Big stacks, better than normal-sized stacks?

Hello. I have been making some tests and watching rolls, since it has always been weird, that when you send big stacks (50 infantries against 8 infantries, for example) you always get insane results, like -3 -8. So I decided to write down rolls, divide them and compare them. From what I saw, when you send big stacks, defenders don't do high rolls that much.

So my point is, when you send more units to a city, the defenders will do lower rolls. And I wanted to discuss it, since it could be something wrong in the code or maybe it's just "luck"?

Okay, here we go.
These were the rolls I got, sending 34 infs + gen (5 attack, 9 critical) against 4 infs (6 defence, 5 critical). Criticals are not the problem in here, as they only appear sometimes.
52
22
31
43
13
22
62
33
11
25

-3 -4

Left numbers = Attackers' rolls.
Right numbers = Defenders' rolls.
Now, in total they are 10 rolls. Summing and dividing, attackers do 2.9 average, and defenders do 2.4
This may have been "just luck", so I'll be doing another one.

123infs+gen (5 att, 9 crit) vs 8 infs (6 def, 5 crit)
Attackers did 1 crit, defenders did 2.

42
21
72
51
43
14
53
18
45
52
31
41
38
21
22
51

-6 -8

Attackers average: 3.5625
Defenders average: 2.8125

Another one.
121 Infs + gen (5 att 9 crit) vs 7 infs (6def 5crit)
Attackers did no criticals, Defenders did 1.

21
22
33
32
31
11
21
43
42
42
21
31
11
51
21
42
37
11
-4 -7

Attackers average: 2.722..
Defenders average: 1.833..

That's it. I did 3 battles in total, TOTALLY Random, I did not select a few battles in which My stack got better rolls. Maybe, I did not do enough battles but in those 3, Attackers always did good rolls, even though they even did less criticals, and have a 5 maxDmg while Defenders got 6.
Please discuss below, and if you do not believe its true, then go ahead and do tests.

Kirjoittanut Permamuted, 10.02.2014 at 10:42

Where did my post go, did you remake the thread? -.-

No, thought I think I double posted by mistake lol. Sorry.

Guys, I double posted by mistake. I deleted the other topic. Sorry.

I don't think it makes too much a difference.

Ultimately, bigger stacks just mean more security. In my opinion, the more manpower you can throw around at your enemy the better.
Playing GW for such a long time as I have, it's been rare that I needed big stacks to accomplish any of my plans.

For PD and other strategies though this might be a lot different.

Kirjoittanut Dr Lecter, 10.02.2014 at 11:40

I don't think it makes too much a difference.

Ultimately, bigger stacks just mean more security. In my opinion, the more manpower you can throw around at your enemy the better.
Playing GW for such a long time as I have, it's been rare that I needed big stacks to accomplish any of my plans.

For PD and other strategies though this might be a lot different.

I did sum 3 random battles, and I got better average rolls, even though Inf def is 6, my inf att is 5. I had better CRIT, though defenders still got more crit hits. That's not just luck. Not to mention you can get like -3 -8 with infantries, like 40% of the times.

It is true about more security but bigger stacks are clearly better, somehow defenders' rolls get weaker.
By the way, unlike some people say, HP does not stack. As for what I understand on battle mechanics, the only explanation to these low rolls, is that the code is wrong.
Dammit, I want admins back :/

Kirjoittanut Guest, 10.02.2014 at 11:46

Kirjoittanut Dr Lecter, 10.02.2014 at 11:40

I don't think it makes too much a difference.

Ultimately, bigger stacks just mean more security. In my opinion, the more manpower you can throw around at your enemy the better.
Playing GW for such a long time as I have, it's been rare that I needed big stacks to accomplish any of my plans.

For PD and other strategies though this might be a lot different.

I did sum 3 random battles, and I got better average rolls, even though Inf def is 6, my inf att is 5. I had better CRIT, though defenders still got more crit hits. That's not just luck. Not to mention you can get like -3 -8 with infantries, like 40% of the times.

It is true about more security but bigger stacks are clearly better, somehow defenders' rolls get weaker.
By the way, unlike some people say, HP does not stack. As for what I understand on battle mechanics, the only explanation to these low rolls, is that the code is wrong.
Dammit, I want admins back :/

Hm. Well, it can be said that bigger stacks provide more results during a specific battle.
But in the long run, will it be enough to effect the out come of war?

My strategy prides itself on not requiring big decisive battles. Instead, GW plays on harassing the enemy into becoming weaker than you.

Kirjoittanut Dr Lecter, 10.02.2014 at 12:15

Kirjoittanut Guest, 10.02.2014 at 11:46

Kirjoittanut Dr Lecter, 10.02.2014 at 11:40

I don't think it makes too much a difference.

Ultimately, bigger stacks just mean more security. In my opinion, the more manpower you can throw around at your enemy the better.
Playing GW for such a long time as I have, it's been rare that I needed big stacks to accomplish any of my plans.

For PD and other strategies though this might be a lot different.

I did sum 3 random battles, and I got better average rolls, even though Inf def is 6, my inf att is 5. I had better CRIT, though defenders still got more crit hits. That's not just luck. Not to mention you can get like -3 -8 with infantries, like 40% of the times.

It is true about more security but bigger stacks are clearly better, somehow defenders' rolls get weaker.
By the way, unlike some people say, HP does not stack. As for what I understand on battle mechanics, the only explanation to these low rolls, is that the code is wrong.
Dammit, I want admins back :/

Hm. Well, it can be said that bigger stacks provide more results during a specific battle.
But in the long run, will it be enough to effect the out come of war?

