[FT] graser-1 slightly overpowered?

I've been running solo escort vs escort test battles with
the new UNSC beta test ships and analysing the results. I've
come to the conclusion that the graser-1 is slightly too
effective for the current mass requirement, and this gives
graser armed escorts a perceptible advantage over those
without. I could be wrong of course, so here is my analysis
for you all to pick apart, and a suggestion for further
playtesting.

I'm not saying that grasers are an uber-weapon. Beam armed
escorts can defeat grasers, but they need to do everything
right. If the tactics don't favour the beam side, or give
only a slight advantage, the grasers will nearly always win.
And my analysis is only for the graser-1 and only tested for
escort vs escort battles. I'd expect similar results for
light cruisers, but not for bigger ships and bigger grasers.

Methodology: my solo battles were two to four beam armed
escorts against a similar number of UNSC Hunters or Lakes.
Mostly I used modified NAC designs, Tacoma/C heavy frigates
(mass 28, hull 7, main drive 6, grade 2 armour, 2 beam-2, 2
beam-1) and Mosquito heavy destroyers (mass 40, hull 12,
main drive 6, screen-1, 3 beam-2) as these are very close in
NPV/CPV to the UNSC Hunter and Lake respectively. The Lakes
were a modified 'Mk IV' design with the beams of a Mk III
replaced by a third forward firing 3 arc graser-1.

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. I also tried 3 NSL Waldburgs
against 2 Lakes in the same scenario, and a circling battle
between Tacomas and Lakes. Each scenario I played four times
with the same moves. The dice themselves were a boxed set of
12, used one after the other by both sides in random order.
I recorded range bands, hit and damage rolls, and threshhold
failures. 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.)

Now that the science report stuff is out of the way :-), on
to the conclusion.

The graser-1 may not have the maximum range or accuracy at
short range of a pulse torpedo, but it's still impressive.
It's accurate enough (escorts hardly ever have screens),
armour piercing, and has the wonderful two die damage on a 6
that any Vandenburg/T captain would sell his or her soul
for.

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. The average
damage from a weapon is not just the to hit and/or damage
rolls, but
	P(survival) x average damage
where P(survival) is the probability (0 to 1) that the
weapon has not yet failed a threshhold check or the ship
itself been destroyed. If the enemy can't shoot back, P is
1. If they can, P gets lower over time.

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, degrading their
chance of survival at a much faster rate. (This is also why
a number of small ships fighting one big ship with equal
firepower and NPV usually lose.) 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.

Less formally, the guy with grasers only needs to roll one
six and you're toast.

It's easy to exaggerate this because of the human tendency
to overrate the chance of unlikely events. A Lake destroyer
handing out 35 points of damage sticks in my memory much
more than a Mosquito doing 9, even though the die rolls to
hit were the same: 46666. So I repeat that I don't consider
graser-1s to be seriously overpowered, just slightly.

None the less, a graser-1 really will inflict heavier hits
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.

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

The probability of survival doesn't depend on damage alone
but also on tactics, protection, and initiative. But an
order of magnitude difference in the chance of getting
incapacitated or destroyed is hard to counter.

Another way of looking at it is that the graser-1 is a great
weapon for gamblers and frustrating for tacticians. 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. Only a small fluctuation in die
rolls is enough to defeat good tactics by the beam escorts.

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. 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.

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.

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

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

	Cheers,
	Hugh