Heavy fighter costs, aka unscrewing (down?) with confidence <g>

Ah well. Time to clean up the mess I made of the fighter points costs
:-/
Forget those hysterical +63 points for Stealth-2 fighters; they're not
that bad. Not quite that bad.

A PDS kills on average 0.8 Standard fighters per shot. Depending on how
you handle the re-rolls, it kills...

0.63333... (19/30) Heavy or 0.4666.... (7/15) Super-Heavy fighters if
the
anti-fighter re-rolls use the basic beam die results, or

0.6 Heavy or 0.4 Super-Heavy (incl. Stealth-2) fighters if the
anti-fighter re-rolls are identical to the initial roll for the weapon.

This means that against PDS and normal fighter weapons, Heavy fighters
take 20.8% (FRN - I'll avoid fractions from now on <g>) or 25% less
casualties than Standard ones while Super-Heavy fighters take 41.7% or
50% less casualties than Standard ones. To express it in a different way, the
survivability (ie, the amount of firepower the enemy has to commit to
destroy a certain number of fighters) of the Heavy and Super-Heavy
fighters is (26% or 33%) and (71% or 100%) higher than the survivability of
Standard fighters.

This assumes that they aren't hit by Class-1 batteries or Interceptors,
but the differences aren't very big in the Interceptor case and the vast
majority of anti-fighter fire is PDS rather than Class-1s in my
experience. I'll ignore them for now.

The combat power of a unit is roughly proportional to the square root of (its
survivability times its firepower). I won't go into why here, but it provides
surprisingly accurate predictions of how FT ships will perform
in statistical mock-up battles like the one I suggested to Sean earlier;
it doesn't cover things like maneuver etc.

The cost of a unit should, in an ideal points cost system, be directly related
to the combat power of the unit. If both sides are of equal
combat power, the battle is balanced - player skill and luck with the
dice will be the only factors to decide the issue. Of course, such an ideal
points cost system is most likely impossible to create, but it is a
good thing to aim for :-)

So, to find the combat powers of Heavy and Super-Heavy fighters
(assuming standard armament) compared to that of Standard fighters, just take
the square root of their relative survivabilities. We get:

Heavy fighters: Combat power 112.4% or 115.5% that of Standards (calculated
from the fractions, not the rounded numbers above)

Super-Heavy fighers: Combat power 130.9% or 141,4% that of Standards
(likewise).

These figures are seducingly exact, aren't they. Funnily enough, if you
pit 12 Super-Heavy fighters against 17 Standard ones, use "screened"
re-rolls and allow simultaneous fire, the odds are extremely close to
even - on average 0.01 Standard fighter will survive when the last
Super-Heavy one dies :-) But then, 12*sqrt(2) = 16.97, not 17... so the
battle should be slightly biased towards the Standard fighters :-) Doing
the same thing for other combinations of Standard, Heavy or Super-Heavy
fighters - always adhering to the force ratios indicated by the relative
combat powers of the fighter types - give very similar results.

Since the cost of the fighters should be proportional to their combat power,
all that remains is to multiply the cost of a Standard squadron with those
combat power percentages to get balanced costs for the heavier fighters.

There's one snag, though. We don't know the exact cost of a Standard
fighter squadron. Oh, sure, we know what the *fighters* cost - 18 points
- but that's not the entire cost to deploy them into battle. We also
need to include the carrier into the calculation.

The cheapest possible FTL-capable carrier (Thrust-1, FTL, Fragile hull)
costs 45 points per fighter bay. However, the average cost for a
carrier-mounted fighter bay (as opposed to bays in DNs and SDNs)
calculated from all ships currently in my database gives a much higher
cost - 69 pts per bay, for a total cost of the Standard squadron of 87
points; the average DN- and SDN-mounted bay is more expensive still
(mainly due to stronger hulls).

At this points cost - 87 pts per Standard squadron - fighters are
usually able to take out their own "full" cost in warships in a duel (ie, no
other units interfere), but they tend to get seriously whipped by
specialised anti-fighter designs like the Beijing/BE or the Radetzky
classes.

Eg, at 87 pts per squadron the Beijing/BE CE costs as much as 14
fighters, whereas the Victoria-class BB costs as much as 28 fighters.
The
Beijing/BE will usually crush the 14 while taking little more than
armour damage itself, but the Victoria dies horribly and messily. I find this
kind of balance rather appealing, but it is of course MO only :-)

(At the lowest "FTL-capable" fighter cost, 45+18 = 63 pts per fighter
squadron, even specialised escort designs are very hard pressed to kill
the fighters. The Beijing/BE, for example, defeats the "equivalent" 19.3
fighters on average, but it passes all three tresholds doing so. Warships
designed to take out enemy ships just die. This, I feel, is a
considerably worse balance than the previous one :-/ )

So, when I multiply the Standard fighter cost with the relative combat
power values of the Heavy and Super-Heavy ones, I have to use the *full*
cost of the Standards - including the bay. Since I prefer the balance
struck at 87 pts/Standard squadron, that's what I'll use.

This gives a total cost for Heavy squadrons including bay of 98 pts
(using standard re-rolls) or 101 pts (using "screened" re-rolls), ie a
cost increase of +11 or +14 pts (both of which are pretty close to the
current +12), and for the Super-Heavies 114 or 123 pts, ie +27 or +36
pts
(both of which are higher than Noam's +24, particularly since he (IIRC)
used "screened" re-rolls - but very, *very* much lower than my panicked
+63 pts of yesterday :-) ).

In equal-cost "duels" between Heavy/Super-Heavy fighters and starships
such as the ones I described above for Standards vs starships, these
costs for Heavy and Super-Heavy fighters give very similar results to
those achieved by the Standard fighters. I hope this is an indication that
these fighter costs are fairly accurate.

'Nuff for now. It's getting late - and you've already seen what happens
if I try to think too late at night :-7