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# Re: (FT) beta variable hull rows

From: Oerjan Ohlson <oerjan.ohlson@t...>
Date: Fri, 11 Jun 2004 22:11:36 +0200
Subject: Re: (FT) beta variable hull rows
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Glen Bailey wrote:

>This sounds like the speech by the engineer that designs the new rifle
for
>the infantry man. My response is like the soldier in the field saying a
whole
>bunch of things, and I'll print the nice ones.  :)

No, it sounds like a maths teacher trying to explain the concept of
algebra
to a mathematically challenged student - and I'm afraid that your reply
matches that student's answers rather closely too.

>Excuse the pun, but we're not playing in a vacuum here.  We're not
playing
>with 3 or 4 hull ships, we're playing with 30-60 hull ships.

Which only makes the argument more solid, because the rounding errors
grow
smaller as the number of hull boxes increases.

You see, nearly all of those 30-60 hull boxes are grouped either into
vertical columns of 3 boxes (if it is a 3-row hull), or vertical columns
of
4 boxes (on a 4-row hull) - there might be a single column with fewer
boxes
on each ship, but on larger ships only a small fraction of the ship's
hull
boxes are in that last smaller column (if it even exists). For *each* of

these vertical columns, your suggestion makes each individual vertical
column of 3 hull boxes on a 3-row ship cost more than the corresponding
column of 4 hull boxes on a 4-row ship.

>In my experience ships with 3 rows of X hull boxes (for a total hull
>integrity of 3*X) are *not* harder to destroy than ships with 4 rows
>of X hull boxes (for a total hull integrity of 4*X) but otherwise
identical
>equipment. Quite the contrary, in fact; in my experience 3*X-hulled
>ships are almost invariably *easier* to destroy than 4*X-hulled ones
simply
>because it takes X fewer damage points to destroy them.
>------------------------------------------------------
>Some more grumblings from me:
>
>How can you say this?	The 3-row hull ship will have the same number
>of hull boxes as the 4-row hull ship

No, it will not. As Dean already explained, if each HULL ROW on both
ships
has the same number of boxes then the ship with 4 hull rows will by
definition have *more* hull boxes than the ship with 3 hull rows -
one-third more, to be exact.

>I'm going to give two examples.  Why these two?  I'm going to use them
in
>another message so they'll do for this as well.  Steve's ship is near
what
>he had, I didn't get the exact numbers; he had 2xclass-1 grazers, also
>(*grumble*), so I have the hull or weapons allotment wrong.  But these
are
>correct designs and will work for this discussion.
>
>BB Steve
>mass: 154, cost: (4-row) 683, (3-row) 737

Should be "mass: 154, cost: (4-row) 684, (3-row) 738"

>hull: 54, armor:  6, FTL, MD 2 (advanced)
>Superior sensor, 4 FC, 1 ADFC
>14 6-arc pulsers

In its 3-row configuration, this ship has 18 hull boxes per hull row and

costs 738 (not 737) pts. Your proposed hull costs will increase its
points
value to 792 pts.

However, there is another way to build a ship with exactly these
weapons,
sensors and thrust ratings which *also* gives you 18 hull boxes per row:

BB Smart Steve
mass: 178, cost: (4-row) 758
hull: 72, armor:  6, FTL, MD 2 (advanced)
Superior sensor, 4 FC, 1 ADFC
14 6-arc pulsers

Let's compare the hull configurations and costs for these two ships:

Ship:		BB Steve (3-row)	BB Smart Steve (4-row)
Row 1		18 boxes		18 boxes
Row 2		18 boxes		18 boxes
Row 3		18 boxes		18 boxes
Row 4		DESTROYED		18 boxes

Cost (current)	738			758
Cost (Glen)	792			758

These two ships have THE SAME hull configuration for the first three
rows -
ie., 18 hull boxes in each of hull rows 1, 2 and 3 - but whereas BB
Steve
is destroyed after losing its third hull row (ie. 54 dmg), BB Smart
Steve
still has one hull row of 18 boxes left after losing the first three
rows
(once again 54 dmg).

With the current costs, Steve can choose whether or not he wants to pay
an
extra 20 pts to
add one more row of 18 boxes to his ship. They won't help very much
since
they're in the 4th row, but what do you expect for a mere 20 pts?

With your proposed cost for 3-row hulls, Steve gets to choose between
paying 792 pts to get a ship with 3 rows of 18 boxes each (54 boxes in
all), or paying 758 pts to get a ship with *FOUR* rows of 18 boxes each
(72
in all). After all your descriptions of him, I can't think of anything
that
could compel him to take the more expensive 3-row ship when he could
SAVE
792 - 758 = 34 pts and get an BETTER hull configuration (*without*
skimping
on weapons, sensors and thrust ratings). Can you?

>BB Isucc
>mass 144, cost: (4-row) 591, (3-row) 634
>hull: 43, armor 8, FTL, MD 4 (advanced)
>Superior sensor, 4 FC, 8 scatterguns
>2 class-6 rail guns, 4 class-1 rail guns

Same thing here. Instead of building a 3-row ship with 15+14+14 = 43
hull
boxes for 634 pts, you could build a TMF 164, 4-row ship with
15+14+14+14 =
57 hull boxes and the above weapons, sensors and engines for 655 pts.
Let's
call this modified ship "BB Smart Isucc".