My strategy prides itself on not requiring big decisive battles. Instead, GW plays on harassing the enemy into becoming weaker than you.

I didn't get it xD
Anyway, what I'm saying is that defenders get way lower rolls, when they are attacked by big stacks. Something must be wrong with the code, that's why I made this topic. I hope admins get back some day ;_;

Bigger stacks used to have a bonus in-battle before HP was implemented, but I don't know the details about the transition and how rolls got affected by that.

Kirjoittanut Pinheiro, 10.02.2014 at 12:34

Bigger stacks used to have a bonus in-battle before HP was implemented, but I don't know the details about the transition and how rolls got affected by that.

Hmm, there used to be no HP? I didn't know that. I only know there were ARB. Maybe there's some old code left? Is it possible to bring this to admins' attention?

I'm sorry, what I meant is that, in early stages, AW mechanics, if I can recall it right, used to work in order to calculate every single battle separated, thus making the winning units HP "reset" every time they won a fight. The effect was that units with higher status had a way bigger advantage than it have today, making one single battleship (old version of destroyers) able to defeat a entire militia stack, for example.

Maybe this Ivan's (old) post can help, from the time we still had ARB:

Kirjoittanut YOBA, 20.09.2011 at 15:25

This is my dream.

Please make it come true. ;__;
Also, please introduce automatic hyperlinks in the chat. That would be quite nice.

Finally, I think you should release the formulae used to determine attack strength and what-not. No offence, but I don't think they are unique enough that a competitor (there is none actually!) would nick them off you. This way the more mathematically-oriented members can take a look and help in balancing. No source code, don't worry! Just the formulae.

The clock would look nicer, I guess, but I'm not sure it's worth embedding a new font just for it.

Links in the chat, written down for the to-do list.

As for the formulae, the entire thing is several pages long and I can't be bothered to edit it into something coherent. This is the main part, see if you can make any sense of it:

Lainaa:

// randomly selecting the defending army
Troop defendingArmy = enemies[model.Random.Next(0, enemies.Count)];
bool inOwnCity = InCity != null && defendingArmy.InCity == InCity;
bool inDefenceLine = DefenceLineOwner == defendingArmy.Owner;

// selecting the defending unit (unit with the highest max attack)
Unit defendingUnit = null;
foreach (Unit unit in defendingArmy.Units.Values)
{
if (unit.UnitType == UnitType.Land && (defendingArmy == Defender && defendingArmy.IsTransportIntercepted || !battleIsOverland && initCanMoveOnWater[defendingArmy.Owner.Id])) continue;
if (defendingUnit == null ||
unit.MaxDefence + unit.GetDefenceBonus(inOwnCity, inDefenceLine, attackingUnit) > defendingUnit.MaxDefence + defendingUnit.GetDefenceBonus(inOwnCity, inDefenceLine, attackingUnit))
defendingUnit = unit;
}
int defenceBonus = defendingUnit.GetDefenceBonus(inOwnCity, inDefenceLine, attackingUnit);
game.Logger.Debug("Defending unit: {0} (in own city - {1}, in defence line - {2})", defendingUnit.ToString(), inOwnCity, inDefenceLine);

// difference ratio between the attacker's and defender's combined initial strength
double attackDefenceDiff = (double)(initTotalMaxAttack[attackingArmy.Owner.Id] + initTotalUnitCount[attackingArmy.Owner.Id]) /
(initTotalMaxDefence[defendingArmy.Owner.Id] + initTotalUnitCount[defendingArmy.Owner.Id] + initUnitCount[defendingArmy.Owner.Id][defendingUnit.Id] * defenceBonus);

// calculating random multipliers
double minMultiplier = 0.5; // minimum cascading random multiplier (max = 0.99)
double multiplier = 0;
if (attackDefenceDiff > 1)
multiplier = (1 - minMultiplier) / attackDefenceDiff + minMultiplier;
else
multiplier = (1 - minMultiplier) / (1 / attackDefenceDiff) + minMultiplier;
double attackMultiplier = attackDefenceDiff >= 1 ? 1 : multiplier;
double defenceMultiplier = attackDefenceDiff <= 1 ? 1 : multiplier;

// rolls
int maxAttack = attackingUnit.MaxAttack;
if (maxAttack < 1) maxAttack = 1;
int attackRoll = Utils.CascadingRandom(model.Random, 1, maxAttack, attackMultiplier);
if (maxAttack > 15 && attackRoll < maxAttack / 2)
attackRoll = maxAttack / 2;

int maxDefence = defendingUnit.MaxDefence + defenceBonus;
if (maxDefence < 1) maxDefence = 1;
int defenceRoll = Utils.CascadingRandom(model.Random, 1, maxDefence, defenceMultiplier);
if (maxDefence > 15 && defenceRoll < maxDefence / 2)
defenceRoll = maxDefence / 2;

// after roll bonuses
double arbMultiplier = 0.66; // arb cascading random multiplier
int arbChance = 25;

// attack ARB
int attackARB = 0;
if (attackingUnit.ARB > 0)
{
if (Utils.ChanceRandom(model.Random, arbChance))
attackARB = Utils.CascadingRandom(model.Random, 1, attackingUnit.ARB, arbMultiplier); // multiplier = 0.66
}

// defence ARB
int defenceARB = 0;
if (defendingUnit.ARB > 0)
{
if (Utils.ChanceRandom(model.Random, arbChance))
defenceARB = Utils.CascadingRandom(model.Random, 1, defendingUnit.ARB, arbMultiplier); // multiplier = 0.66
}

// damage
// int damage = (attackRoll + attackARB) - (defenceRoll + defenceARB);
int attackDamage = attackRoll + attackARB;
int defenceDamage = defenceRoll + defenceARB;

Kirjoittanut Pinheiro, 10.02.2014 at 13:16

.

