fix Combat

[Adrien]

Warning: Requires calculus.


Assume a unit with attack value A.

Assume a unit with defense value D.

Thus, the chance of an attacker winning can be generalized as

A/(A+D).

If we make A arbitrarily large, the expression derived is

lim A/(A+D).
A>infinity


Evaluating this limit using l'Hôpital's Rule, which says the limit of the function at infinity is equal to the limit of its slope at infinity...

lim 1/(1+D)
A>infinity

or simply 1/(1+D).


This means that after a certain point, raising the attack and defense values is pointless, because the rate of increase in the percent chance that an attacker will win is constantly declining.


Translation: Raising attack/defense values of modern units won't solve the problem in the combat system.

Observe the following...

Assume an attack value of 50, defense 2.

The defender has a 2/52, or 3.8% chance of winning.

Now, increase the attack value to... let's say, for the sake of argument, 100.

The defender has a 2/102, or a 1.9% chance of winning.

By doubling the attack value, you've increased the attacker's chance of winning by 1.9 percent.

Not very useful at all..

[GePap]

Dangerous ground!

Adrien:
You have entered the perilous and dangerous ground of the 'combat system' debate
I hope you like long threads....

[yavoon]

I'm glad you are taking first semester calculus. and while that is true for attack values approaching infinity, NO1 is suggesting attack values that approach infinity.

[Excelsior]

Re: Why Upping Attack Values Won't Fix Combat

Originally posted by Adrien
Observe the following...

Assume an attack value of 50, defense 2.

The defender has a 2/52, or 3.8% chance of winning.

Now, increase the attack value to... let's say, for the sake of argument, 100.

The defender has a 2/102, or a 1.9% chance of winning.

By doubling the attack value, you've increased the attacker's chance of winning by 1.9 percent.

Not very useful at all..

Well, you've halved the probability of the defender winning, isn't that useful? What more do you want doubling the attack value to do?

Moreover, the probability of a 2 defense unit defeating a 50 attack unit is not 3.8%, it is 3.8% per round. The chances of the unit winning are virtually non-existant, assuming 4HP each, around 1 in 14,000. Further, with a 100 attack unit vs a 2 defense unit, the odds drop to 1 in 200,000.

So, I disagree. Increasing the values will "fix" combat, if that's what you want.

[Skanky Burns]

Originally posted by yavoon
I'm glad you are taking first semester calculus. and while that is true for attack values approaching infinity, NO1 is suggesting attack values that approach infinity.

LOL

Increasing attack values (and defence values) of the more modern units will increase the more modern units chances of winning. Even your "proof" shows that this is true. And thats just what most people are asking for - that the modern units win more often (or lose less often) against units from previous ages.

[Xerxes314]

Actually, you applied L'Hopital's rule wrong:
lim A->oo, A/(A+D) == 1/1 == 1

As A->oo, the chance of winning goes to 100%.

After a certain point, adding value to A is pointless, because the attacker is already guaranteed to win.

Xerxes

[civ-n00b]

=o

doesn't that alrdy happen by the time we get modern armor and they still have cavalry or below?

[TheDarkside]

Ugh I play games like Civ3 to escape from stuff like this

[Zanzin]

Originally posted by TheDarkside
Ugh I play games like Civ3 to escape from stuff like this

rofl, I hear ya!

Still, it's interesting to find out how all this stuff works.