Averages aren't that simple[]

Guys you must realise that average attack minus average defence doesn't give the average damage!

Average attack incorporates all possible attack values from 0 to max. Same about defence. So if you're using the "atk - def = dmg" formula with averages it must work for ALL possible cases. Does it? No, it does not work when the defence roll is higher than the attack roll. According to the formula, this gives "negative damage". And this affects the actual calculation, because when you're using this formula it assumes that high defence rolls RESTORE hitpoints.

Think logically if you attack with an avg dmg 2 vs avg def 2 is the avg dmg 2 - 2 = 0? No, but the zero is there because "negative damage" is added to averages too. The actual average damage is 0,444 but I have yet to come up with a proper formula for this.

I can't believe the whole article is built on this flawed argument.

Its a non-linear equation, so a simple formula won't be easy. A spreadsheet could do it easy enough, methinks.

An example[]

Lets say a 3 atk ship attacks a ship with 2 def.

This is what the atk - def = dmg formula assumes:

(columns show attack rolls, rows show defence rolls)

	0	1	2	3
0	0	1	2	3
1	-1	0	1	2
2	-2	-1	0	1

Average dmg = (0+1+2+3-1+0+1+2-2-1+0+1)/12 = 6/12 = 0.5.

Or using the simpler formula 1.5 - 1 = 0.5.

This is obviously wrong.

This is how is really works:

	1	2	3
0	1	2	3
1	0	1	2
2	0	0	1

Average dmg = (1+1+1+2+2+3)/12 = 10/12 = 0.83

So far I haven't found any simpler way for calculating average damage, any ideas?

	1	2	3
0	1	2	3
1	0	1	2
2	0	0	1

This is also wrong. There attack can't roll 0 and also defence can't roll 0, unless u don't have attack or defence, acording to GalCiv2Manual.pdf(see page no. 46 Ship VS Ship combat). If u don't have attack is easy avg dmg=0 and if u don't have defence avg dmg= (1+A)/2. EDIT: I think it can me indeed a roll of 0 in both cases (ATK, DEF). this can be easily checked by attacking a ship with 0 defense and check for 0 damage rolls

So we have to change that matrix removing colomuns and rows that contains imposible rolls, actualy they aren't imposibile, but are not posible when u have attack and defence higher than 0.

	1	2	3
1	0	1	2
2	0	0	1

Now let's update the calculation (1+2+1)/6= 0.66 . This is the average dmg recived.

(SUM(a*(a-1)/2))/(A*D)= AVG DMG           Values of a = A-x
                                          x={0,1,...D}

A=attack D=defense

This should be the formula, but it's not realy much easier than drawing matrix. Hope i got it right.

But there is one infinite loop in this formula ship with 1 beam attack and 1 shield vs 1 beam and 1 shield.

fsk+ says[]

The value for attack and defense is a number from 0 to the value. **CORRECTION** Attack is a number from 1 to the value, and defense is a roll from 0 to the value, confirmed by the experiment indicated below.

So, two ships with 1 point of defense and 1 point of attack won't be stuck in an infinite loop because the defense roll is 50/50 zero or one points.

I agree that the combat system needs better explaining.

I tested round 200 shots: 1 beam attack vs 0 defence. Result "damage" = "no. of shots fired". So every shot did exactly 1 dmg. Tested mostly(80%) vs ships with 0 attack(starbases) and some with attack present.

So attack roll can't be lower than 1 or higher if u have 1 beam(any weapon), unless my test was subject to extreme luck aka.statisticaly imposibile.

Next thing that should be tested is 1 beam vs 1 shield to see the % of 0 dmg attacks. If the previous post is correct it should be 50%.

Thanks to quick programming and Excel, here is a graph of average damage with various attack/defense. X axis is defense (from 0-24), the Y axis is weapon strength (1-24), and the Z axis is average damage. I ran this for numbers from 0-100 and 1-100, but the results were difficult to read and the graph has the same shape. Running it for different configurations such as using diverse weapons (eg: 4/4/4 vs 12/0/0) showed that spreading weapon power quickly reduced the average damage as defenses grew larger. Mixing defenses varies when faced against mixed attack ships, improving quite as both offense and defense numbers grew larger. However, this assumed a perfectly even distribution of both weapons and defense. Should the attacker focus on one weapon type, the defender does better by focusing on that defense.

