[Ogre] Armor Unit and Ogre Cost Formula (loooong post)
Douglas R. Pearson
pearsond at odsgc.net
Sat Jan 1 17:26:56 CST 2005
Okay. Henry Cobb's Cost Formulae.
WARNING: If you have no interest in Henry's formulae,
either the math or how it applies to various units,
you'd better skip this entire post. This is all just
me wrestling with "how Henry does this".
I sure don't _need_ to understand these formulae to play
the game, but I _really_ want to understand the
assumptions behind The Formula, and I can only do that
if I understand the math.
I thought about sending this message (or series of messages,
we'll see how it turns out) to Henry off-list to avoid
portraying myself as a total idiot. Since I'm sure that
others may have a hard time with The Formula, I'll stick my
neck out and be The Village Idiot . . .
----------------------------------------------------
Here's The Formula as represented in The Ogre Book (Y2K ed.).
Cost = Atk * OS * AP * (Rng + (OR + (Move1 * MM)))
+ (2 * Def) * DM * ((Rng * OS) + (Move2 * MM))
Atk - attack strength
OS - 1.0, except for one-shot weapons where its 0.333
AP - 1.0, except for antipersonnel only weapons, where its 0.333
Rng - Range, in OM "inches" or G.E.V. "half-hexes"
OR - 0.0, except for weapons that are doubled in overruns,
which get 1.0
Move1 - First movement phase distance, in OM "inches" or
G.E.V "half-hexes"
MM - Movement Mode:
MIL: 0.9 INF: 1.5 MAR: 1.7
GEV: 1.2 HVY: 1.33 OGR: 1.4
standard tracked vehicles, TNK: 1.0
Def - defense strength
DM - Defense Multiplier:
normal units: 1.0 militia: 1.5
infantry: 2.54 marine infantry: 3.05
Ogres: 1.8
Move2 - Second movement phase distance, in OM "inches" or
G.E.V "half-hexes"
Cost - is in "henries", divide by 12 for Victory Points.
The "average" armor unit is 6 Victory Points.
Here's some terminology:
Attack Strength factor: Atk * OS * AP
Advance Reach factor: (Rng + (OR + (Move1 * MM)))
Defense Strength factor: (2 * Def) * DM
Withdraw Reach factor: ((Rng * OS) + (Move2 * MM))
----------------------------------------------------
I follow all of this OK, and I don't really disagree with
any of it. I can tool around with this when tinkering
with "new" armor units. I find this formula very useful.
Now I need to switch gears. Here's Henry's formula for
Ogre units from 2001/gevoct31.txt: (I've taken Henry's
numbers and made a generic equation from them and added
a few pairs of parenthesis here and there.)
"value" = [(Atk * (Rng + OR)) + (2 * Def * Rng)]
+ [(Atk * MM * ½) + (Def * MM)] * X
where X is the movement rate for the Ogre, expressed
in OM "inches" or G.E.V. "half-hexes". Note that this
equation is used to calculate the "value" of each Ogre
weapon one at a time.
In the table Henry presents in the same message, the first
part of the equation is labelled the "cost":
[(Atk * (Rng + OR)) + (2 * Def * Rng)]
while the second part of the equation is labelled "weight":
[(Atk * MM * ½) + (Def * MM)] * X
FIRST STUPID QUESTION: What are the "units" of "value"? Is it
in "henries"? I'm not following something here, because I
would assume that the whole equation is the "cost". Hmmmm.
Why is the entire equation "cost" when calculating for an
Armor Unit but only part of the equation "cost" when calculating
for Ogres?
Algebraically, I transformed this equation back into a form
that looks like the Armor Unit Formula shown above. Here's
what I got:
Atk * _OS_ * _AP_ * (Rng + (OR + (1/2 * Move * MM)))
+ (2 * Def) * DM * ((Rng * _OS_) + (1/2 * Move * MM)) =
I did not originally have _OS_ or _AP_ in the formula because
they're equal to 1.0 in most cases.
STUPID QUESTION TWO: Should the OS and the AP terms be in
the Ogre Equation? I'm not sure that I follow the discussion
in your post well enough to answer this on my own. It appears
that the AP is included.
