Re: [FT] graser-1 slightly overpowered?

Hugh Fisher wrote:

[Snip sound-looking methodology]

Thanks for the report!

 >Tactics were very simple since I was controlling both sides,
 >mostly head on encounters with either the NAC opening fire at
 >18-24 and then closing to 6-12, or both opening fire at 12-18
 >and then closing to 6-12.

Hm. This sounds as if you were flying *very* slowly - 9 mu/turn or less,

unless the ships were in each others' AP/A/AS arcs for the 6-12 shot
(which 
would've favoured the Tacomas and Waldburgs, since they have more of
their 
total close-range firepower available in those arcs than the UNSC ships
do.)

 >[...] I recorded range bands, hit and damage rolls, and threshhold
 >failures.

Excellent. Do you have the data in electronic format, BTW?

 >The NAC won if they avoided the 12-18 MU band and
 >closed, otherwise lost. (And note that I'm favouring the NAC,
 >as the UN ships are quite zippy themselves and should do
 >better at keeping the range open.)

I don't think that you're favouring the NAC significantly, because if
the 
UNSC escorts open the range just a smidgeon too *much* (say to 18.2 mu 
instead of 18.0) they play straight into the NAC's hands.

 >The average damage of a graser-1 and equivalent beams are
 >theoretically balanced, but the low threshhold levels in
 >escorts gives the advantage to the graser.

Not exactly, no :-/

 >In an escort vs escort fight the heavier damage inflicted by
 >grasers is more likely to cause a threshhold check or
 >completely destroy a beam armed opponent,

Nope. In an escort-vs-escort fight the G1-armed ship is more likely to 
*completely destroy* a beam-armed opponent than vice versa, but except
for 
the 12-18mu range band the beam-armed ship is more likely to *cause 
threshold checks* (thanks both to the G1's higher risk of missing 
completely and to the low number of damage points needed to inflict 
threshold checks on the FB escorts) - and the beams' advantage in
causing 
threshold checks is considerably higher than the G1s' advantage in
complete 
destruction.

 >My statistics isn't good
 >enough to know how to model this properly, but I think the
 >effect is a random walk problem where the steps in one
 >direction become lower probability but of greater magnitude.

Correct. However, for escort-sized ships even the
smaller-but-more-likely 
steps are surprisingly large.

[...]

 >None the less, a graser-1 really will inflict heavier hits
 >more often than the beams.

Of course it will; and I don't think that any of us playtesters has said

anything to the contrary. The other side of the coin however is that the
G1 
will also *miss* considerably more often than the beams.

 >I worked out the probability of
 >doing ten or more points of damage in one turn from a 3-arc
 >graser-1 and the equivalent mass beam-2 and beam-1 (or three
 >beam-1) at 0-12 MU range against an unscreened target. (Mass
 >is more the limiting factor on weapon load for escorts than
 >points cost.) Ten points is enough to cause at least a double
 >threshhold check on every escort in Fleet Books 1 and 2, and
 >some light cruisers.

I have two problems with this part of your analysis:

First, as Noam has already pointed out you're comparing weapons of equal

MASS instead of
weapons of equal COST. Since the Grasers cost about 20% more than the 
equivalent MASS of beam batteries (when you take into account the extra 
cost for the larger engines etc. needed to support the beams), it
shouldn't 
come as a big surprise that they also inflict more damage in a straight 
MASS comparison! I've already gone into this in a fair amount of detail
in 
my earlier replies to Glen Bailey, so won't repeat it all again here.

Second, and specific to this analysis, for escort-sized ships 10+ pts is

very often overkill. 6 pts will destroy a Hunter; 9 pts is sufficient to

destroy a UNSC Lake- or NAC Ticonderoga-class DD, your own Tacoma/C
design, 
or any Fleet Book design smaller than a DD. (The other FB DDs - other
than 
the Tico and Lake, that is - all have 11 or 12 hit points; a 10-pt hit
will 
inflict a triple threshold on any of them.) In addition all of these
ships 
start losing weapons to threshold checks long before they're destroyed.

This means eg. that if you're fighting against a UNSC Hunter it is 
completely irrelevant to know
how likely you are to inflict *10+* damage pts at it - because you only 
need *6* pts to destroy it completely. 4 pts is very likely to cripple
it 
(55% risk of losing either the FCS or both G1s, and an additional 27%
risk 
of losing one G1), and even a mere 2 pts of damage causes a significant 
risk of losing one or both G1s (19% chance of either losing both G1s or
the 
FCS, 23% chance of losing one G1).

And this is where the G1's higher risk to *miss* compared to the same
cost 
(not same Mass!) of beams becomes important: if you calculate the
chances 
of inflicting at least 2, 3, 4 etc. pts of damage with a G1 or the 
equivalent cost of beams, you'll find that the beams beat the G1 to
(ie., 
have a higher probability to inflict at least) 2, 3 and 4 pts of damage 
(ie., to reach the first, and often also the second, threshold). The G1 
only catches up around 5-6 pts if it is 3-arc (the 4-arc one takes even 
longer to catch up), and only pulls ahead significantly for 8-pt hits
and 
higher - but these high-power killing hits aren't nearly as common as
the 
low-powered crippling ones.