Now, with your proposed hull costs the 3-row version of BB Isucc would
cost
*677* pts. Let's do the same comparison between the two Isuccs:

Ship:		BB Isucc (3-row)		BB Smart Isucc (4-row)
Row 1		15 boxes		15 boxes
Row 2		14 boxes		14 boxes
Row 3		14 boxes		14 boxes
Row 4		DESTROYED		14 boxes

Cost (current)	634			655
Cost (Glen)	677			655

With the current costs, you get the choice of adding 14 extra hull boxes
in
a 4th row for 21 pts. Note that this isn't as good a deal as Steve got
(18
extra hull boxes for 20 pts) since  your ship has a higher thrust rating

than Steve's (which means that your engines increase faster in size and
cost than his does), but even so 1.5 pts per extra hull box isn't very
much.

With your proposed cost for 3-row hulls you can either get 43 hull boxes
in
3 rows for 677 pts, or you could SAVE 22 pts by ADDING a 4th row of 14
boxes (and still get those 43 boxes in the first 3 rows you wanted to
pay
677 pts for). Which of these two ships would you choose? It certainly
looks
like a no-brainer to me - I'd go for the cheaper ship with the better
hull
integrity every time.

>Ship Steve's cost increase for 3-rows is 7.9%. Ship Isucc's (can you
tell
>who won the battle between them?)  cost increasse is 7.3%. Ship Steve's

>1st-row hull increase went from 14 to 18, this is a 28.6% increase in
>critical damage prevention.  Ship Isucc's 1st-row hull increase went
from
>11 to 15, this is a 36.4% increase in critical damage prevention.

Which would be relevant if the value of the increase in "critical damage

prevention" were linear with the damage prevention itself. Unfortunately

for your argument it isn't, and since it isn't your "critical damage
prevention" measure isn't very meaningful either.

The relevant measure here is "how much damage does it take before an
average weapon *becomes* unable to fire due to threshold damage (either
to
itself or to every FCS aboard the ship)?". For some reason I have long
since forgotten I tend to refer to this value as the ship's "TAWA" - I
*think* it stands for something like "Total Average Weapon
Availability",
but I'm not sure :-/ The combat power of the ship is proportional to
among
several other things the square root of the ship's TAWA.

(The TAWA is calculated like this:

(# armour + # hull boxes in the 1st row)*(screen factor for undamaged
screens)+
(# hull boxes in the 2nd row)*(screen factor for the 1st threshold
check)*(Probability that the weapon survived the 1st threshold
check)*(Probability that AT LEAST ONE FCS remains undamaged after the
1st
threshold check)+(# hull boxes in the 3rd row)*(screen factor for the
2nd
threshold checks)*(Probability that the weapon survived the 1st AND 2nd
threshold check)*(Probability that AT LEAST ONE FCS remains undamaged
after
the 1st AND 2nd threshold checks)+...etc. for hull rows 4, 5 and 6 if
present.

Note that this is something quite different from "how much damage is
needed
before a weapon runs *any risk at all* of becoming unable to fire due to

threshold damage?", which is what your "critical damage prevention"
measures - after all most weapons survive the first threshold check!
Also
note that I haven't weighed in the effects of DCP rolls in the TAWA
calculation - when you do include them it tends to reduce the difference

between 4-and 3-row row ships slightly because the 3-row ships generally

lose more DCPs before they start losing systems.)

So, let's take a look at the TAWAs of your two example designs, and at
the
TAWA and combat power increases when you change from 4 to 3 hull rows:

Ship		3-row TAWA	4-row TAWA	TAWA incr.:	Value
incr.:
BB Steve	48.60		41.23		17.9%		8.6%
BB Isucc	42.13		36.05		16.9%		8.1%

IOW, by going from a 4-row hull to a 3-row hull BB Steve increases 7.9%
in
cost in order to gain an 8.6% increase in combat power, while BB Isucc
pay
a 7.3% cost increse to gain an 8.1% increase in combat power.

Granted, the points increases don't match the combat power increases
*exactly* - but it is close enough that even normal swings in dice luck
(as
opposed to your and Steve's respective dice luck :-/) will drown the
differences out completely. (And when you take the DCP rolls into
account -
which as I noted above helps the 4-row ships slightly more than it helps

the 3-row ones - the combat power increases drop a little whereas the
cost
increases remain the same, thus improving the match further still.)

>So, if we increase the 3-row hull cost from 3 to 4, Steve's cost
increase
>is 15.8%, while Isucc's cost increase is 14.6%; both are still below
the
>increase in damage prevention.

But as you can see above, it is way ABOVE the increase in *combat power*

caused by this increased damage prevention - which makes avoiding the
3-row
hulls like the plague a no-brainer...

>So, Oerjan, tell me some more numbers.  :)

Done.

***
From Glen's other post, the battle report:

>But you want to know the real kicker?	My 2x class-6 rail guns, with
both
>hitting for max damage (24), would have only given his BB one threshold

>check (it would be close to a
>second...).  Unless I got real lucky knocking out weapons (on a 6) my
ship
>was still pretty much dead, at least mission killed.  And this for two
>ships that only differ in mass of 10.)

A difference in mass of 10, but if your ship had 4 rows and his 3 the
difference in *points* cost was 147 pts - ie., his ship was almost 25%
more
expensive, and thus should be nearly 25% more powerful, than yours. If
you
too had a 3-row hull the points difference was "only" 104 pts, ie. 16%
more
expensive than yours.

Either way that's a pretty big difference in combat power... even before