> At 10:16 AM 2/3/99 -0000, you wrote:
[snip]
Thanks for the info, Tim. I still want an Official Ruling that can be properly
FAQ'ed in the Fleet Book section, just so there aren't *any* questions when
gaming from group to group.
However, if that's the actual answer, I don't like it - not a bit.
While
the Salvo Missile is a wonderful abstraction of the Weber/White missile
paradigm, the MT 'Capital' missile makes a very nice representation of the
Wing Commander style of Torpedo, and I think that I can make a fairly strong
case for treating the two missiles systems differently as far as point defense
and fighter interceptions are concerned. As far as I'm
concerned, the MT 'Capital' missile has enough disadvantages -
centerline
launch only, no rear-arc attacks, limited mobility - to warrant it's
increased effectiveness against PDS. Otherwise, it becomes a fairly
useless weapons system as far as damage / points cost / mass cost
tradeoff are concerned.
Here's the game effects I'd personally like to see ("Salvo Missile" means a
standard Salvo Missile attack):
System Damage: PDS vs: Ftr/Class 1 vs:
------------- ------- ---------- ---------------
Salvo Missile 1d6*1d6 1->3=n/a 1->4=n/a
4,5=1Kill 5=1Kill 6=2Kill,rr 6=1Kill,rr
MT Missile 2d6 1->4=n/a 1->5=n/a
5,6=Kill 6=Kill
Given this type of point defense, the average expected damage per attack
against a ship is as follows [*]:
System vs: 0 PDS 1 PDS 2 PDS 3 PDS 1 C1 2 C1 3 C1
------------- ----- ----- ----- ----- ----- ----- -----
Salvo Missile 12.25 9.45 6.65 3.85 10.85 9.45 8.05
MT Missile 7.00 4.67 3.11 2.07 5.83 4.86 4.05
Notice the nice correlation - the MT missile does roughly half the
average damage. Compared against SMRs, it does so at half the mass & point
cost.
SMLs are always more cost effective compared to MT Missiles - unless
your magazine capacity is one <g>.
If you allow PDS to kill a MT missile only on a 6 per the original MT rules,
then here's the average expected damage per attack:
System vs: 0 PDS 1 PDS 2 PDS 3 PDS
------------- ----- ----- ----- -----
Salvo Missile 12.25 9.45 6.65 3.85
MT Missile 7.00 5.83 4.86 4.05
Here's what happens if PDS works the same against both (makes the MT missile
basically useless in Fleet Book games):
System vs: 0 PDS 1 PDS 2 PDS 3 PDS
------------- ----- ----- ----- -----
Salvo Missile 12.25 9.45 6.65 3.85
MT Missile 7.00 3.50 1.75 0.88
=====================================================================
[*] Probabilities were computed as follows:
The Salvo Missiles were abstracted into 'dice'. The average number of missiles
that are 'on target' in a salvo attack is 3.5. The average number of missile
kills by a PDS system, taking in to account the repeating rerolls on a roll of
'6', is 0.8. The average damage per missile is 3.5 points.
Since we have a cumulative attack total being defended against by a cumulative
total, the average attacks vs the average PDS kills were simply summed to
determine the final average damage totals. It's been *quite* a while since I
took statistics, so someone please correct me if this premiss is incorrect (it
seems 'right' to me).
salvo @ 3.5 missiles vs 0 PDS = (3.5 - 0) * 3.5 = 12.25 points
salvo @ 3.5 missiles vs 1 PDS = (3.5 - 0.8) * 3.5 = 9.45 pts
salvo @ 3.5 missiles vs 2 PDS = (3.5 - 1.6) * 3.5 = 6.65 pts
The Fighter / Class 1 defenses were calculated in a similar manner, but
the average kills in this instance is 0.4 instead of 0.8 for PDS.
The MT missile figures I am completely sure of, since this is a simple
repeating probability sum. MT missiles always average 7 points of damage if
they hit (standard warheads), and in order to attack they must survive *all*
PDS fire directed against them. The probability of success is computed by
raising the success probability by the power of the number of PDS defenders as
follows:
MT missile @ 7 pts vs 0 PDS = 7 * (4/6)^0 = 7 * 1 = 7 points
MT missile @ 7 pts vs 1 PDS = 7 * (4/6)^1 = 7 * 0.67 = 4.67 points
MT missile @ 7 pts vs 2 PDS = 7 * (4/6)^2 = 7 * 0.44 = 3.11 points
> However, if that's the actual answer, I don't like it - not a bit.