If you're shooting at cruisers or capitals rather than at escorts, the 
ability to roll 10+ pts of damage with a single Graser die is relevant 
since you're usually not overkilling them - but if you're shooting at 
cruisers or capitals, you usually have more than one Graser die to fire 
(otherwise you're most likely rather badly outgunned!), and this reduces

the probability for really extreme results (of course some of the dice
can 
score high, but you'll usually also have a bunch of other dice which 
doesn't inflict any damage at all).

 >For the beams, factoring in up to 5 rerolls after an initial
 >6, I make the chance of doing at least ten points damage to
 >be 31/7776, or 1 in 250.

If you factor in an infinite number of re-rolls (easy to do since all 
combinations which score more than 10 pts are baked into the "10+"
group) 
you get a ~1/229 (~34/7776) probability to score 10 or more pts on 3
beam dice.

However, since you compare equal MASS instead of equal COST you're 
short-changing the beams a bit. An equal COST of beams gives you closer
to 
4 beam dice, with IIRC a ~1/79 (~98/7776) probability to score 10+ pts.
(I 
don't remember which way the rounding goes; it could be closer to 1/80 
instead.) Still not quite up to the G1's high-hit probability of course,

but the gap between them has suddenly dropped from a factor ~17 to a
factor 
~6 - and that doesn't take the lower-level hits into account at all.

 >For the graser-1, only factoring in
 >the first reroll after a 6, the chance is 573/7776, or 1 in 14.

With 4 re-rolls included it increases to 1/13.3 (~583/7776). But let's
go 
back to the main problem with your analysis:

 >[...] an order of magnitude difference in the chance of getting
 >incapacitated or destroyed is hard to counter.

IF you only count 10+ damage points as "incapacitated or destroyed",
then 
there's roughly one order of magnitude between them.

But as discussed above it takes much less than 10 pts to incapacitate
most 
of the Fleet Book escorts, and 10+ pts will destroy all but the largest
of 
them - and for those lower damage levels, the advantage lies with the
beams 
instead.

 >Another way of looking at it is that the graser-1 is a great
 >weapon for gamblers and frustrating for tacticians.

Very good description, yes.

 >In an escort vs escort battle against grasers you have fewer
 >offensive options such as missiles or fighters than with
 >larger ships. It's harder to dodge because 3 arc graser-1s
 >are cheap enough to be carried by most ships. And simply by
 >having a lot more graser-1s to fire than would be the case
 >with graser-2s or -3s, those low probability megahits start
 >to occur unpleasantly often.

Yet at the same time those high-probability Graser misses occur quite
often 
too, and so do the beams' lower-level but nevertheless crippling hits.
And, 
of course, if there aren't any G2s or other long-ranged weapons around,
the 
beam-armed escorts can afford to err on the side of caution and stray
more 
than 24mu away from the enemy; the G1 escorts don't have that luxury.

 >Only a small fluctuation in die rolls is enough to defeat good tactics
by 
the beam escorts.

...or defeat good tactics by the Graser-armed ships, when they miss 
slightly more than average instead of hitting slightly better than
average.

 >It's not a big difference, but IMHO still a problem. One
 >option would be to increase the mass cost to +1 per extra
 >arc, so a single arc stays at mass 2, two arc is 3, three
 >arc 4, and a six arc 6.

Six arcs would be 7 Mass under this scheme, not 6.

 >The other would be to increase the
 >base mass by 1, so the single, three, and six arc mass 3, 4,
 >and 5 respectively. I think either of these would be sufficient.

Either of these would be sufficient to allow an equal cost of beams to 
outgun	the 3+-arced G1 versions rather impressively at range 0-12 and
(of 
course) 18+, and come quite close to matching them at range 12-18.
That'd 
effectively make these G1s useful *only* at range 12-18mu, which is not
a 
good thing for the game balance.

 >My second suggestion is for those playtesting the UNSC ship
 >designs to try replacing beams with grasers and see if this
 >makes the ships more effective. For instance:
 >
 >Lake Mk IV: replace the beam-2 and beam-1 on a III by a
 >third fore 3 arc graser-1.

This makes the Lake even more sensitive to being outflanked than it
already 
is, reduces its max range by 25% (quite significant when defending a
task 
force against enemy strikeboats) and weakens its point defence by 20%,
in 
return for an increase of the FP/F/FS firepower of ~5% in the 0-12mu
band 
and 31-55% in the 12-18mu band. The refit is worth the extra points as
long 
as the ship never has to fight strikeboats, fighters or missiles,
doesn't 
get outflanked, and is always able to rapidly close the range to 18mu or

less; otherwise it is a bit more dubious :-/

 >Mountain Mk II: replace beam-2s and 1s by three 3 arc
 >graser-1s, port, starboard, and fore.

Works fine as long as the enemy stays in front of the ship, but cuts the

firepower in the rear 180 degrees roughly in half... and since the
Mountain 
is only thrust-4, it can't rely on Cinematic-moving enemies staying in 
front of it (and can have problems getting into range of nimbler
opponents, 
too).

 >It might also be interesting to do the same experiment with
 >the River heavy cruiser or larger UNSC ships.

Same for them as for the Mountain. I already find the UNSC heavies to be

too vulnerable to being outflanked in Cinematic; your suggested refits 
would make them even more so.

Later,

Oerjan
oerjan.ohlson@telia.com

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