Request article cleanup[]

I've noticed that a lot of the discussion is being carried out in the article itself, which makes it confusing for readers. At times, the sections contradict one another, and, on one occasion, there is even a refutation within the section itself.

I'm not familiar with the GalCiv wiki, but if it runs on similar principles as Wikipedia, shouldn't all this take place in the discussions page? Drastic article cleanup is required, in my opinion.

Huge vs. Tiny[]

1 strategy that i use is to mix them with varying ratios of armor to atack. for example i have arion missle defence researched, and am up to disruptors and antimatter torps (midlevel AI wont research 2 types of armor). if i put 2 PDs on a tiny hull and stick in a antimatter torp II and a warp drive, my attack to defence ratio is 8/20 (with bonuses its 9/34. play as drath legion with 50 def boost FTW! also have other boost up to 70% def boost, 25% atk boost). than i put 3 antimatter torps II and 5 disruptors (mabye II's) (cant remember exactl)y, then 3 PDs and a warp drive for 58/30 atk/def ratio (actual is like 65/51). when combat starts the large ship is targeted since it is percieved as a more easly dealt with threat than the tiny ships. with this strategy you can get high level tiny size ships (i have a trio of them with 22 HP). if you dont fight to often the huge ship will repair. Githyan 21:47, 2 December 2008 (UTC)

Minor Point[]

There's a note that suggests that the effect of the extra half a point for each type might be even greater when the range is [luck*max,max] instead of [1,max], but this isn't the case. The effect comes from the fact that 1 is a constant, independent of the value of max, whereas luck*max is still multiplied by max. The expected outcome for [luck*max,max] is ((1 + luck)/2)*max, meaning that, if max_missiles+max_beam+max_driver=total, then the expected outcome for total damage is ((1+luck)/2)*total, regardless of how it is split up amongst the different types.

Rules not well understood and bad math make a mess[]

Two above posts already state these things

1. The averages are wrong. For example, the correct average damage for 4 atk vs 4 def is 1 not 0 that is (1 * 4 + 2 * 3 + 3 * 2 + 4 * 1) / 20 (see also 2. if you don't understand why 20)

2. The rules are poorly understood and clearly some things were never tested by people who posted a lot of math based off false assumptions.

One such issue was pointed out in one of the above posts: the minimum roll for attack is 1 while the minimum roll for defence is 0

Another assumption at the base of a lot of strategic choices was that values add up for fleets, which is simply not true. Fleets mean more ships fighting together, which indeed enhances their fighting power. However, each ship attacks and defends individually. That is to say, having 8 1/0 fighters is not the same as having one 8/0 ship. Consider the following table listing average damage as a function of the defender's defence strength:

Defence	8x1 Attack	1x8 Attack
0	8	4.5
1	4	4
3	2	3.125

More to the point, when a ship is lost, its attack power is lost as well, so having a fleet of 8x 6hp, 1/0 fighters most certainly is not equivalent to having one 8/0, 48hp ship

To support these claims I staged an experimental fight: 1x 1/15 ship (33hp) vs. 8x 1/0 ships (6hp each)

BATTLE STATS	1x1/15	8x1/0
Shots Fired	48	216
Damage Done	48	8

To make the conclusions obvious:

Each shot from the 1/0 laser on the 1/15 ship did 1 damage => attack rolls are 1-based

216 = (8 + 7 + 6 + 5 + 4 + 3 + 2 + 1) * 6, that is, the number of surviving ships left to attack is decreasing by 1 every 6 turns as expected

The expected damage if the ship defends against each individual 1 attack is 216/16 or 13.5. The expected damage should the fleet's total damage be pooled into one big 8 attack would have been ~1/turn for the first 6 turns, 0.75 the next 6 turns, ~0.6 the next 6 turns and so on, with 1/16 damage only for the last 6 shots, so the expected total damage would have been considerably bigger (14.1 for he first 18 turns alone)

As for strategic advice in terms of selecting your fleet, I think that should be discussed here, and published to the page when there is some sort of consensus (probably never but meh); I for one would go for large ships early on when HP really matters, and small fighters in the late game when one-shot kills are the norm. Why? Because a 50dmg hit against a 6hp fighter is still a 6dmg hit, whereas a 50dmg hit against a 50hp battleship is a 50dmg hit some fighters are capable of. But a 50hp 1/0 vessel will take out a fleet of 8 1/0 6hp fighters and live to fight another day.

Talk: Ship design strategies

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