Core hits and striking the colours (LONG!)

> Tom B wrote:

TL;DR version: the chance of a ship being destroyed by a core hit on the 2nd
threshold is 22% for escorts, 15% for cruisers, and 10% for capitals. Striking
the Colours is much nastier.

I've done some number crunching to try and get an idea of what
kind of difference striking the colours and/or core systems make
to the game. Maybe it will be useful in deciding points adjustments.

These are notepad calculations, not from a massively detailed computer model.
All percentages have been rounded off to the nearest whole integer. For Full
Thrust I believe this is still accurate, because all threshold checks get made
only 3 times per ship per game at most. If FT were like, say, ACTA where a
"critical hit" can occur with every shot, this would be misleading because
even small fractions add up over tens or hundreds of rolls.

As the basis for calculations I've used Fleet Book 1. Unless you design your
ships on radically different principles (10% hulls?) the results aren't going
to vary significantly.

Both core system hits and striking the colours can cause Bad Things to happen
on threshold checks. First step, what can happen normally?

I've defined the worst thing that can happen on a threshold as being fight
disabled, unable to shoot at other ships, for at least one turn. Sure, in some
circumstances it might be disastrous to lose your screens, or drive; but
remember the aim here is to get an approximation and being unable to shoot is
almost guaranteed to be a Bad Thing. It's very nearly a core bridge hit.

Without core systems this can happen in two ways: either you lose all your
FireCons on the threshold and can't repair any, or you lose all your weapons
and can't repair any.

On the first threshold, chance of losing a single FC or weapon
is 1/6, or 17%. The chance of losing two is 1/6 x 1/6, or 3%.
Chance of losing three is under 1% and therefore ignored.

Chance to repair any one system is 1, 2, or 3 / 6 depending on
how many damage control parties the ship has left.

(Repeating, I am not saying that you can't lose 3 FireCons or 3 weapons on a
threshold check, just that the chance of doing so is sufficiently low that
it's an act of $DEITY for any game without dozens of ships per side.)

The very small escorts in FB1, mass 14 or less, can have a 28% chance of being
disabled. For escorts up to mass 20 it's around 16% to 13%. This seems high,
but these are ships that can be annihilated by a single torpedo. Being hit by
anything can be catastrophic.

Heavy frigates and destroyers mostly have 2 or more weapons so are primarily
at risk of losing their one and only FireCon. Percentages are 11% or 8% for
these bigger escorts, except for an NSL missile destroyer which only has 2
weapons and thus goes up to 16%.

Cruisers, and a couple of small battlecruisers with only 2 FireCons, have a 1%
chance of being disabled, as they all have lots of weapons and also more DCPs.
The only exception is an NSL escort cruiser with a single FC which has an 8%
chance.

Capital ships (ignoring carriers) don't get disabled on the first threshold.

On to the second threshold. Here it gets a bit more complicated, because some
systems might have been lost on the 1st and not yet repaired.

For simplicity, I've assumed best case for FireCons, that any lost on the
first have been repaired; and worst case for
weapons, none repaired. So FireCons have a 2/6 = 33% chance of
being lost after this second threshold and weapons have a 3/6 =
50% chance. There's now a 1% chance or better of losing 4 FireCons or 6
weapons.

As before, there's a 1, 2, or 3 in 6 chance of being able to repair at least
one FC or weapon, ignoring multiple attempts which are possible with bigger
ships.

The really tiny escorts are dead at this point. Corvettes and light frigates
have a 48% to 33% chance of being disabled. Heavier frigates and destroyers
have a 38% to 31% chance, most often 33%.

Cruisers and 2 FireCon battlecruisers have a 11% to 6% chance of being
disabled, except for the previously mentioned NSL escort cruiser on 24%. Most
are 9% or 6%.

Capitals (again, other than carriers) are no longer immune. There's a 2%
chance for the smaller ones under 180 mass, and 1% for the superdreadnoughts.
(And this is overstating, because these ships can make multiple repair
attempts even after losing two hull rows.)

To sum up, unless I've made some serious mistakes in my math (please tell me)
the chance of being disabled for at least one turn without Core Systems or
Striking the Colours is:

Frigate or smaller: 28% to 13% on 1st, 48% to 33% on 2nd. Large escort: 11% to
8% on 1st, 38% to 31% on 2nd. Cruiser: 1% on 1st, 11% to 6% on 2nd. Capital:
none on 1st, 2% or 1% on 2nd.

OK, now let's add Core Systems. On the second threshold there's now a 30%
chance of 1 core hit, 3% chance of 2, and once again all 3 is an act of $DEITY
which I'll ignore. (Plus, if you've got both life support and power core hits,
bridge problems don't seem so bad.)

Resistance to core hits is number of DCP, or mass. Because FT has "super"
destroyers with mass over 40 and "super" cruisers with mass over 80, the
biggest escorts are as good as cruisers and the biggest cruisers as
battlecruisers. Escorts <= 40 mass have 1 DCP on the 2nd threshold, super
destroyers and most cruisers <= 80 2 DCP, super cruisers and capitals <= 100 3
DCP, capitals <= 180 4 or 5 DCP, and the superdreadnoughts all have at least 6
DCP.

