TLDRMost vessels in leviathans are made of paper because their own profiles negate the protection provided by their breach numbers. Smaller ships tend to be better armored because of their smaller profiles and so swarms of destroyers are disproportionately effective.AbstractProfile dice and breach numbers can be combined to give a more concise idea of how hard a given vessel is to damage. The first and easiest measure is Effective Armor. This is calculated by subtracting the average roll for a facing's profile dice from the lowest breach number on that facing. This is the number that your opponent must roll in order to cause a hit. The second is Percentile Armor, or the percentage chance that your armor will provide no armor and any shot fired at the vessel will produce a hit.
Anatomy of an Attack Roll
Any attack in Leviathans is a sum of many dice against a static number. The range of the dice are pulled from many source, namely:
- The size of the attacking gun
- The skill of the attacking crew
- The profile of the defending ship
- The breach number of the defending ship
The final equation looks like this:
D
g+D
c+(D
p1+D
p2) >= B
nWhere D
g is the result of Gun Die, D
c is the result of the crew die, B
n is the breach number, and D
p1 and D
p2 are the results of the profile dice.
This is all well and good, if unexciting. The big problem is that over the set of all leviathans, these numbers will vary quite a bit. However, two of these numbers, the profile dice and the breach number, are specific to a single vessel. Isolating these factors together gives us a rough idea of how this section of the attack equation will look like. Some algebra later:
D
g+D
c >= B
n-(D
p1+D
p2)
Effective Armor The B
n-(D
p1+D
p2) half of the equation is what I would call the
Defense Term. This is only dependent on the vessel in question and theoretically firmly under the control of the vessel designer. Of course, all these values are actually ranges. A decent approximation of this term can be create by simply taking the average result of the profile dice and breach numbers using them as static terms.
As an example, the port side of the
HML Evesham:
Breach Numbers:
14 - 14 - 14 - 14 - 15 - 16
B
n =~ 14.5
Profile:
Blue (d6: Avg 3.5) + Yellow(d8: Avg 4.5)
D
p1+D
p2 =~ 8
HML Evesham Effective Armor: 6.5
Compare this with the port side of the
HML Charger, a smaller, more lightly armored ship
B
n =~ 12.33(3)
D
p1+D
p2 =~ 6.5
HML Charger Effective Armor: 5.833(3)
Despite having much lower breach numbers, the charger doesn't actually lose all that much protection because it's smaller profile helps to make up for it.
As a third example, let's look at the French Destroyer
Pelletier, again at the port side
B
n =~ 11.33(3)
D
p1+D
p2 =~ 4.5
Pelletier Effective Armor: 6.666(6)
This destroyer is tougher than the armored cruiser.
Percentile ArmorWhile Effective Armor is a good, off-the-cuff measure of how well defended a ship is, it's hardly a complete look. Because both breach numbers and the results of the profile dice vary what we really want to know is how often our armor protects us. We can ask ourselves how often will our armor provide no protection at all, such that any gun fired will damage us. This event is called a
Profile Breach. The math for calculating the probability of a profile breach is:
Dg+Dc = 1 (Any die will roll at least a one)
D
g+D
c+(D
p1+D
p2) >= B
n::B
n-1 <= D
p1+D
p2D
p1 and D
p2, being dice, are relatively easy to calculate odds for. I have a small program on my computer that does the brute force math of counting all possible sums of an arbitrary set of dice and determining how many of them exceed a given number. I'm going to be using that to calculate the probabilities of the profile dice although I'm not 100% sure it is bug free.
Compensating for the fact that breach numbers vary is also relatively straightforward. We simply calculate the odds of the profile dice breaching each breach number on a side and then calculate the probability of any breach as 6 independent events (based on the roll of the slot die). This gives us the
Percentile Armor, or the chance that our armor will simply fail to protect us against any incoming fire.
Again, the
HML Evesham:
Modified Breach Numbers:
13 - 13 - 13 - 13 - 14 - 15
Profile:
Blue (d6) + Yellow(d8)
Percentile Armor - 13: 0.0625
Percentile Armor - 14: 0.02083(3)
Percentile Armor - 15: 0
(4/6) * 0.0625 + (1/6)*0.02083 + (1/6) * 0 = 0.0451 = 4.51%.
The
Evesham appears to have a golden BB problem.
How about the
HML Charger:
Modified Breach Numbers:
10 - 10 - 10 - 12 - 13 - 13
Profile:
Black (d12)
Percentile Armor - 10: 0.25000
Percentile Armor - 12: 0.08333
Percentile Armor - 13: 0
(3/6) * 0.25 + (1/6)*0.08333 + (2/6) * 0 = 0.1388 = 13.88%
Charger has a real golden BB problem.
If we cross over to the other side of the channel and look at the
PelletierModified Breach Numbers:
10 - 9 - 9 - 11 - 12 - 12
Profile:
Yellow (d8)
Percentile Armor: 0
Pelletier mocks your golden BB a second time!
ConclusionThe balance between profile and armor numbers needs to be looked at. The increase in firepower from larger profiles more than negates the armor advantage of larger ships and turns them into floating deathtraps. When it comes time to play, I will field fleets of the theoretical Napoleon class destroyer. It will have a tiny profile, decent armor, and mount a single turreted 240mm cannon in it's nose, which I imagine would be roughly equivalent to the Evesham's 9.2in guns. Short, common, ugly, and exceptionally effective.