While
> the Salvo Missile is a wonderful abstraction of the Weber/White missile
I'd assume MT missiles have better stealth, better targeting, a bigger
warhead.
(snip)
> salvo @ 3.5 missiles vs 0 PDS = (3.5 - 0) * 3.5 = 12.25 points
Your example here is not exactly right because you neglected the possibility
of PDS killing more missiles than are on target, which when taken into effect
increases the average damage. No time to work out the figures right now but
the effect should be fairly small.
> -MWS- wrote:
> However, if that's the actual answer, I don't like it - not a bit.
While
> the Salvo Missile is a wonderful abstraction of the Weber/White missile
Sorry I haven't waded into this discussion yet... I've been meaning
to...
the search for employment after being suddenly layed-off has kept me
busy.
It's important to remember that there are also several advantages with the MT
missiles that haven't been mentioned (or maybe I missed them in earlier emails
on this thread).
1) The engagement range is 54" for MT missiles instead of 24" (or 36" if
you care to use the extended range Salvo Missile). To be fair, the three turn
movement process on the MT missiles does provide the enemy with a change to
turn an run for it (or to streak on by), however it provides a
way for the firing ship to keep pretty much out of direct fire range.
2) Another major advantage to MT missiles is their ability to pick their
target from the eligible targets in range. The ability to use escorts as
possible soak off targets versus Salvo Missiles is something the MT variety
never has to worry about.
3) The final item is the variety of MT missiles available - the normal
(2d6 damage), the EMP, and the Needle. This versatility is something the SMLs
have no counter part to. The EMP missile has gained a bit with the
maximum active shielding being limited to two levels of screens in FB1 and the
subsequent shift with ships depending more on armor now.
Besides the above, MT missiles are smaller in mass, thus making them a natural
for the Big Saturation Factor". Being 2 mass in size makes it much more likely
that a see that massive one shot barrage that I've seen
and heard about in earlier FT games. The ammo load alone for the SMLs (normal
range) are the same size as the MT missile.
For instances let's take an FSE ship from FB1 - the Jerez class CA -
with SMLs it has the ability for fire 2 barrages of 2 salvos each. If one
replaces the SMLs with MT missiles this becomes 7 MT missiles. To be fair we
need to replace the SMLs with SMRs so we can get the largest one
shot barrage possible - providing us with 4.5 SMRs.
I believe a base or slow ship would rather defend against the 4.5 SMRs than 7
harder to effect MT missiles (of an undetermined variety). Granted if the MT
missiles were shot up as easily as the Salvo Missiles I'd rather go against
the MT missiles, however again the MTs could have been delivered from further
away and thus greatly limiting the chances for the missile's target to have
returned the favor.
> On Wed, 3 Feb 1999, Laserlight wrote:
[snip]
> >salvo @ 3.5 missiles vs 0 PDS = (3.5 - 0) * 3.5 = 12.25 points
You're right, but the effect is larger than I would have thought. Using a
matrix sum to work out the figures manually, a salvo missile against 1 PDS has
an actual average damage of 3.078 dice for 10.77 points of damage -
instead of
the 2.7 dice/points I originally estimated. This is an increase of +14%
over my original figure.
Here's the matrix I used - at least this time I know the figures are
correct.
:)
S/P| 1 2 3 4 5 6
---+-----------------
1 | 1 1 1 0 0 0
2 | 2 2 2 1 1 0
3 | 3 3 3 2 2 1, reroll PDS
4 | 4 4 4 3 3 2, reroll PDS
5 | 5 5 5 4 4 3, reroll PDS
6 | 6 6 6 5 5 4, reroll PDS
The row header represents the die roll of the PDS, the column header
represents the salvo missile number roll, while the table contents represent
the number of missiles that make it through the PDS fire (vs 1 PDS). Recurse
the table on rerolls. The proper probability is therefore expressed by the
following:
Average number of salvo missiles vs 1 PDS =
( 3/6 + 8/6 + (14/6 + (3/6 * 1/6)) + (20/6 + (8/6 * 1/6))
+ (26/6 + (14/6 * 1/6) + (3/6 * 1/6 * 1/6))
+ (32/6 + (20/6 * 1/6) + (8/6 * 1/6 * 1/6)) ) / 6 = 3.078 missiles
Average damage = 3.078 * 3.5 = 10.77 points
-MWS- wrote in reply to Laserlight:
> > Your example here is not exactly right because you neglected the
Using a
> matrix sum to work out the figures manually, a salvo missile against 1
> PDS has an actual average damage of 3.078 dice for 10.77 points of
This is wrong. I'm not sure where you went wrong, but if you ignore the
PDS re-rolls in your matrix below you'll find that on average 103/36 =
2.861 missiles manage to lock on and get past the single PDS; 2.861*3.5
=
10.014. I'd find it very strange if the PDS re-rolls *increase* the
damage :-/
I got the average SM salvo damage vs 1 PDS to 9.75, which is a 3.2% increase
from the "intuitively expected" value.
