Is Barrage broken?

[vicawoo]

From combat explained, this might explain the barrage discrepency:

http://forums.civfanatics.com/showthread.php?t=137615

"Then, the likely damage is half what it would be if the units were fighting directly with those relative strengths. That is, damage = floor(10*(3*A+D)/(3*D+A)). This amount is reduced only if the damage would put the defender past the damage threshold discussed above."

Ok, so for equal strength, the damage is 10 points. In our case, A is 5*(1+barrage bonus), D is 6. DP is damage points (without floor, just so we can see), listed is damage seen (like 0.5 out of 6)
No barrage barrage 1 barrage 2 barrage 3
DP 9.13 10 11.2 12.9
floor 9 10 11 12
listed 0.54 0.60 0.66 0.72

For trebs
No barrage barrage 1 barrage 2 barrage 3
DP 8.2 8.9 10 11.5
floor 8 8 10 11
listed 0.48 0.48 0.6 0.66

So, yes, because of the combat engine using some weighted quotient, barrage 3 does not give +100% damage. To determine where barrage has the highest effect:
f(r)=((3*r*(1+b)+1)/(3+r*(1+b)))/((3*r+1)/(3+r))
df/dr=d/dr (3*r^2*(1+b)+(10+9*b)*r+3)/(3*(1+b)*r^2+(10+b)*r+3)
This derivative is always negative, so it is highest when r is lowest. Unfortunately, this is when the floor function has the most effect.

 

[vicawoo]

Forgive me if I misunderstand these ...



I think this is [only] true when the non-Siege attackers begin with a good chance of survival.

In the Lvl1 Swords vs D1/CG3 Longbows, even after 6 Lvl1 Cats, the loss rate averaged -25%.

As long as I'm protecting my heavy hitters, 25% losses are acceptable, in which case Barrage vs City Raider does come down to the survival rate of the Siege.​

But in the 2nd example, after sending in just 3 Lvl1 Cats against D1/CG3 Longbows, the loss rate of the Lvl1 Swords went up to 75% -- in which case the goal is either minimizing non-Siege losses (presumably via Barrage) or minimizing Siege losses or balancing all losses (presumably via CR).



In BtS, collateral damage is capped at 75%, 80% and 85% (Cats, Cannons, Artillery) since Siege units can't kill anymore.

Are you suggesting I increase the quantity of all units? So maybe 12 Cats & 48 Swords vs 24 Longbows?

Actually I'm suggesting you increase the sample size of the tests. 3 tests with a high variation in survivors isn't going to get you an accurate mean. I thought the damage dealt to the primary defender is 75%, I didn't think collateral is capped.

 

[UncleJJ]

In BtS, collateral damage is capped at 75%, 80% and 85% (Cats, Cannons, Artillery) since Siege units can't kill anymore.

Are you sure it is the collateral damage that has those caps? I think those damage caps apply to the defending unit the siege unit is attacking. That is also the damage the attacker needs to do in order to "win" the combat and withdraw. But that is not collateral damage which by definition is done to other unengaged units. So I think vicawoo is correct and the collateral damage is capped at 50%. However, a unit that has already been damaged to 50% by collateral damage can still be the top defender for later attacks by seige units and can then be, and probably will be, taken to the direct damage cap.

For instance if you attack a stack of 10 defenders with lots of seige units after a number of attacks all the defenders will have received a minimum of 50% damage due to collateral damage and some of those who defended will have been reduced to the lower direct damage cap (unless they killed the attacking seige beforehand). At that stage no further collateral damage can be done but seige units can still attack and damage individual units down to their damage caps. Eventually all the defenders will be reduced to the direct damage caps and seige units can no longer attack.

 

[siggboy]

Are you sure it is the collateral damage that has those caps? I think those damage caps apply to the defending unit the siege unit is attacking. That is also the damage the attacker needs to do in order to "win" the combat and withdraw. But that is not collateral damage which by definition is done to other unengaged units. So I think vicawoo is correct and the collateral damage is capped at 50%.

OTAKU is wrong, and Vicawoo is correct for the case of cats and trebs.