Escorts, cruisers, and small capitals don't have enough DCP to repair both a
core hit and other systems, so the chance of being
disabled by FC/weapon loss goes up. I'm not going to include
these calcs because core system failures are much more dangerous: if the power
core blows up, it doesn't really matter how many FireCons you have.

A bridge hit can mission kill the ship on a 6. This is the only FT "critical"
that the defending player doesn't have a chance to negate.

When doing calculations for core systems, I often use an F for
failure term. If the chance of repairing a system is N/6 where N
is 1, 2, or 3 DCPs, the chance of failing is F/6 where F = 6 -
N.

For bridge hits the chance of being disabled on the next turn is
5/6 x F/6. (Any bridge roll other than 6.) I won't go into the
chances of being disabled for 2, 3,... because the previous calculations have
only looked one turn ahead.

So ships are killed 3% of the time (6 then 6). The chance of being disabled
for 1 or more turns is: escorts with 1 DCP 12%,
cruisers with 2 DCP 9%, super cruisers and up with 3+ DCP 7%.

If you don't try to repair straight away, say because your ship only has 2 DCP
left and you got the 3% chance of a double core system, it's 14% chanced of
being disabled next turn. This only happens to escorts and cruisers, including
super and battle cruisers, but battleships and up are pretty safe.

Aside from the 3% chance of a mission kill, bridge hits are less dangerous to
escorts and cruisers than the existing odds of losing all your weapons or FC.
For capitals, the chance of being disabled is higher, but still less than 10%.

A life support hit will kill the ship if it isn't repaired. The number of
repair attempts you get is equal to the number rolled on the die, and one
success is enough. So in T turns the ship is
killed only if every attempt fails, which is (F/6) ^ T (raised
to power T). T is from 1 to 6, each value of T has a probability
1/6, and there's a 1/6 probability of a life support hit to
begin with. Final result is

         (F/6)^1 + (F/6)^2 + ... (F/6)^6
         -------   -------       -------
36 36 36

As a sanity check, if you make no attempt to repair then F = 6,
the result is 1/36 + 1/36 ... + 1/36 = 6/36, or 1/6 chance.

Final probability of a kill from life support is: escort 9%, cruiser 5%, super
cruiser and up 3%.

Lastly, power core (or "reactor") hits are the trickiest to
calculate. On the first turn, there is a DCP/6 chance of
successful repair. If that fails, there's a 2/6 chance of
explosion. The tricky part is the second and subsequent turns: the chance of
having to roll again is equal to the chance of neither exploding nor repairing
until then.

Explosion = F/6 x 1/3 = F/18
Repair = DCP/6 = (3 x DCP)/18
Chance of neither = 1 - (F + 3 x DCP) / 18
Since F = 6 - DCP,
Chance of neither = 1 - (F + 18 - 3F) / 18,
= (18 - F - 18 + 3F) / 18
= 2F/18 = F/9

So the probability of exploding on any turn T is F/6 x 1/3 x
((F/9) ^ (T-1)) Again, plugging in F = 6 for no repair attempts
gives a 1/3 chance of exploding at T = 1, 2/9 for T = 2, which
looks right to me.

Since there's no duration, it is possible but very, very, unlikely that this
can go for many turns. The actual chance of exploding falls below 1% quite
rapidly, in just 4 turns if you've got 3 DCP on the job, so the probability
(not certainty) of being destroyed converges on a limit.

Final probability of a kill from power core is only a little bit worse than
life support: escort 10%, cruiser 7%, super cruiser and up 4%.

Adding bridge rolls of 6, life support, and power core all together, the
probability of being destroyed on the first threshold is:

Escort: 22% Cruiser: 15% Super cruiser and up: 10%

My head hurts, so I'm not going to repeat this for the 3rd row threshold
checks.

What does all this mean? Well, it sucks to be an escort and bigger is better,
but we already knew that.

The odds of a "critical" destroying the ship are reasonably low in Full Thrust
(compared to, say, ACTA B5) and only after the ship has already taken 50%
damage. Me, I wouldn't remove them. Sometimes a shell hits the magazine, the
circuit breakers pop in the brand new battleship, a fighter crashes into the
bridge of the super star destroyer.

On the other hand, I can see the merits for some kind of crew quality factor.
I suggest rather than taking out core hits
altogether, give better quality crews a "+1" on their damage
control effectiveness. That is, 1 DCP counts as 2, 2 as 3, and 3 as 4. Also
replace the Bridge hit 6 result as "6 turns disabled" rather than permanently
out of action. This would make a big difference to escorts, both on regular
thresholds and core systems, and push the chance of bigger ships being
destroyed on the first threshold down under 5%.

Striking the Colours, though, is really nasty. There's now a 17% chance of
being destroyed on the first threshold, and 33% chance on the second, far
worse than before. So without giving an exact figure, I suggest that the
points reduction for such ships needs to be a double digit percentage.