Thanks Pinheiro. Is that the current system, though? Or the old one?

Its the formula with after roll bonus, so it is outdated.

Alex, I made very similar experiences in game but as far as I remember there is NO mechanic thats buffs bigger stacks stat wise. But I think everyone has seen something like 250 bombers attacking 10 infantry and only 2 bombers die while all infantry is lost... some big mystery making it look like 3 bombers wiped out all defenders.

Kirjoittanut VRIL, 10.02.2014 at 13:50

Its the formula with after roll bonus, so it is outdated.

Alex, I made very similar experiences in game but as far as I remember there is NO mechanic thats buffs bigger stacks stat wise. But I think everyone has seen something like 250 bombers attacking 10 infantry and only 2 bombers die while all infantry is lost... some big mystery making it look like 3 bombers wiped out all defenders.

Thanks for your opinion.
And yeah, we would never find out until Admins say something. I know how battles work from trusteable sources (FAQ, old Admin posts, and answers) and I don't see anything that buffs them. I don't think it's even possible to download the Silverlight App and see the code. I'll bump this when Admins come back, since they are not posting on forums anymore.

Kirjoittanut Guest, 10.02.2014 at 09:58

initial observation about rolls

What would strengthen your argument would be if you used statistics. You have 3 "results", so you could do a simple T-test on the 3 observed averages vs. 3 randomly generated averages. Then you'll get the probability of your observation happening by chance.

Kirjoittanut Grimm, 10.02.2014 at 16:50

Kirjoittanut Guest, 10.02.2014 at 09:58

initial observation about rolls

What would strengthen your argument would be if you used statistics. You have 3 "results", so you could do a simple T-test on the 3 observed averages vs. 3 randomly generated averages. Then you'll get the probability of your observation happening by chance.

Hmm?
Well, these battles were random and not "selected". I could do about 10 battles and in EVERYTHING, there will be good rolls in BigStacked stacks.

Kirjoittanut Guest, 10.02.2014 at 17:04

Kirjoittanut Grimm, 10.02.2014 at 16:50

Kirjoittanut Guest, 10.02.2014 at 09:58

initial observation about rolls

What would strengthen your argument would be if you used statistics. You have 3 "results", so you could do a simple T-test on the 3 observed averages vs. 3 randomly generated averages. Then you'll get the probability of your observation happening by chance.

Hmm?
Well, these battles were random and not "selected". I could do about 10 battles and in EVERYTHING, there will be good rolls in BigStacked stacks.

Yes yes, I know they were random. But you want to proove that average rolls differ in large stacks vs. small stacks correct? If you want to prove that your observations are not just occuring by chance, you can do a simple statistic test. You can do this in excel. I can even do it for you if you like, but I don't have all the parameters. I'm not sure that I understand the details of how rolls are calculated for example. I'd be interested in looking into this. Send me a PM with all the details and I can look into doing statistics.

Just to be clear: a statistic test could, for example, allow you to affirm that the results you observed have < 1% chance of occuring by random chance. Therefore, your hypothesis that large stacks get bonuses is > 99% likely to be correct. That makes it much more convincing!

Big stacks do help a lot. Once I had like 30 inf up against 6 tanks, I destroyed all the enemy's tanks and only lost one infantry.

Kirjoittanut Grimm, 10.02.2014 at 19:40

Kirjoittanut Guest, 10.02.2014 at 17:04

Kirjoittanut Grimm, 10.02.2014 at 16:50

Kirjoittanut Guest, 10.02.2014 at 09:58

initial observation about rolls

What would strengthen your argument would be if you used statistics. You have 3 "results", so you could do a simple T-test on the 3 observed averages vs. 3 randomly generated averages. Then you'll get the probability of your observation happening by chance.

Hmm?
Well, these battles were random and not "selected". I could do about 10 battles and in EVERYTHING, there will be good rolls in BigStacked stacks.

Yes yes, I know they were random. But you want to proove that average rolls differ in large stacks vs. small stacks correct? If you want to prove that your observations are not just occuring by chance, you can do a simple statistic test. You can do this in excel. I can even do it for you if you like, but I don't have all the parameters. I'm not sure that I understand the details of how rolls are calculated for example. I'd be interested in looking into this. Send me a PM with all the details and I can look into doing statistics.

Just to be clear: a statistic test could, for example, allow you to affirm that the results you observed have < 1% chance of occuring by random chance. Therefore, your hypothesis that large stacks get bonuses is > 99% likely to be correct. That makes it much more convincing!

I'll work into this, thanks.

Agreed.
No matter what approach you use, in order to be able to make a claim about an 'externality' affecting the battle mechanics, your first task would be to establish the expected outcome and compare it to the anecodotal (experienced) outcome.

That being said, in any case, your sample size would be too small to 'generalize' -- you could speak with some authority to the expected vs. experienced outcome for that particular experience, but you would need several thousand observations (greater than 1000, probably more like 100 000 -100 000 000) to determine that an observed difference between expected outcomes and actual outcomes point to a large-force nerf on defensive outcomes. Of course, there might *actually be* a difference between large-stack combat and small-stack combat!

