Re: Points balance on K-guns vs Beams, part 1

This got a bit long, since I'm replying to the entire thread :-/

Tim Bancroft wrote:

 >><Oerjan>[I'm] quite interested in seeing these calculations,
 >>both on the K-guns and on the human beams.

 >Finding that KV were consistently outclassed at equal points, even
with
 >differing tactics, I was trying to balance out the KV vs human ships
 >situation at the smaller ship scales (Cruiser and below).

This depends very much on which movement system you use, and also on the
size of your gaming table measured in mu. The movement system, because
the
KV manoeuvrability advantage is considerably larger in Cinematic than it
is
in Vector; the size of the gaming table because the KV are pretty much a
"boom'n'zoom" style of force so if the table is too small to allow them
to
zoom they risk going boom themselves instead of doing unto the enemy
first.

FWIW the entire FB1/2 ship design system is created for Cinematic; so if
you
use the FB2 Vector movement rules it seriously overvalues wide firing
arcs... which is why most custom designs created for Vector movement are
heavy on 1- and 2-arc guns rather than the 3-arc ones which dominate the
(Cinematic) Fleet Book designs.

 >I'd also seen (laserlight's?) comments on a site on a 50% pts bias
towards
KV.

The 50% pts bias refers to the More Thrust version of the Kra'Vak, and
was a
bias *favouring* the Kra'Vak, not a bias *against* them - ie., it was
the
*human* FT2/MT forces who needed roughly 50% more points than the MT KV
had
to get a reasonably even fight.

However, the MT Kra'Vak rules have been completely replaced by the FB2
rules
so this "50% pts bias" no longer applies.

 >As a result I set up a spreadsheet to try and calculate reasonable
 >weightings based on weighted "most common range" groups and average
 >damage at the range, with some additional weighting due to armour.

Sounds OK so far, but...

 >The KV results came out very similar to those mentioned in FB2, which
 >suggests they were calc'd in a similar way, whilst the Beams didn't.

...here you go badly wrong, because it doesn't suggest this at all.
Apologies for the long lecture below:

What a weight function does is basically to bake the weapon's
damage-vs-range profile and its peak average damage into one single
number
(which I refer to as the weapon's  "firepower" below) to allow easy
comparisons between weapons with different such profiles and peak
averages.
However, it doesn't matter if you multiply the peak average damage with
the
damage-vs-range profile before or after you apply the range weight
function:
the function *only* operates on the damage-vs-range profile, not on the
peak
average damage. Below, I refer to the result of the range weight
function
operating on the damage-vs-range profile as the weapon's "weighted range
value".

(If it *does* somehow operate on the peak average damage independently
of
its effect on the damage-vs-range profile, then it isn't a range weight
function but measures something else.)

The "peak damage" is the weapon's average damage at the range where it
is
highest - usually but not always range zero - while the "damage-vs-range
profile" describes how the weapon's average damage varies with the range
measured in percent of the weapon's peak average damage.

To take a very simple example, let's compare two weapons: one which
inflicts
2 pts of damage in range band (RB) 1 and 1 pt of damage in RB2, and
another
which inflicts 2 pts of damage in either RB. Both weapons have the same
peak
average damage (ie. 2), but they have different damage-vs range
profiles:

RB:	Weapon 1:	Weapon 2:
1	100%		100%
2	50%		100%

The entries on each line are the weapons' respective "damage
percentages"
(or "dmg%") for the corresponding range bands.

If the range weight function used gives range band 1 weight "1" and
range
band 2 weight "2", weapon 1's weighted range value is

(dmg% in RB1)*(RB1 weight) + (dmg% in RB2)*(RB2 weight) = 100%*1+50%*2 =
200%

and its firepower value is

(weighted range value)*(peak average damage) = 200% * 2 = 4

For weapon 2, the weighted range value is

(dmg% in RB1)*(RB1 weight) + (dmg% in RB2)*(RB2 weight) = 100%*1+100%*2
=
300%

and the firepower value becomes

(weighted range value)*(peak average damage) = 300% * 2 = 6

In other words, with *this particular range weight function* weapon 2 is
deemed to have 50% higher firepower than the weapon 1 (6/4 = 1.5), and
"should" therefore cost 50% more to buy for your ships.

(If you haven't broken the peak average damage out from the
damage-vs-range
profile, the firepower calculation for weapon 1 becomes

(avg dmg in RB1)*(RB1 weight) + (avg dmg in RB2)*(RB2 weight) = 2*1+1*2
= 4,

and for weapon 2 it is

(avg dmg in RB1)*(RB1 weight) + (avg dmg in RB2)*(RB2 weight) = 2*1+2*2
= 6

...IOW exactly the same as above.)

Now let's see what happens if the range weight function changes! To keep
the
example simple, we reverse the weights of the range bands, so RB1 is
worth
"2" and RB2 is worth "1". For weapon 1, we get

(dmg% in RB1)*(RB1 weight) + (dmg% in RB2)*(RB2 weight) = 100%*2+50%*1=
250%

and its firepower value becomes

(weighted range value)*(peak average damage) = 250% * 2 = 5

For weapon 2, the weighted range value is

(dmg% in RB1)*(RB1 weight) + (dmg% in RB2)*(RB2 weight) = 100%*2+100%*1
=
300%

and the firepower value becomes

(weighted range value)*(peak average damage) = 300% * 2 = 6

...IOW, by simply changing the range weight function, the firepower
ratio
between weapon 2 and weapon 1 has fallen from 6:4 ( = 1.5:1) to 6:5 ( =
1.2:1) - so all of a sudden weapon 2 is only worth *20*% more than
weapon 1,
and not 50% more like the previous calculation suggested!