Here are the facts (as given in the Combat Explained article, verified by my own testing and examining the respective XML file):

• Damage done by siege weapons to the defending unit is capped to the values given in the tooltip. You can bring a unit down to the theoretical minimum HP (the cap) by repeatedly attacking with siege.
• Damage done by collateral damage is capped to 50%/50%/60%/70% for cats/trebs/cannons/artillery. Precisely, if the collateral damage would bring the unit HP below these thresholds, it is ignored. So, for example a Longbow with 3.2 strength can NOT receive collateral damage anymore AT ALL from a trebuchet because another loss of 10 HP would bring it below 50% HP.
• As long as at least one unit in the stack is above the "max damage" threshold you can attack the stack with the siege weapon.
• As long as at least one unit in the stack except for the actual defender is above the "max collateral" threshold your siege weapon will cause collateral damage in the stack, unless the collateral damage would carry the unit HP below the threshold (in which case no collateral damage occurs).

 

[OTAKUjbski]

RE: collateral damage capped at 50%:

My mistake ... collateral damage is capped at 50%. Direct damage is 75%, 80% & 85%.

Actually I'm suggesting you increase the sample size of the tests. 3 tests with a high variation in survivors isn't going to get you an accurate mean.

Oh ... yeah ... well, I already realized that and even stated my intent to increase the sample size in upcoming tests.

I only started with 3 tests to get a rough guesstimation of where to take the tests from here so as not to needlessly "spin my wheels" too much.

This is why I want to know what you guys think'll be the best set of parameters to use; since I'll be doing hundreds (even thousands) of trials manually, I'm going to need to narrow down the variables to whatever situations are most likely to result in conclusive results.

... barrage 3 does not give +100% damage. To determine where barrage has the highest effect ...

Isn't this statement and the formula evidence enough that something is wrong with Barrage?

@ vicawoo: Do you think Barrage is working as intended or [at least somewhat] broken?

 

[siggboy]

RE: collateral damage capped at 50%:

My mistake ... collateral damage is capped at 50%. Direct damage is 75%, 80% & 85%.

Collateral is capped to 50% for catapults and trebuchets, to 60% for cannons and to 70% for artillery.

 

[vicawoo]

Actually it turns out the numbers for barrage work out perfectly. It's just that the unit strength goes through the crazy civ 4 damage formula. Technically, it's not broken, a +100% barrage catapult would do just as much damage as a 10 strength siege unit. It's just that 10 strength units do not do twice as much damage as 5 strength units.

 

[OTAKUjbski]

It's just that 10 strength units do not do twice as much damage as 5 strength units.

Nor should they ...

... but when a tooltip states a total "+100% Collateral Damage", shouldn't that translate to "twice as much collateral damage"?

I think the basic collateral damage formula is fine as it is ... it's the Barrage promotion that's broken.

 

[Alsn]

I really like where this thread is going, keep up the good work!

One thing that feels weird for me though is your unit numbers. Maybe im just weird but i tend to have *way* more siege units than i have normal units. If i was to have a stack of 18 units it would usually be something like 12 cats and 6 swords and not the other way around.

That way i *never* lose any non-siege units and can just keep producing siege units and defenders while conducting my wars.

Anyway, dont let me bother you too much and just keep up the good work!

 

[VoiceOfUnreason]

Nor should they ...

... but when a tooltip states a total "+100% Collateral Damage", shouldn't that translate to "twice as much collateral damage"?

I think the basic collateral damage formula is fine as it is ... it's the Barrage promotion that's broken.

Maybe everything except the tooltip is right. Then what?

That is to say, if it said "collateral strength", we would then realize that its going to have the same issues that strength does in other contexts - weird formulas, weird jump points thanks to the truncated precision, and so on?

 

[siggboy]

Barrage is correctly implemented so it's not broken in a strict sense.

Two things are heavily flawed about the promotion:

1. The tooltip description is misleading to the point that the player can not be expected to interpret it correctly without very in-depth knowledge of game mechanics -- which includes the boneheadedness of some combat formulas and Firaxis' obsession to rounding DOWN as soon as a decimal point appears.

2. The actual benefits of the promotion are not worth the cost.

If you need to resort to simulation or developing insanely complex mathematicals models (which we don't have right now, mind you) to even begin to evaluate if the promotion is worth using in mundane situations such as Catapult Stack vs. Longbowmen then something has gone wrong.

Let's not call it broken, let's say it smells fishy.

 

[OTAKUjbski]

Maybe everything except the tooltip is right. Then what?