And, in any case, the ultimate difficulty we will face trying to look at large sets of outcomes is that we can't absolutely correlate the *pseudorandom* nature of computer-based rolls with the truly random -- computers and computer games almost always use *pseudorandom* algorithms to determine 'RND' outcomes -- over a long series, there is repetition. It does not matter in-game, because any sufficently-small subset of the outcomes will still 'look' random, and up to the point that a series repeats, it still meets 'random' expectations.

Kirjoittanut Grimm, 10.02.2014 at 19:40

Kirjoittanut Guest, 10.02.2014 at 17:04

Kirjoittanut Grimm, 10.02.2014 at 16:50

Kirjoittanut Guest, 10.02.2014 at 09:58

initial observation about rolls

What would strengthen your argument would be if you used statistics. You have 3 "results", so you could do a simple T-test on the 3 observed averages vs. 3 randomly generated averages. Then you'll get the probability of your observation happening by chance.

Hmm?
Well, these battles were random and not "selected". I could do about 10 battles and in EVERYTHING, there will be good rolls in BigStacked stacks.

Yes yes, I know they were random. But you want to proove that average rolls differ in large stacks vs. small stacks correct? If you want to prove that your observations are not just occuring by chance, you can do a simple statistic test. You can do this in excel. I can even do it for you if you like, but I don't have all the parameters. I'm not sure that I understand the details of how rolls are calculated for example. I'd be interested in looking into this. Send me a PM with all the details and I can look into doing statistics.

Just to be clear: a statistic test could, for example, allow you to affirm that the results you observed have < 1% chance of occuring by random chance. Therefore, your hypothesis that large stacks get bonuses is > 99% likely to be correct. That makes it much more convincing!

I normally wouldn't stake a conjecture based on so little information (30 rolls). But I did observe something very interesting from the data.

First, do we agree that the expected outcome of (5 attack, 9 critical) should be 3.45? (1-5, avg 3.0. 5*.09, avg .45) and (6 defence, 5 critical) should be 3.8? (1-6, avg 3.5. 6*.05, avg .30)? I think we do. Post here if not. My assumption of these averages assumes an equal possibility of (1,2,3 ... through the max roll).

30 results don't have enough information to speak to our expected results being flawed UNLESS we had experienced results which dropped below or above the ABSOLUTE expectations. (units always do a minimum of 1, never do more than 2x max). We do not have either of those results in this data.

Here is the result from the data i DO find very very interesting: The Defenders NEVER rolled a 6. Ever.

In 30 results, we should expect a 6, five times. To get it zero times is (5/6 x 5/6 ... 30 times)? The odds of no sixes is about 1/250, assuming a 1/6 chance of getting a 6.
Not impossible, but unlikely.

They also rolled a 5 only TWICE and a 4 only ONCE, again, an improbable result IF we expect that the odds for the defenders to roll a (4,5,6) are the same as the odds to roll a (1,2,3).

The utter lack of a roll of 6, coupled with the near-absence of 4s and 5s are not only improbable, but confusing. If it was merely a -1 nerf to defense, but with a surety of a 1, this would explain the lack of 6, and the unusual number of 1s and 2s. But, the near absence of 4 (expected 1/6 or 5 times, appears once, or 1/30) and 5 (appears 1/15) is puzzling. The dearth of 4 and 5 (but not absence) is more probable than the absence of 6, but still puzzling.

I will run a similar experiment. No generals in mine. The results I will focus on are the rolls. Pray for the virtual Indians about to suffer the bomber-depredations of the Chinese.

[Edited once I look at pseudocode]

Kirjoittanut Guest, 10.02.2014 at 09:58

Hello. I have been making some tests and watching rolls, since it has always been weird, that when you send big stacks (50 infantries against 8 infantries, for example) you always get insane results, like -3 -8. So I decided to write down rolls, divide them and compare them. From what I saw, when you send big stacks, defenders don't do high rolls that much.

So my point is, when you send more units to a city, the defenders will do lower rolls. And I wanted to discuss it, since it could be something wrong in the code or maybe it's just "luck"?

Okay, here we go.
These were the rolls I got, sending 34 infs + gen (5 attack, 9 critical) against 4 infs (6 defence, 5 critical). Criticals are not the problem in here, as they only appear sometimes.
52
22
31
43
13
22
62
33
11
25

-3 -4

Left numbers = Attackers' rolls.
Right numbers = Defenders' rolls.
Now, in total they are 10 rolls. Summing and dividing, attackers do 2.9 average, and defenders do 2.4
This may have been "just luck", so I'll be doing another one.

123infs+gen (5 att, 9 crit) vs 8 infs (6 def, 5 crit)
Attackers did 1 crit, defenders did 2.

42
21
72
51
43
14
53
18
45
52
31
41
38
21
22
51

-6 -8

Attackers average: 3.5625
Defenders average: 2.8125

Another one.
121 Infs + gen (5 att 9 crit) vs 7 infs (6def 5crit)
Attackers did no criticals, Defenders did 1.

21
22
33
32
31
11
21
43
42
42
21
31
11
51
21
42
37
11
-4 -7

Attackers average: 2.722..
Defenders average: 1.833..

