Combat Stats Clarification - Attack / Defense

kingsword

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So, attack & defense both used or just one, depending on the combat initiation?
 

Pugman

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So, attack & defense both used or just one, depending on the combat initiation?
It's not completely clear, but it appears the attack stat is used primarily by the attacking army and the defense stat is used primarily by the defending army. There's a possibility they are both used to a lesser degree by both armies but that's just not clear from the testing I did...I think if it is it's probably negligible.
 

GC13

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I messed with this some today, using armies that had generals with irrelevant stats (Sam Houston and his +6 defense and -25% speed was leading the attack, against a general who gave morale and speed) each leading three brigades of infantry. The defender had the same 1/1 dig-in to start every battle off, and the attackers always used 5 atk/5 def infantry.

When going up against 5 atk/5 def defenders, the results were about even. Despite the dig-in bonus, after twenty battles the defenders averaged a few more casualties, but it's all within the margin of error and could easily be a statistical fluke.

Then I set the attackers against 5 atk/14 def defenders (obtained by unlocking all inventions that give a only defensive boost, but not the techs that go with them). Well, the AI would terminate the attack immediately, so I had to control them. The attackers' losses were about as horrible as you'd expect: on average, the casualties went 3:1 in favor of the defenders. I ran this test only ten times, because the closest the attackers came to a win was only suffering 6,792 losses versus the defenders' 3,630. No matter how you cut it, the defensive stat clearly allowed the defenders to not only win the fight but dominate it.

After that, I unlocked all of the attack-only inventions to give the defenders 11 atk/5 def. This was the question we all wanted to answer, and I can only give you an educated guess: the AI stack was just as afraid of the 11/5 defenders as it was of the 5/14, so again I had to control it. It's a safe bet that if the AI is programmed not to attack them, the battle calculation takes their Attack value into account. The average casualties also imply that the Attack value matters: the casualties were 5:4 in the defenders' favor.

That's a very small difference for such a large increase in stats, though, and I was only able to run that test fifteen times before I got frustrated (it takes longer and longer to resign and load as you do it over and over). I calculated confidence intervals for this and for the even-stats run, and they overlap significantly: that means that I cannot say with full confidence that the average casualties between the two cases are actually different and that the apparent difference isn't just a statistical oddity.

I'm almost certain to run this test more, but I'd have to run forty-five more tests for the Up Attack scenario to cut the confidence range in half. If anyone wants to try it themselves, I've uploaded the saves I used to Google Drive, and you can get the package here).

Note that the one that says Texas, you'll load by default as Mexico (just sit there and let the Texans finish their move order to begin the attack). The two that mention Mexico (Attack Up is the 11/5 Infantry, Defense Up is the 5/14) you'll need to deliberately load as Texas, because the AI will not willingly allow that attack to continue if it's in charge. Again, just let the army finish their attack order, and the battle will begin quickly.

If you want to share your outcomes with me, just write down the losses of both sides in some format I can easily paste into a spreadsheet, with Texas's casualties on the left (a text file where you put a tab in between the two should do the trick, and you can post it directly into the forum if you use the Code tag). Don't count the battle if a leader dies during it (Sam Houston has died on me a few times) or if Mexico gets more troops into the fight.

Make sure to let me know which scenario your numbers are for. Obviously, the Attack Up scenario is the one I most need data for, but to compare it to the base scenario (Texas1836_01_17.v2) it would be helpful if the both had skinnier confidence intervals.
 

KevinG

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If you actually played the game it doesn't take a genius to figure out attack value is used when you attack and defense value is used when you defend.

And if you actually tested it it doesn't take a genius to figure out there's much more to it then that.

I wish paradox was more open with game mechanics, because really nothing they say is ever correct in any of their games. Any veteran paradox MP player knows this.
 

chrism2012

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Based on the tests made by Pugman and GC13 it appears that the roll dice acts as some kind of modifier, giving 100% (*1,0 + leader stats) attacking stats to the attacker when the roll is 9 and something small >0% (e.g. *0,001) when the roll is 0 to still take leaders and other values into account.