But what happens if two weapons have the *same* damage-vs-range profile
but
different peak average damage values? Let's take a look at weapon 3,
which
inflicts 4 pts of dmg in RB1 and 2 pts in RB2. Its peak average damage
is 4,
and its damage-vs-range profile is

RB:	Weapon 3:
1	100%
2	50%

- ie., it has the same damage-vs-range profile as weapon 1 above. If we
apply the first range weight function above to this weapon, we get a
weighted range value of

(dmg% in RB1)*(RB1 weight) + (dmg% in RB2)*(RB2 weight) = 100%*1+50%*2 =
200%

(which is of course the same as we got for weapon 1) and a firepower
value
is

(weighted range value)*(peak average damage) = 200% * 4 = 8

...ie., exactly twice as much as for weapon 1 (so weapon 3 should cost
twice
as much as weapon 1).

If we use the other ("reversed") range weight function instead, we get

(dmg% in RB1)*(RB1 weight) + (dmg% in RB2)*(RB2 weight) = 100%*2+50%*1 =
250%

which again is the same as for weapon 1 (of course), and a firepower
value
of

(weighted range value)*(peak average damage) = 250% * 4 = 10

...which is again exactly twice as much as for weapon 1 (so this range
weight function *also* says that weapon 3 should cost twice as much as
weapon 1!)

You can try any other range weight function you like (except the zero
function, ie. where all the weights are identical to zero): the
firepower
ratio between weapon 3 and weapon 1 will *always* be exactly 2, since
they
have exactly the same damage-vs-range profile but weapon 3's peak
average
value is exactly twice that of weapon 1. There is no doubt that weapon 3
is
indeed worth twice as much as weapon 1.

The firepower ratio between weapon *2* and weapon 1 (or weapon 2 and
weapon
3), however, depends greatly on which range weight function you use,
since
weapon 2 has a different damage-vs-range profile than weapons 1 and 3.
Is
weapon 2 worth 50% more than weapon 1, or only 20% more?

And this is where you go wrong: all K-guns have exactly the same
damage-vs-range profile (which they also share with the human P-torps),
so
no matter which (non-zero) range weight function you use you will
*always*
get the same firepower ratios between the different K-gun size classes,
and
thus get the same relative costs for them. All you do when you use your
range weight function to compare them to one another is to compare how
much
damage they inflict when they hit a target - for example, a single-arc
K2
will always be worth just under 60% of what a single-arc K3 is worth
since
the K2 inflicts 2.67/4.5=59% as much damage per hit (and the K3 is also
better at penetrating armour, which pushes its value up a bit further
still).

However, the various FB1 beam weapons do *not* share this K-gun/P-torp
damage-vs-range profile - so if you compare K-guns with beams, or if you
compare the various beams with one another, the results depend heavily
on
the specific range weight function you use - just like the relative
value of
weapon 2 compared to weapon 1 in the example above depended on which
range
weight function I used.

This means that when you get similar relative values for the K-guns as
the
FB2 designers got but different relative values for the FB1 beams, it
doesn't suggest anything at all about what the various weapon
calculations
done during the fleet book design work looked like... all you have shown
is
that your range weight function is different from the one used in the
Fleet
Book design work!

Which of course begs the question: what *does* the range weight function
you
used look like? <g>

***
John Atkinson wrote:

 >I've run and won fights against K'V with even points.

Um, John? Tim's problem is that the KV always *lose* in his games, not
that
they always *win*...

 >P-torps are a workable counter vs. K'V weapons, as they are the only
thing
 >that can generate _more_ damage per round (do the math!) than
railguns.

Not entirely accurate, I'm afraid :-/ The (single-arc) P-torp is the
only
human weapon that can generate more damage per turn than an equal points
value of K-guns (with supporting hull structure, engines etc) *at every
range the K-gun can shoot at* - but the margin is quite small at all
ranges,
and if the P-torp-armed ships use any significant amount of armour (eg.
NAC
levels) it shrinks even further.

The "at every range the K-gun can shoot at" is the crucial bit though,
since
without it John's statement is outright wrong: against unscreened
targets
both B1s (ie. Class/1 beams) and B2-3s (3-arc Class/2 beams) seriously
outgun the K-guns at any ranges where these *beams* can fire (ie., 0-12
and
0-24 mu respectively), but of course the K-gun inflicts more damage if
it
can stay outside the beams' ranges. Similarly the only range where a
B3-1
(single-arc Class/3 beam) is outgunned against an unscreened target by
any
K-gun is range 0-6 mu; outside range 6 mu the B3-1 inflicts more raw
damage
on unscreened targets than the K-guns do.

The key to winning with Kra'Vak is to not try and match the human forces
blow for blow, but instead use their manoeuvrability advantage to get
onto
the humans' flanks and rear arcs *and stay there*. Doable (though not
exactly *trivial*) in Cinematic unless the human forces come to a full
stop
and just spin in place or the table is too small to allow manoeuvres
outside
the enemy's weapon ranges; very difficult in Vector no matter how large
the
table is.

 >I feel that missles would be useful, but only en
 >masse.  That's a hypothesis, and an unproven one at that.

Missiles *can* work against the KV... if your fleet consists of IF-style
missile barges, which certainly qualifies as "missiles en masse" <g>
Otherwise you're not too likely to have enough missiles to both hit the
KV
in spite of their high manoeuvrability *and* to overload their
scattergun
defences and inflict any serious missile damage on them... and not even
these missile barges are guaranteed to win this encounter <g>

***
Finally, in reply to Tim's off-list question: I live in Sweden, about 50
miles west of Stockholm.

Regards,

Oerjan
oerjan.ohlson@telia.com

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