If anyone is still awake and wishes to criticize or comment, please do!

cheers,

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Hugh,

Your analysis was in a bit more depth than I would have went, but it seemed
more or less sound.

The only points I'd critique are whether effects from cores or general
shooting beyond 2-3 rounds after the initial shot matter. My experience
has been most FT games have no more than about 1 or 2 more rounds of combat
after ships start taking threshold #2. Often, with smaller ships, threshold #2
and #4 fall in the same firing....

I am convinced from what you've shown that the impact of cores is worse on
smaller ships and lesser on larger ones (but as you say, we knew that it
sucked to be small). I'd say CPV vs. NPV would be sufficient since the
difference is a few percent and probably obscured by the natural skewness of
the D6 based system we've got with the number of rolls that can play out
heavily one way or the other as the average is not a very strong indicator
(from experience at the table).

Now, you have proven pretty conclusively that striking the colours should have
a significant change to valuation *assuming only one side was using it*. If
both sides are using it, perhaps it comes out in the wash.

That didn't quite get to my point of curiosity or I missed if it did: If you
have 3 row ships under strike the colours, 4 row, and 5 row, is there a
suggestion that strike the colours hits 5 row disproportionately hard and 3
row disproportionately easy based on the minor difference in hull costs? I'm
thinking if everyone is on 4 row and everyone is using STC, there's no great
difference assuming somewhat equal fleet size distributions. IF you've got
some folk using 3 row and others using 5, I'm not sure that the 5 row guys
don't get the shaft harder than their slightly cheaper hull cost would suggest
(or the 3 row get a benefit beyond what their slightly cheaper hull cost would
provide). Off the top of my head, if you have STC, I'm betting you need to up
the cost for the 3 row hull and drop the cost for the 5 row hull.

Thanks for poking at the issue.:)

> Tom B wrote:
If
> you have 3 row ships under strike the colours, 4 row, and 5 row, is

After a couple of evenings trying to analyse this and crunching numbers, I
came up with several interesting results with little or no relevance to the
question. Eventually I decided that I was
over-thinking things, and in fact there isn't
a problem.

So, my opinion is that there is no significant or qualitative difference
between the different hull types with the Striking The Colours (STC) rules in
force. Or if there is a difference, it's so small that it will be hidden in
the statistical noise.

 From my previous mind-numbing episode, we learnt
that STC can be regarded as an extremely dangerous threshold check. Since it
can't be repaired, big ships are just as much at risk as small.

The best defence against STC is obviously not to get thresholded. With a 3 row
hull, the amount of damage needed to reach the 1st threshold is 33% more, or
you can say that the threshold rate of occurrence for such ships is only 0.75
of standard. For 5 row hulls it's 20% less or 1.25 faster rate, 6 row 33% less
or 1.5 rate.

That's all else being equal, which of course it isn't. For a given points
budget (NPV) with more hull rows you can build more ships with the same mass
as their more 'advanced' equivalents, or the same number of ships with higher
mass each.

But, there are other ways to increase the damage needed to reach a threshold.
Adding a level 1 screen is almost as good as an advanced hull, reducing
incoming damage by 20% and the rate to 0.8. A strong 40% standard hull is the
same as an advanced 30% average hull. And a layer of armour boxes over the top
of standard 30% hull is even better.

These are all valid design approaches to making a ship more robust. Reducing
the rate at which you get thresholded is not only useful in STC games. Unless
you think that advanced hulls are
always too cost-effective, I can't see why they
would attract a cost penalty in STC games, but not strong hulls or screens.

And why stop at defence? Maximizing the first strike is a good tactic with
STC, so should salvo missiles be penalized?

Overall, I think that STC changes the conditions of combat enough to make
certain types of ships, or design styles, more attractive than others. But I
don't believe you will find that any
individual FT system becomes more cost-effective
than in regular games.

One change you should consider is using NPV rather than CPV, since big ships
are just as likely to be 'destroyed' on the first threshold as escorts.

cheers,

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Hugh,

I follow some of your logic, but disagree with other parts of it.

I think CPV is still the best choice. Yes, the STC means that a big ship has
the same chance as a small ship at being lost. That does counterbalance big
vs. small to some extent. However, the odds on threshold #1 are not so high.
You have to get into the 2nd or 3rd threshold before having lost your ship to
STC becomes decently likely. Thus there is usually time for your superior mass
to play its usual role. I do agree that it slightly changes valuation of big
vs. small and can (in dice driven particular cases) make a big difference from
time to time, but I think the big ship advantage is still there most of the
time statistically.

If you want to think of this another way, both big and small ships can be
taken out on the same values on the die with STC. So effectively, you can
just consider each battled 1/4 to 1/3rd shorter for everyone. If this is
true, then big ships and small ships both end sooner.

But that's only one bit of the math.... many small ships would not make the
end of an mixed-ship battle, so perhaps they get their normal in-game
span of life and the big ship actually has to leave sooner. Lots of ways to
slice this one and not sure which one is most accurate to on-table
results.

I think you might be right on the '3-hull row vs. 5-hull row issue'. I
can argue a bit to the contrary, but the more I think about it, the more it
feels like your answer is right.