Firepower formulae, was Re: Idle Torpedo Thoughts

Binhan Lin wrote:

> Well there is a caveat to the more damage more mass idea.  That rule 
> should apply when everything else is equal - range, hit probabilities
etc.

"More damage" usually means "higher average damage", which includes the
hit probabilities. Not sure what Tom meant here - I haven't seen Noam's
original post yet :-(

> If, for instance a system does twice the damage, but has half the
range
> I'd be willing to let it go for the same mass.

Depends a lot on how long "half the range" is compared to your playing
area. If half the range is short enough to leave plenty of space for
maneuver, the full range/half damage weapon is too good at the same
Mass IMO. If half range is enough to cover most of the playing area
anyway the half range weapon is too strong.

>  This is currently seen with
> Class 1 Vs Class 3 batteries - you can choose more damage at shorter
> ranges and get a limited PDF capability or more range for equal
masses.

> Perhaps someone is willing to create a formula where you can equate 
> mass,  damage, range, hit probabilities, and fire arcs to a set of
numbers > that would allow direct comparison of various weapon systems.
 This 
> would probably break down when you hit the extremes of the system 
> (light damage at extreme ranges or heavy damage at very short ranges)
> but at least it would give an idea if a weapon was balanced compared
to > the known weapon systems.

Aaron, did you remember to take notes during the recent FT battles? <g>

There are several problems with this type of formulas, not least of
which is that several weapons rely on player skill to hit - salvo
missiles, for example.	The value of wide fire arcs is another example;
skilled players are more able to keep the enemy within narrow fire arcs
and thus get more use out of single-arc (low-mass) weapons, etc. The
favoured tactics of a gaming group, and the size of the gaming table
used, are also very important; small tables naturally favour
short-ranged weapons since they cover most of the playing area anyway.
Finally, the value of screen-skipping etc abilities depend entirely on
the enemy designs, and those aren't always very predictable.

Having said that, my FT tinkering experience (largish playing areas)
suggests that the range bands for the different beam range bands are
"weighted" roughly 1, 2 and 3 for the 0-12, 12-24 and 24-36 mu bands
respectively. Multiply the average damage in each band with the
"weight" for that band to get a rough firepower value; then you divide
this value by the Mass of the weapon. This gives the Class-1 a "value"
of 0.8, the Class-2 (6-arc) 1.07 and the Class-3 (6-arc) 0.89, but of
course this doesn't take the Class-1's PDS capabilities into account.
Given the popularity of Class-2 batteries and the scarcity of 6-arc
Class-3's, I think these values are fairly OK :-/

Unfortunately this simple formula breaks down for weapons which don't
use 12-mu range bands. It is possible to use an integral formula:

			  Max range
				/
(Norm * Mass)^-1 * | (Average damage at range X)*X^y*dRange
			       /
			  Range 0

where "y" is a rather arbitrary constant between 0.5 and 1 - I usually
use y = 0.75, but it is pretty much a matter of taste - and Norm is,
well, whatever number you want to compare everything else against. I
use the value for the Class-1 battery as the Norm.

But, as I said above, this formula a) only works if you can determine
the hit probability at each range, and b) doesn't take defence-skipping
or other special abilities into account at all.

Hope to be able to download mail soon, and not just send it...

Oerjan Ohlson
oerjan.ohlson@telia.com

"Life is like a sewer.
  What you get out of it, depends on what you put into it."
- Hen3ry