Here's the matrix again:
> S/P| 1 2 3 4 5 6
The difference between the real and the "expected" averages increase when
you add more PDS - vs 2 PDS, I got the average damage to 7.62 (+14.5%),
vs 3 PDS it seems to be 5.84 (+51.7%). I didn't have time to
double-check
these results, but they're at least lower than what they would be without
the PDS re-rolls - I take that as a good sign <g>
Kevin's point about overloading the point defences is very true as well.
If you compare an SMR salvo with two MT-style missiles (same Mass, same
cost), you have to pit the SM salvo against twice the number of PDSs as
each MT missile meets - eg, if the target has 2 PDS the SM salvo would
inflict on average 7.62 pts compared to the 7 the MT missiles together
would (each one is shot at by a single PDS), ie +8.9%. Against 3 PDS the
SM salvo would inflict 5.84 pts compared to the 5.25 of the MT missiles
(+11%).
Since I haven't calculated the true average SM damage vs 4 PDS per salvo I
can't carry the comparision further, but... well, if the enemy has that many
PDS, you probably shouldn't use any weapon vulnerable to it <g>
I submit that the extra range and (particularly) the ability of the MT
missiles to attack other targets than the closest one compensates for the
slightly reduced damage compared to the SMs :-/
Regards,
> On Thu, 4 Feb 1999, Oerjan Ohlson wrote:
[snip]
> This is wrong. I'm not sure where you went wrong, but if you ignore
2.861*3.5 =
> 10.014. I'd find it very strange if the PDS re-rolls *increase* the
[Sigh] Sign inversion again; I'll redo the math with the correct
polarity
this time. I *told* you it's been a while since statistics - I guess I
lost more grey matter than I thought when I passed the '40' milestone a few
years
back .:)
> On Thu, 4 Feb 1999, Oerjan Ohlson wrote:
> -MWS- wrote in reply to Laserlight:
[snip]
> This is wrong. I'm not sure where you went wrong, but if you ignore
2.861*3.5 =
> 10.014. I'd find it very strange if the PDS re-rolls *increase* the
The actual value for SM against 1 PDS is 2.644 dice for 9.255 points average
(got the signs correct this time:) I'll try and work up the rest of the
figures sometime this week.
Formula - corrected after brain fart was removed <g> is:
Average Dice = ( 3/6 + 8/6 + (14/6 - (3/6 * 1/6) + (20/6 - (8/6 * 1/6))
+ (26/6 - ((14/6 * 1/6) + (3/6 * 1/6 * 1/6))
+ (32/6 - ((20/6 * 1/6) + (8/6 * 1/6 * 1/6)) ) / 6
= 2.644
Average Damage = 2.644 * 3.5 = 9.255
In a message dated 99-02-04 14:13:27 EST, you write:
<< [Sigh] Sign inversion again; I'll redo the math with the correct polarity
this time. I *told* you it's been a while since statistics - I guess I
lost more grey matter than I thought when I passed the '40' milestone a few
years
back .:) >>
They say that after the age of 40, 50 or 60 you start growing more brain
cells.
-Stephen
-MWS- wrote in reply to me:
> > I got the average SM salvo damage vs 1 PDS to 9.75, which is a 3.2%
average
Um... no. That's *less* than the "intuitively expected" average damage of
(3.5-0.8)*3.5 = 9.45. The real value should be higher than this if you
take the effects of overkilling missiles into account.
Let's see - here's the matrix again:
> S/P| 1 2 3 4 5 6
I get:
First and second lines, no problem - 3/6 and 8/6, respectively.
Third line: 13/6 + 1/6 * 3/6 (or 14/6 - 1 * 1/6 * 3/6), also no problem.
Fourth line: 18/6 + 1/6 * (2 * 3/6 + 1 * 2/6) - aha, here's a
difference. You seem to have deducted the missiles that get through the PDS
fire
instead of those which get nailed by the re-rolls.
Later,