Well ... that's exactly what I'm trying to figure out.

Is everything right about the Barrage promotion right? Is it working as the developers intended?

Based on comparisons to other promotions, how they work and how their tooltips are worded as well as my recent experience, I'm led to believe the Barrage promotion is not everything it's supposed to be.

 

[OTAKUjbski]

2. The actual benefits of the promotion are not worth the cost.

So far, I totally agree. (I'm hoping to discover with these tests I'm wrong and have just been expecting more than it was ever intended to deliver.)

 

[Alsn]

I conducted a few tests of my own actually.

6 Swords 12 cats both with 5 xp(swords had combat 1 though because i accidently picked stalin when creating the game).

I did 2 sets of tests, one vs protective longbows with 50% walls and one without the walls. Both cases were barrage 2 vs city raider 2.

Walls(50% def bonus)+CR2:
1: 2 cats 5 swords left, city doomed.
2: 4 cats 6 swords left, city doomed.
3: 6 cats 6 swords left, city doomed.
4: 4 cats 6 swords left, city doomed.
5: 6 cats 6 swords left, city doomed.
6: 6 cats 6 swords left, city doomed.
7: 3 cats 5 swords left, city doomed.
8: 3 cats 6 swords left, city doomed.
9: 0 cats 4 swords left, remaining units dead the following turn, city safe.
10: 5 cats 6 swords left, city doomed.
11: 6 cats 6 swords left, city doomed.
12: 7 cats 6 swords left, city doomed.
13: 7 cats 6 swords left, city doomed.
14: 5 cats 6 swords left, city doomed.
15: 3 cats 5 swords left, city doomed.
16: 7 cats 6 swords left, city doomed.
17: 7 cats 6 swords left, city doomed.
18: 3 cats 5 swords left, city doomed.
19: 6 cats 6 swords left, city doomed.
20: 3 cats 6 swords left, city doomed.

Walls(50% def bonus)+Barrage 2.
1: 5 cats 6 swords left, city doomed.
2: 4 cats 6 swords left, city doomed.
3: 3 cats 5 swords left, city doomed.
4: 3 cats 4 swords left, remaining units dead the following turn, city safe.
5: 3 cats 6 swords left, city doomed.
6: 7 cats 6 swords left, city doomed.
7: 3 cats 6 swords left, city doomed.
8: 6 cats 6 swords left, city doomed.
9: 3 cats 6 swords left, city doomed.
10: 3 cats 6 swords left, city doomed.
11: 4 cats 6 swords left, city doomed.
12: 4 cats 6 swords left, city doomed.
13: 7 cats 6 swords left, city doomed.
14: 6 cats 6 swords left, city doomed.
15: 2 cats 5 swords left, city doomed but had to sacrifice cats the following turn turn.
16: 7 cats 6 swords left, city doomed.
17: 5 cats 6 swords left, city doomed.
18: 4 cats 6 swords left, city doomed.
19: 4 cats 6 swords left, city doomed.
20: 4 cats 6 swords left, city doomed.

At this point i wasnt all that surprised since the city raider promos for the cats only bumped the initial success chance from 0,2% to 1,8%. Even when the odds were that low however both promotions showed really good success rates when you have twice the amount of siege compared to the defending units. I guess collateral damage in itself really packs a punch.

0% + CR2
1: 9 cats 6 swords left, city doomed.
2: 9 cats 6 swords left, city doomed.
3: 9 cats 6 swords left, city doomed.
4: 8 cats 6 swords left, city doomed.
5: 10 cats 6 swords left, city doomed.
6: 9 cats 6 swords left, city doomed.
7: 8 cats 6 swords left, city doomed.
8: 9 cats 6 swords left, city doomed.
9: 9 cats 6 swords left, city doomed.
10: 9 cats 6 swords left, city doomed.
11: 5 cats 6 swords left, city doomed.
12: 9 cats 6 swords left, city doomed.
13: 8 cats 6 swords left, city doomed.
14: 9 cats 6 swords left, city doomed.
15: 10 cats 6 swords left, city doomed.
16: 9 cats 6 swords left, city doomed.
17: 9 cats 6 swords left, city doomed.
18: 7 cats 6 swords left, city doomed.
19: 9 cats 6 swords left, city doomed.
20: 6 cats 6 swords left, city doomed.