STUPID QUESTION THREE: Why is the Move in each section of the
equation divided by 2 (which is unlike the original Armor Unit
Formula)? Why not have it like the Armor Unit Formula where
the full movement is given in the Advance Reach portion and
not _have_ a second movement value if there is no second
movement phase?
STUPID QUESTION FOUR: Since I'm not sure that I have represented
the "complete" Ogre Formula correctly (that is, included all of
the "hidden" factors, such as AP or OS), I can't deduce how this
formula gets the values given in Henry's table for the following
components:
Ogre Missile
Empty Tube
Empty Rack
STUPID QUESTION FIVE: When using the formula to calculate costs
of missiles, is this for _each_ missile, internal and/or external
that the Ogre carries? Is the "empty tube" the missile tube that
the external missiles are carried in?
The ramming attack formula is explained pretty well in David Walend's
follow-up message (from 2001/gevnov02.txt) as:
> But the Mark I has an additional weapon! It can ram for one
> die of damage, once per overrun. This I count as a one-shot
> weapon, due to the self damage and all, but the equivalent
> attack strength to average that amount of damage is 10.
>
> So the value of the ram is:
> 10 * (X/2 * 1.4) + 2 * 3 * 1.8 * (X/2 * 1.4) or 14.56 * X.
>
(dice damage done * 3.5 average roll * 3 for a one-in-three
chance to damage treads) * (speed/2 * movement factor)
+ 2 * 3 * 1.8 * (speed/2 * movement factor) = load factor
of ramming.
Hmmm. The "(dice damage done * 3.5 average roll * 3 for a
one-in-three chance to damage treads)" factor certainly equals
out (close enough) to the "10" value that Henry gives in his post.
STUPID QUESTION SIX: Is this discussion of ramming only
dealing with the ramming of buildings (as in 5.043 in Shockwave)?
If not, then where are the dice of damage given for Ogre vs.
Ogre ramming except for the Mark III and the Mark V? See
also STUPID QUESTION EIGHT.
STUPID QUESTION SEVEN: But where does the "3 for a one-in-three
chance to damage treads" come from? This seems exactly opposite
from the OS factor in the Armor Units Formula (which would be
0.333 in this case).
Here's the table that Henry gives in his message following the
above discussion (2001/gevnov02.txt):
> Known Items cost weight Hardpoints
> One tread 1 1 -
> Four APs 1 4 1
> Secondary 6 9 1
> Main 10 12 1
> Missile 3 1 -
> Empty Tube 2 3 0.5
> Empty Rack 6 9 1
The only thing that I can see that is not listed that would
contribute to the Ogre's calculated cost is ramming. I've
deduced the ramming dice to be used for each Ogre from
the statement in Shockwave that states: "Note that in each
case Ogres do one more die of damage against a building than
they do when ramming other Ogres." So, what I use for
Ogre ramming Ogre is:
Mark II: 1 die
Mark III: 2 dice
Mark IV:, V, & Fencer: 4 dice
Mark VI & Dopp: 6 dice
STUPID QUESTION EIGHT: If one follows this logic, then
how can a Mark I ram another Ogre since it can only ram
a building for 1 die of damage? Further, since a GEV
or a SHVY can ram a building for two dice of damage,
shouldn't they be able to ram an Ogre's treads for one
die of damage (and, I assume, be destroyed in the process)?
STUPID QUESTION NINE: In an attempt to be ridiculously
comprehensive, shouldn't both the Armor Unit Formula but
particularly the Ogre Unit Formula have a "Ramming Factor"
in it to calculate ramming values? Is the ramming value
of the Ogres already calculated into your javascript
calculator? If so, is it constant for any ogre? Else,
how do you distinguish between the marks of ogres?
Enough.
This post has taken about an hour and a half to compose
and my brain is burnt. Depending on the answers I get
to these questions, I'm sure there will be further questions,
but for now I'll have to give it up.
For those of you that stuck it out thru all of this, first
my apologies for giving you a headache, and second, my thanks
for giving these questions any consideration at all.
Later,
Doug Pearson "Bowser" pearsond at odsgc.net
===========================================================================
OGRE Geek Code:
S+++ O1() O2+ G+++ S++ RP++ OM() B+ GO() PO+++ HR/NU- MK3() MK5-- CM-- W()
thanx to Michael Powers 2001/gevfeb23.txt
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