Upon this might come another modifier mixed of organisation, morale, tactics, discipline etc.; or even a total modifier of all aspects which is then modified by the roll dice 0-9.


Same for defenders the other way round.


What would be interesting are 0/0 stats for attacker/defenders to see how (if) the battle develops...


But basically, if the devs don't post their internal battle formula then all our assumptions can't be proved for certainty.
 

Gyorn

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I will probably do some testing myself later on (once i find the free time...). Might be helpfull to go after specific questions.

- Is Defense used only when defending or in every battle? If yes, is there a switch, e.g. every new diceroll?
- Why are defense and offense stats differing in tests (see GC13s tests)? How?
- How important are dice rolls vs. stats?
- How important are generals/hills/rivers?
- What are the other stats doing (org/morale)?
- What is the damage formula (the grail)?

Did i miss anything important? Feel free to add, i will however first try to get down only a single day of combat to get the values effects and relations straight.
 

Pugman

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The wiki article below explains the formula for land combat. Is there any reason to think that this is no longer correct?

http://www.paradoxian.org/vicky2wiki/Land_combat_reference
The formulas in that article make no mention of the defense stat and it's not clear specifically when each are used. It's obvious the attack stat is used more by the attacker and the defense stat is used more by the defender but the exact formulas are a mystery at least to me.
 

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I will probably do some testing myself later on (once i find the free time...). Might be helpfull to go after specific questions.

- Is Defense used only when defending or in every battle? If yes, is there a switch, e.g. every new diceroll?
- Why are defense and offense stats differing in tests (see GC13s tests)? How?
- How important are dice rolls vs. stats?
- How important are generals/hills/rivers?
- What are the other stats doing (org/morale)?
- What is the damage formula (the grail)?

Did i miss anything important? Feel free to add, i will however first try to get down only a single day of combat to get the values effects and relations straight.
I think that's a great list of questions. If you have the time and know-how to find answers to those then you will have at least one grateful admirer (me), and I suspect many more. :)
 

GC13

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Alright, halfway through testing the 11/5 defenders some more, I realized that comparing end-of-battle casualties was a sucker's game. Not only was it getting skewed in favor of the defenders because usually when they brought reinforcements to the battle it was because they were losing, but the game shows us the die roll, right?

So this time, I went and compared the armies' org and str on the fifth day of battle (i.e. after all fighting using the first die roll was done). These numbers are unequivocal: defenders only use their def stat, not their atk stat at all. So cheers to that.

It also gives me a good idea of how crucial the die roll is. Having a general that gives you a mere +1 in the battle is probably more important than having a +3 to your units' relevant stats. For very low rolls, it's can trump a five-point disparity.
 

Pugman

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Alright, halfway through testing the 11/5 defenders some more, I realized that comparing end-of-battle casualties was a sucker's game. Not only was it getting skewed in favor of the defenders because usually when they brought reinforcements to the battle it was because they were losing, but the game shows us the die roll, right?

So this time, I went and compared the armies' org and str on the fifth day of battle (i.e. after all fighting using the first die roll was done). These numbers are unequivocal: defenders only use their def stat, not their atk stat at all. So cheers to that.

It also gives me a good idea of how crucial the die roll is. Having a general that gives you a mere +1 in the battle is probably more important than having a +3 to your units' relevant stats. For very low rolls, it's can trump a five-point disparity.
This is consistent with what I found and posted further up in the thread. Die rolls are by far the most important. They also play a role in determining how bad losses are on the losing side (the greater the gap between the winning and losing roll, the more the losses will be).
 