Losing the 50% wall defense bonus bumped the city raider 2 cats initial success chance to 18,6% which really helped alot with the consistency(it wasnt as reliant on the first few cats luck). 18% is nothing id bet on though as a couple of times there were some heavy losses.

0% + Barrage 2.
1: 4 cats 6 swords left, city doomed.
2: 8 cats 6 swords left, city doomed.
3: 8 cats 6 swords left, city doomed.
4: 7 cats 6 swords left, city doomed.
5: 7 cats 6 swords left, city doomed.
6: 0 cats 3 swords left, city doomed.
7: 7 cats 6 swords left, city doomed.
8: 8 cats 6 swords left, city doomed.
9: 7 cats 6 swords left, city doomed.
10: 6 cats 6 swords left, city doomed.
11: 6 cats 6 swords left, city doomed.
12: 9 cats 6 swords left, city doomed.
13: 7 cats 6 swords left, city doomed.
14: 9 cats 6 swords left, city doomed.
15: 7 cats 6 swords left, city doomed.
16: 7 cats 6 swords left, city doomed.
17: 6 cats 6 swords left, city doomed.
18: 6 cats 6 swords left, city doomed.
19: 6 cats 6 swords left, city doomed.
20: 7 cats 6 swords left, city doomed.

All in all, this round was pretty consistent with the first round, both promotions did well even though they had real low initial success rates but barrage performed slightly worse. Worth noting though is that when the RNG decided to play tricks on you failure was way more catastrophic with barrage as opposed to with CR.

I conducted the test by creating a small pangea with random leaders and no special settings other than "random seed on reload" and then proceeded to give myself 6 swordsmen and 12 cats via the worldbuilder and handed wang kon 6 longbowmen(cg1 drill 1) in his capital that had not yet expanded its borders while making sure i waited 5 turns so that the longbowmen had the 25% fortify bonus.

I then simply saved the game with different promotions and attacked + reloaded 20 times for each set and recorded the results.

Averages and initial stats:
Walls + CR2:
1,8%
4,65 catapults remaining alive on average.
5,5 swords remaining alive on average.
95% city capture rate(19/20).

Walls + BR2:
0,2% Success chance.
4,1 catapults remaining alive on average.
5,6 swords remaining alive on average.
90% city capture rate(18/20).

No Walls + CR2:
18,6% Success chance
8,5 catapults remaining alive on average.
6 swords remaining alive on average.
100% city capture rate(20/20).


No Walls + BR2:
2% Success chance
6,6 catapults remaining alive on average.
6 swords remaining alive on average.
100% city capture rate(20/20).


Final thoughts would probably be that with such low success rates that barrage actually stood a better chance at looking good than with higher success rates normally achieved with trebs/cannons/artillery. On the other hand though using such overwhelming amounts of siege units didnt leave any challenge whatsoever for the "mop-up" troops(in this case 6 swords) the difference was only 0,1 on average in the two tests where swords actually died at all. So in effect the only survival rates that changed were the siege weapons themselves.

Even then however having CR seems like the better choice since in many of the second set of tests the CR2 cats actually were forced to stop attacking because the longbowmen were already at minimum health(was usually about 2-3 cats that still had a movement point left).

I would also like to point out that there were unfortunately an archer in the city which skewed results a little but I doubt it changed much since at worst one of the latter 3 or so catapults would be the ones having to face it at which point they should all be pretty much dead.

I was initially gonna do some tests with maces + trebs vs longbowmen on a hill but im too bored to do it now. Maybe some other time or perhaps someone else can do it.

Edit: Also, I suspect that the higher initial success chances you get the more the results will skew in favour of city raider. I believe the problem barrage has going for it is that collateral damage is plenty powerful already, simply having higher strength will give the units more chances to use that base collateral while a lower strength will too often result in one dead siege unit and a small net gain.

 

[vicawoo]

Barrage 2 11 hp damage, 0.66 damage vs longbows. If collateral below 50% is canceled anyways, then any catapults after 4 are just weak attackers. With no barrage (9 damage), 5 attackers do 45 hp of damage, barrage 1, 5 do 50 hp, barrage 2, 4 do 44, barrage 3, 4 do 48.