That's it. I did 3 battles in total, TOTALLY Random, I did not select a few battles in which My stack got better rolls. Maybe, I did not do enough battles but in those 3, Attackers always did good rolls, even though they even did less criticals, and have a 5 maxDmg while Defenders got 6.
Please discuss below, and if you do not believe its true, then go ahead and do tests.

Preliminary Data: 126 rolls.
Scenario: Casual game, Strategy NONE. No generals.
Bombers vs. Neutral Infantry (6 damage, 5 Critical for each). Assuming 1-6 damage, .05 *6 for Critical, each should do an average of 3.8 damage. Each attack was done with at least 15x the number of bombers as defending infantry (usually 18 to 20 times).

- The attackers did an average of 4.02 damage, 6% deviance, well within expectations.
- The defenders did an average of 2.26 damage, 40% deviance. The sample size is small, so this result is 'suspicious' but not proof of a nerf.

The defenders DID roll some sixes, so IF there is a nerf, it isn't a simple -1.
The weirdness comes when looking at the distribution of the rolls. I removed the 2 critical rolls, so the sample size is 124.
1: 56
2: 33
3: 12
4: 10
5: 8
6: 5
The average damage, ignoring all rolls where there was a critical? 2.16? The average roll should be 3.5. Each number should have been rolled about 20 times.

6 (and 5,4,3) are indeed rolled however!

So, if there is a nerf to defending infantry (based on what idk) it seems like it would be difficult to characterize. idk C (++/#) very well, but the code above doesn't indicate something that would allow defenders to have a max Damage, non-critical roll, but at a lower-chance, EXCEPT the call to Utils.CascadingRandom.

Possibilities (not mutually exclusive)
1. Alex and I have just stumbled onto an unusual-but-expected deviation from expected average, which happens when dealing with small sets of data. We are confused by an anomaly; if we kept looking, everything would be fine.
2. Our understanding of Battle Mechanics is wrong. Max Damage 6 does not mean (1-6) with a mean of 3.5. Max damage of 6 means something else [but the attackers performed within expected limits in Alex's and my sets of data].
2. There is a deviation, and it is related to (generals, defending neutrals, mass stacks vs small stacks) and the nerf to the affected units is more complex than guaranteeing a minimum damage and removing the possibility of max damage.
The call to Utils.CascadingRandom and the other calls to ...Random may be implicated in this.

A possible clue? The method for determining damage:
// damage
// int damage = (attackRoll + attackARB) - (defenceRoll + defenceARB);
int attackDamage = attackRoll + attackARB;
int defenceDamage = defenceRoll + defenceARB;

If there are cases where the defender's damage is reduced due to a result rolled by the attacker (a damage reducing roll), in order for the defender to achieve an outcome of 6, the defender would have to roll the 6 (1/6 or .167 chance) and the attacker would have to have a corresponding 'bad' roll.

Kirjoittanut zombieyeti, 11.02.2014 at 11:09

That being said, in any case, your sample size would be too small to 'generalize' -- you could speak with some authority to the expected vs. experienced outcome for that particular experience, but you would need several thousand observations (greater than 1000, probably more like 100 000 -100 000 000) to determine that an observed difference between expected outcomes and actual outcomes point to a large-force nerf on defensive outcomes.

I'm fairly sure you won't need that many samples in order to establish this with over 99% confidence. Unless the nerf is very tiny. I'm not an expert in statistics, but I am somewhat familiar with basic statistical analysis.

I would need to understand the mechanics a bit better to do the analysis. For instance, I'm not sure I understand how rolls are calculated. In your bomber example, with an attack rating of 6, is there an equal chance of rolling 1, 2, 3, 4, 5 & 6? Or are 3 and 4 more likely (1 & 6 being the least likely)? And in the case of critical rolls, does each unit get a critical separately or does a critical roll apply to the whole stack for that unit type?

These questions aside, I have a simple suggestion to test Alex's idea. If one you guys could get me some rolls, similar to what Alex provided, but with bombers (if the attackers & defenders have equal attack rating, it's more simple to calculate). You'd need to provide me with rolls for at least 3 identical battles (ideally more, 10 would be better). For example, 50 bombers attacking 10 bombers. I'm pretty sure this will get us somewhere.

We believe, and our limited data *suggests* that the player attacker with a max damage of 6 and crit of 5, when attacking a neutral defender, in large stacks, does indeed effect an average damage of 3.8, inline with the Max Damage 6 (1,2,3,4,5,6 all with a chance of .1667, so an average of 3.5) and with a .05 critical (5 critical) on a max damage of 6, thus .3. That being said, our data seems to suggest that defender neutrals, in small stacks relative to the attacker, do NOT defend with a Max Damage 6 (1...6 etc.).
Nor, if the nerf exists, is the nerf a simple '-1', as defenders did manage to achieve 4,5,6, but in lesser-than-expected quantities.

The reason why a large set of data is likely necessary is that Alex's initial results (30 attacks and defenses) indicated that the defenders never 'rolled' a 6. With a 1/6 chance of rolling a 6, the odds against a 6 NOT appearing in 30 rolls is ~.004, or 1/250, which might lead one to conclude that defenders never rolled a 6. My 126 rolls indicated that 6's may be rolled by defending neutral infantry, but that the outcome was much rarer than expected.
What is confusing is that attacker's average damage is in-line with what was expected (4.02 v. 3.8, with 126 data points, closer than I would actually expect).

I'll post in a different reply my understanding of Battle Mechanics, which has been refined over time.