Gyorn

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Im by far not done yet, however ive got some interesting finds:
- The attacker only uses the attack stat, the defender only the defence, at least for the first round of combat (5 days). Did not test for switching yet.
- Inflicted casualties by the attacker are not modified by the defenders defence stat and dice roll and vice versa. I did not test for the defenders attack stat yet (probably unused too). Its about absolute dice rolls, not the gap.
- Generals/Hills/Rivers are all treated the same and applied directly to the dice rolls. Having no general (-2) and a 9 gives the same results as rolling a 7 without modifiers. I did not test general specific attack/defence differences yet (e.g. +0 attack and +1 defence), propably only the matching value is used.
- Effective rolls (= with modifiers) are capped at -2. Did not look into a upper cap yet, probably at 11.
- Upping the stats 4 fold gives approx 2 times the damage. Im not entirely sure here yet, it holds for a jump from 5 to 20, however an approximation based on this does not hold for 100.
- There seems to be a jump in effective roll effectiveness, ranges are -2 to 3, 4 to 5, 6 to 7+ (did not test above 7 yet).


Its a lot more complicated than i imagined, this might take some more time...
 

GC13

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Im by far not done yet, however ive got some interesting finds:
- The attacker only uses the attack stat, the defender only the defence, at least for the first round of combat (5 days). Did not test for switching yet.
- Inflicted casualties by the attacker are not modified by the defenders defence stat and dice roll and vice versa. I did not test for the defenders attack stat yet (probably unused too). Its about absolute dice rolls, not the gap.
- Generals/Hills/Rivers are all treated the same and applied directly to the dice rolls. Having no general (-2) and a 9 gives the same results as rolling a 7 without modifiers. I did not test general specific attack/defence differences yet (e.g. +0 attack and +1 defence), propably only the matching value is used.
- Effective rolls (= with modifiers) are capped at -2. Did not look into a upper cap yet, probably at 11.
- Upping the stats 4 fold gives approx 2 times the damage. Im not entirely sure here yet, it holds for a jump from 5 to 20, however an approximation based on this does not hold for 100.
- There seems to be a jump in effective roll effectiveness, ranges are -2 to 3, 4 to 5, 6 to 7+ (did not test above 7 yet).


Its a lot more complicated than i imagined, this might take some more time...
The old formula tossed around for damage includes a 10+Unit stat, which sits perfectly with the ~40% gain in damage I saw going from 5 to 11 (21/15=1.4), and you saw going from 5 to 20 (30/15=2). I also confirm that casualties are not modified by the other side's stat or roll, except indirectly in that if they kill your soldiers, dead soldiers can't hurt them.

I saw 5, 6, 7, and 9 (especially 7 and 9) be very important die rolls for increasing your damage. Even 8, in absolute terms, was up there, but by that point it's pretty small relative to what's already being done on a 7. I don't know what this means, except to assume that the die roll refers to some table which has a base damage amount for that roll.

As for whether the attacker uses the defense stat on subsequent rounds of battle or not, I don't think so. Since it's so hard to get good comparisons for a second round of battle, I went back to the old method to test 5/14 attackers against 5/5 defenders. Statistically, it looks a lot like the 5/5 defenders versus 5/5 attackers.
 

Gyorn

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The old formula tossed around for damage includes a 10+Unit stat, which sits perfectly with the ~40% gain in damage I saw going from 5 to 11 (21/15=1.4), and you saw going from 5 to 20 (30/15=2).
Oh my...thanks for that! Saved me a lot of grey hair. Have to leave in like 2 minutes, however looking over the numbers gives us this:
Stats used for calculation are base (=10) + shown numbers. Double the stats = double the inflicted damage.
E.g: Shown attack of 10 does twice the damage as shown attack of 0 (10+10 = 2* 10+0) while 30 (shown) does twice that of 10 (shown).

Tihs holds for values of 0, 10, 20, and 100, did not check the others yet but it seems solid.

EDIT: Note im not talking statisticts but hard numbers here. No rounding errors or anything, exact match.
EDIT2: The same rule applies to morale damage