# Re: Peasant Stack Leader

Carl Edman (cedman@cedman.remote.Princeton.EDU)
Fri, 23 Sep 94 11:55:19 -0400

The Painful One writes:
> In message <9409231139.AA10908@capitalist.princeton.edu>you write:
> >An "average AF" of a stack is just not a meaningful concept in Olympian
> >combat.
>
> It's not? All other things being equal, a stack with a higher AAF will
> beat a stack with a lower AAF. But I think what you're saying is that
> AAF alone isn't a good predictor of outcome. Of course I agree with
> that.

An average attack factor is just not a useful way of thinking about
battles. It doesn't figure in the real algorithm. It doesn't figure in
any approximation scheme (of which I've posted a few). Thinking about it
doesn't lead to any valid conclusions. In some cases it correlates with
success, in others it doesn't. There are countless such quantities.
Consider for example the IAF (the Improved Attack Factor).

IAF = sum of all attack factors + #peasants*#dragons*10000000

Will this correlate with success in battle ? Sure, if for no other reason
than that most stacks don't contain peasants and dragons. Can I conclude
from the fact that this quantity is the largest for stacks with a dragon
and peasants, that they will beat all other conceivable stacks ? Of course
not.

> >If you don't believe that a stack with a peasant leader and a dragon is
> >stronger against any enemy than a dragon alone, imagine that the peasant
> >misses whenever it gets to attack... But if the peasant never hits and
> >can never be hit, the combat proceeds as if he wasn't there.
>
> No. Even if the peasant has a zero attack value, he definitely has an
> effect on the battle. The peasant is making some attacks which the
> dragon would be making if the peasant wasn't there.

No, it does not. If a dragon fights against N enemies, it is going to get
1/(N+1) of the attacks and the enemies are going to get N/(N+1) of the
attacks. If a dragon and a peasant fights against N enemies, and you
ignore all hits the peasant makes, the dragon gets 1/(N+1) of the
significant attacks and the enemies get N/(N+1) of the significant attacks.
No matter what you do the enemies are going to get exactly N times as many
of the attacks as the dragon gets. Adding a peasant doesn't hurt you on
either the attack or the defense. It can only help you.

Carl Edman

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