Kirjoittanut Grimm, 11.02.2014 at 14:40

Kirjoittanut zombieyeti, 11.02.2014 at 11:09

That being said, in any case, your sample size would be too small to 'generalize' -- you could speak with some authority to the expected vs. experienced outcome for that particular experience, but you would need several thousand observations (greater than 1000, probably more like 100 000 -100 000 000) to determine that an observed difference between expected outcomes and actual outcomes point to a large-force nerf on defensive outcomes.

I'm fairly sure you won't need that many samples in order to establish this with over 99% confidence. Unless the nerf is very tiny. I'm not an expert in statistics, but I am somewhat familiar with basic statistical analysis.

I would need to understand the mechanics a bit better to do the analysis. For instance, I'm not sure I understand how rolls are calculated. In your bomber example, with an attack rating of 6, is there an equal chance of rolling 1, 2, 3, 4, 5 & 6? Or are 3 and 4 more likely (1 & 6 being the least likely)? And in the case of critical rolls, does each unit get a critical separately or does a critical roll apply to the whole stack for that unit type?

These questions aside, I have a simple suggestion to test Alex's idea. If one you guys could get me some rolls, similar to what Alex provided, but with bombers (if the attackers & defenders have equal attack rating, it's more simple to calculate). You'd need to provide me with rolls for at least 3 identical battles (ideally more, 10 would be better). For example, 50 bombers attacking 10 bombers. I'm pretty sure this will get us somewhere.

Kirjoittanut zombieyeti, 11.02.2014 at 11:48

I normally wouldn't stake a conjecture based on so little information (30 rolls). But I did observe something very interesting from the data.

First, do we agree that the expected outcome of (5 attack, 9 critical) should be 3.45? (1-5, avg 3.0. 5*.09, avg .45) and (6 defence, 5 critical) should be 3.8? (1-6, avg 3.5. 6*.05, avg .30)? I think we do. Post here if not. My assumption of these averages assumes an equal possibility of (1,2,3 ... through the max roll).

30 results don't have enough information to speak to our expected results being flawed UNLESS we had experienced results which dropped below or above the ABSOLUTE expectations. (units always do a minimum of 1, never do more than 2x max). We do not have either of those results in this data.

Here is the result from the data i DO find very very interesting: The Defenders NEVER rolled a 6. Ever.

In 30 results, we should expect a 6, five times. To get it zero times is (5/6 x 5/6 ... 30 times)? The odds of no sixes is about 1/250, assuming a 1/6 chance of getting a 6.
Not impossible, but unlikely.

They also rolled a 5 only TWICE and a 4 only ONCE, again, an improbable result IF we expect that the odds for the defenders to roll a (4,5,6) are the same as the odds to roll a (1,2,3).

The utter lack of a roll of 6, coupled with the near-absence of 4s and 5s are not only improbable, but confusing. If it was merely a -1 nerf to defense, but with a surety of a 1, this would explain the lack of 6, and the unusual number of 1s and 2s. But, the near absence of 4 (expected 1/6 or 5 times, appears once, or 1/30) and 5 (appears 1/15) is puzzling. The dearth of 4 and 5 (but not absence) is more probable than the absence of 6, but still puzzling.

I will run a similar experiment. No generals in mine. The results I will focus on are the rolls. Pray for the virtual Indians about to suffer the bomber-depredations of the Chinese.

[Edited once I look at pseudocode]

The code is from the VERY old battle system, so I doubt we can get some info on it. Admins won't do anything, they did read my PM but didn't help in another topic, for example.

For grimm,
Rolls are random number between 1 and maxDmg. maxDmg is replaced with attack if you're attacking, and defense if you're defending.
Neutrals don't get the bonus defense, by the way, so their maxDmg is 6.


Anyway, zombie I think we shouldn't rely on critical hits since they don't happen all the time, in this case, I had almost as twice as chances than defenders, but still got less criticals. I'll do some "statistics" with militias because they have 0 critical hit chance by default.

Kirjoittanut Guest, 11.02.2014 at 15:27

Kirjoittanut zombieyeti, 11.02.2014 at 11:48

I normally wouldn't stake a conjecture based on so little information (30 rolls). But I did observe something very interesting from the data.

First, do we agree that the expected outcome of (5 attack, 9 critical) should be 3.45? (1-5, avg 3.0. 5*.09, avg .45) and (6 defence, 5 critical) should be 3.8? (1-6, avg 3.5. 6*.05, avg .30)? I think we do. Post here if not. My assumption of these averages assumes an equal possibility of (1,2,3 ... through the max roll).

30 results don't have enough information to speak to our expected results being flawed UNLESS we had experienced results which dropped below or above the ABSOLUTE expectations. (units always do a minimum of 1, never do more than 2x max). We do not have either of those results in this data.

Here is the result from the data i DO find very very interesting: The Defenders NEVER rolled a 6. Ever.

In 30 results, we should expect a 6, five times. To get it zero times is (5/6 x 5/6 ... 30 times)? The odds of no sixes is about 1/250, assuming a 1/6 chance of getting a 6.
Not impossible, but unlikely.

They also rolled a 5 only TWICE and a 4 only ONCE, again, an improbable result IF we expect that the odds for the defenders to roll a (4,5,6) are the same as the odds to roll a (1,2,3).

The utter lack of a roll of 6, coupled with the near-absence of 4s and 5s are not only improbable, but confusing. If it was merely a -1 nerf to defense, but with a surety of a 1, this would explain the lack of 6, and the unusual number of 1s and 2s. But, the near absence of 4 (expected 1/6 or 5 times, appears once, or 1/30) and 5 (appears 1/15) is puzzling. The dearth of 4 and 5 (but not absence) is more probable than the absence of 6, but still puzzling.