 

[Sanchez]

This is why I want to know what you guys think'll be the best set of parameters to use; since I'll be doing hundreds (even thousands) of trials manually, I'm going to need to narrow down the variables to whatever situations are most likely to result in conclusive results.

I think the most interesting parameters with respect to barrage are the ones that result in approximately half (or slightly more) of the non-siege units dying in the base case. For example, I like the CG3 longbows against unpromoted or CR1 non-siege. This should do a good job of giving barrage a chance, since in the case where almost all non-siege already survive (many of the tests) there is little absolute improvement possible (going to 11.5 to 12 surviving units isn't too interesting) and in the case were almost all non-siege die, even with promoted siege, the battle is too stacked too show much benefit. Somewhere in the middle is where the biggest variability should occur. It is also a interesting scenario because if you like to attack with "just enough" troops (which some will argue is optimal) then you are likely to be near that region, rather than the weak defenders case (that is still relevant to many people who like overwhelming force, however) or the very strong defenders case (not too interesting - you probably made a mistake if you end up in this scenario and should avoid attacking, unless desperate).

 

[TheMeInTeam]

Basically, this thread seems to imply:

Barrage, as a promotion line, needs a buff for balance reasons. Things should generally not be in the game if they don't have a use. If combat outperforms barrage in the field (which it seems to), there is literally no use for this promotion.

There are few things that useless in civ 4...maybe explorers or something (kind of can be used on terra maps, but can't capture guarded huts or do much other than scout, just above useless I guess). IMO it seems like barrage is the single most useless element in the game atm. AKA - needs rework or a buff.

 

[VoiceOfUnreason]

Well ... that's exactly what I'm trying to figure out.

Is everything right about the Barrage promotion right? Is it working as the developers intended?

Right - but I'm not at all following why it is that assortments of various contrived combinations of attackers and defenders is going to tell you anything about what the intended results were.

There are a few things that we know - the assortment of promotions was supposed to offer real choice. The fact that there seems to be One Right Answer [tm] is a violation of the basic definition of strategy game. We also know something about how the promotions were intended to change the combat outcomes of various events from the facts that not all units which can receive collateral promotions inherently do damage (Tanks being the exception that proves the rule).

The "problem", if there is one, certainly isn't in the rounding (because they implemented that same problem everywhere). You may be able to make some reasonable deductions about intent based on the history of the implementation - although that may be non trivial to discover (how to get the original SDK, or even the first patch)?


If I ran the zoo, the first comparison I would look at is the effect that using a damage modifier, rather than a strength modifier, implementation would do. In particular, what would the integer truncated results be (that can be done with a spread sheet), and what impact would that have in some common situations, keeping in mind of course that if it's too overpowering then the Principle of choice is still violated (although my suspicion is that, if you did over shoot, you would later be able to compensate by adjusting the numbers).

 

[vicawoo]

i have to point out if barrage 3 were +100% collateral damage, in the unlikely event that a siege weapon is much stronger then the defending units, you would go from 30 hp damage (highest possible collateral) to 60 hp damage. Of course, due to collateral damage caps and how little it matters when you have such a unit advantage, that may be more of a quirk than an imbalance.

 

[Fezzik]

Even if the percentage is deceiving, they may have some value. Barrage 2 does cause more collateral damage, correct? In my informal test, it was a difference of 5.2/5.3 remaining vs. 5.4/5.5 for CR2. So that's significant after a couple of attacks.

I'm mostly interested in 2-promotion cats. At least one city is able to produce them by the time I get construction. Most cats have 2 promotions, until they win and get more promotions. Which Barrage 2 cats probably won't do. So the question is, how many of them should get barrage 2, and how many should get CR2? The goal is to produce as few cats as possible in your war. So the goal of the individual battle is to lose as few cats as possible. The melee units are secondary, and imho a separate issue.

So I would first try a small test of 6x CR2 cats vs. a typical set of defenders (Sitting Bull notwithstanding, ie 2x CG3 LBs + 2x CG2 LBs + 2x CG2 CBs). Try it a few times, see how many cats survive on average. In my test, only 1 survived. So make that number + 1x CR2 cats. Make all the rest (dead cats - 1x) Barrage 2. Try it again. Did you get any more survivors this time? I got 2 survivors. That's an improvement.

That's not a real test, and not data, but it is the test I would like to see. To see if there is a sweet spot on the number of Barrage 2 cats you should build. My 2c...