I will run a similar experiment. No generals in mine. The results I will focus on are the rolls. Pray for the virtual Indians about to suffer the bomber-depredations of the Chinese.

[Edited once I look at pseudocode]

The code is from the VERY old battle system, so I doubt we can get some info on it. Admins won't do anything, they did read my PM but didn't help in another topic, for example.

For grimm,
Rolls are random number between 1 and maxDmg. maxDmg is replaced with attack if you're attacking, and defense if you're defending.
Neutrals don't get the bonus defense, by the way, so their maxDmg is 6.


Anyway, zombie I think we shouldn't rely on critical hits since they don't happen all the time, in this case, I had almost as twice as chances than defenders, but still got less criticals. I'll do some "statistics" with militias because they have 0 critical hit chance by default.

I've done some investigating on this matter. As far as I can guess without reading the whole code, the problem arises from the fact that the units select a random unit to deal damage to, not the one that was previously defending or attacking. Therefore, the chances of a damaged unit taking damage in a 8 units versus 8 units situation is higher than in 50 vs 8.

CUAWBM - Elementary (Current Understanding of AtWar Battle Mechanics), with a clear attacker and a clear defender (elementary).
Sources
- Authoritative but may be dated:
http://atwar-game.com/home/faq.php?faq_id=14 aka 3.13 Battles
http://atwar-game.com/home/faq.php?faq_id=17
http://atwar-game.com/forum/topic.php?topic_id=4007 < found by AlexMeza

- Non authoritative (May be wrong but the best info I have until I receive better info):
http://atwar-game.com/forum/topic.php?topic_id=8019
http://atwar-game.com/forum/topic.php?topic_id=12115

Scenario:
- Player A's unit/stack of units attacks Player N's (neutral) units, OR Player A's units attacks Player B's units.
- Player B's units did not move that turn.
- There are no modifiers to the unit stats as described (strategies, bonuses etc.)

Player A has 3 units with a Max Attack of 7, HP 7, Critical 5. Average total damage: 4.35
- The average normal damage of each unit is 4. The critical damage will always be a bonus of 7, added to the normal damage, although critical damage only occurs 5% of the time.
- As the damage shown in the Battle Replay (Settings | My Settings | Battle Speed = Very Slow) are always Counting Numbers, this, coupled with the sources, and reference to 'rolls' lead us to conclude that Player A will do 1-7 damage, with an equal chance of any Counting Number, between 1-7 inclusive, with a 5% chance to do an additional 7 damage.

Player B has 3 units with a Max Attack of 6, HP 7, Critical 5. Average total damage: 3.8

Other considerations, based on sources above (ordered to degree of certainty, first is most certain)
- (most certain) There is always a victor: No battle ever concludes without at least one unit remaining, with all opposing units defeated.
- Surviving units have HP restored at the conclusion of a battle.
- 'Attacking' and 'Defending' occurs simultaneously. Therefore, attackers and/or defenders will always do at least 1 damage PER BATTLE.
- Every unit that has a chance to skirmish in a battle will always do at least 1 damage.
- No unit will do more than 2x Max Damage per round of a skirmish, in a battle.
- If damage to a unit exceeds the HP of that unit, the next unit on that side receives the damage BEFORE the next skirmish of the battle. Therefore, it is possible that multiple units are killed by the same enemy unit, with just one round of damage.
- (least certain) If the final units in a battle annihilate each other, the unit with the greatest remaining HP survives. All we know for certain is that there is always a victorious side, and that it is certainly *otherwise* possible that units annihilate each other. We do not know how the surviving unit is selected.

Example of Battle
Skirmish 1
Round 1: Unit A1 attacks with 3 damage. Unit B1 defends with 4 damage. No critical hits occur. Unit A1 has 3 HP remaining. Unit B1 has 4 HP remaining.
Round 2: Unit A2 attacks with 7 damage. Unit B1 defends with 2 damage. No critical hits occur. Unit A1 has 1 HP remaining. Unit B1 is killed, and 3 damage is passed to Unit B2, which now has 4 HP.

Skirmish 2
Round 3: Unit A2 attacks with 13 damage. Unit B2 defends with 2 damage. Unit A2 has inflicted a critical hit. The 6 normal damage, plus 7 critical damage. Unit A1 is killed, and 1 damage is passed to Unit A2 which now has 6 HP. Unit B2 is killed. The 9 damage passing to Unit B3 also kills Unit B3, which has no opportunity to counterstrike.

Team A is victorious. One Unit remains.
-
-

Developing a baseline or 'expectation' is a necessity to understand if our understanding of Battle Mechanics apply to the game, and critical damage is authoritatively well-documented. That you received any critical hits in your set of 60 rolls, 30 rounds, speaks more to the concern of reliance on small data-sets as anything but anecdotal.

A small dataset is only useful to disprove a boundary condition, and only if an exception to that condition happened to occur.

For example, we conjecture: "normal damage does not exceed max damage".
If you see normal damage that exceeds max damage occur in a small dataset, our conjecture would be disproved, however, that it does not appear doesn't prove our conjectures truth or falsity.

Think to your data set of 30. IF there is a 1/6 chance an Infantry would defend at 6, the fact that a 6 was not rolled in 30 attempts would be distressing: That happens only 1/250 times. We cannot conclude that a 6 cannot be rolled, however. In this case, further testing by me indicated that, indeed, a 6 can be rolled -- but that 6s are rolled, in my larger-but-still-small data set, less frequently than one would expect.

Kirjoittanut Guest, 11.02.2014 at 15:27

Kirjoittanut zombieyeti, 11.02.2014 at 11:48

I normally wouldn't stake a conjecture based on so little information (30 rolls). But I did observe something very interesting from the data.

First, do we agree that the expected outcome of (5 attack, 9 critical) should be 3.45? (1-5, avg 3.0. 5*.09, avg .45) and (6 defence, 5 critical) should be 3.8? (1-6, avg 3.5. 6*.05, avg .30)? I think we do. Post here if not. My assumption of these averages assumes an equal possibility of (1,2,3 ... through the max roll).

30 results don't have enough information to speak to our expected results being flawed UNLESS we had experienced results which dropped below or above the ABSOLUTE expectations. (units always do a minimum of 1, never do more than 2x max). We do not have either of those results in this data.

Here is the result from the data i DO find very very interesting: The Defenders NEVER rolled a 6. Ever.

In 30 results, we should expect a 6, five times. To get it zero times is (5/6 x 5/6 ... 30 times)? The odds of no sixes is about 1/250, assuming a 1/6 chance of getting a 6.
Not impossible, but unlikely.

They also rolled a 5 only TWICE and a 4 only ONCE, again, an improbable result IF we expect that the odds for the defenders to roll a (4,5,6) are the same as the odds to roll a (1,2,3).

The utter lack of a roll of 6, coupled with the near-absence of 4s and 5s are not only improbable, but confusing. If it was merely a -1 nerf to defense, but with a surety of a 1, this would explain the lack of 6, and the unusual number of 1s and 2s. But, the near absence of 4 (expected 1/6 or 5 times, appears once, or 1/30) and 5 (appears 1/15) is puzzling. The dearth of 4 and 5 (but not absence) is more probable than the absence of 6, but still puzzling.

I will run a similar experiment. No generals in mine. The results I will focus on are the rolls. Pray for the virtual Indians about to suffer the bomber-depredations of the Chinese.

[Edited once I look at pseudocode]

The code is from the VERY old battle system, so I doubt we can get some info on it. Admins won't do anything, they did read my PM but didn't help in another topic, for example.

For grimm,
Rolls are random number between 1 and maxDmg. maxDmg is replaced with attack if you're attacking, and defense if you're defending.
Neutrals don't get the bonus defense, by the way, so their maxDmg is 6.


Anyway, zombie I think we shouldn't rely on critical hits since they don't happen all the time, in this case, I had almost as twice as chances than defenders, but still got less criticals. I'll do some "statistics" with militias because they have 0 critical hit chance by default.

Lainaa:

@ Pulse [deleted for brevity]

I've done some investigating on this matter. As far as I can guess without reading the whole code, the problem arises from the fact that the units select a random unit to deal damage to, not the one that was previously defending or attacking. Therefore, the chances of a damaged unit taking damage in a 8 units versus 8 units situation is higher than in 50 vs 8.

Observation of battle results seems to indicate otherwise: If, for example, you take 268 bombers vs. 13 Infantry (one of my tests), and if damage is spread to a random unit each time, and not the next in line, odds are that not one bomber would die. Reason: Without Critical, no one hit by Infantry would kill a bomber. Each infantry does a max damage of 6, each bomber has an HP of 7. The odds of any particular bomber being hit in a given round is (1/267) or ~.0037. There were 21 rounds of combat. The same bomber being hit twice isn't that small, but for 6 bombers to be hit more than twice are pretty small (on round 2, 1/267 that any bomber is hit twice, on round 3, 1/266, on round 4, 1/265 etc.)

In the example I bring up, indeed 6 bombers did die. The question is why did 13 Infantry die, for a cost of 6 bombers, when they should be doing the exact same thing to each other, over time. And they aren't, apparently.

Agreed, but the code makes a call to an external procedure/object that could have been easily put inline.
Again, for me, the confusing things is that the anecdotal results for attackers are inline with our expectations of how Battle Mechanics works, but the results for defenders (in my case, and I suppose yours, defending neutrals) is far out of line.
[deleted for brevity]

[Alex] The code is from the VERY old battle system, so I doubt we can get some info on it. Admins won't do anything, they did read my PM but didn't help in another topic, for example.

I think Alex's request for independent verification is on point.
At a high level, just start a casual game, allow joining until zero. Pick Asia, and give yourself fifty large.
Turn off your buffs if you have premium, and choose Strategy = none.
Choose China, build up a 1/2deathstack (200 bombers).
Then go bomb Indian cities.

Repeatedly, I lose 5 to 7 bombers for every 10 to 13 neutral infantry I kill. 10 times in India this has happened.
Only on try 11 did I lose 9 bombers for 10 infantry killed.

No need to adjust your game settings or record your results in a spreadsheet (I did that for the first 126 rounds of combat).

Again, I don't know if this is because I am attacking neutrals, if it is big stack v small stack, Attacking v Defending, or just blind chance, but after ten results in a row of overwhelming defender losses, I am placing less credibility on a statistical anomaly and more credence on our collective lack of understanding of Battle Mechanics.

The shit thing: Attackers are doing the average damage that my stated expectations indicate. It's just that defenders are doing much less, like 40.5% less damage than we should expect.