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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.

I've observed this too. It seems that +3 leaders far outperform +30 org +30 morale leaders. And when you get a +5 leader, thank your gods!
 
# attack = + or - on dice roll in combat when attacking. (like skill in eu3)
# defence = + or - on dice roll in combat. (like skill in eu3)
# morale = % modifier on morale.
# organisation = % bonus on org.
# reconnaissance = % bonus on reconaissance.
# speed = % bonus on movement
# attrition = penalty on attrition. (negative is good)
# experience = % bonus on experience gain.
# reliability = mil gain or loss for pop associated.
 
Conclusion: They don't know how it works either. :D

Or it could be worse, they could be lying about it. In my second ever game of Victoria 2 I discovered that being sphered while civilizing always gives you less techs than civilizing while sphered, and that if you want the max amount of techs you need 5 reforms from each column, no more and no less. This is literally the direct opposite of what the manual says, what the devs wrote, and what all the beta testers told us when they were writing AARs. I figured this out on my second game ever and when I posted about it people just kept repeating all the old useless advice at me like "you should try to get sphere'd by the UK" or how I should totally ignore the econ reforms.
 
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Have you checked if this is fixed in 3.02?
 
Result time! For now im fed up with testing (want to play the new patch) so here is what i found:

The stats
Attack: Only used when attacking, modifies damage done
Defence: Only used when defending, modifies damage done
Organization: The green % bar, determines how long your units will stay in battle
Discipline: Reduces org loss
Tactics: Reduces casualties
Morale: No impact on fighting behaviour, probably only speeds up org regain
Experience: Not tested, i only used 0 xp units

Rolls
Rolls are used as modifers for inflicted casulties and organization loss (duh!). All modifications to rolls (Rivers, Hills, Generals...) are treated the same and the effective dice roll is just the sum of all values (roll of 6 with general +2 and river -1 is 6+2-1 = effective 7).

The effective rolls are converted into multipliers using this table:

Roll Multiplicator
-2 1
-1 2
0 3
1 4
2 5
3 6
4 8
5 10
6 12.5
7 15
8 17.5
9 20
10 22.5
11 25
12 30
13 35
14 40
15 45

The table is capped at -2, going lower will not decrease the multiplier below 1. Note the increase in growth after 3 (+1 to +2), 5 (+2 to +2.5) and 10 (+2.5 to +5). I did not test for values higher than 15.

Damage done
Casualties inflicted per round of combat:
Per soldier: (10+Stat)*Roll_Multiplier/(2500*[1.5+tactics])
Per 3000 soldiers: (10+Stat)*Roll_Multiplier*1.2/(1.5+tactics)

Organization inflicted (total, not % based!):
Per soldier: (10+Stat)*Roll_Multiplier/(250000*[1.5+tactics])
Per 3000 soldiers: (10+Stat)*Roll_Multiplier*0.012/(1.5+tactics)

In both cases the result is rounded down.
Note that 'Stat' only is the corresponding one, e.g. when attacking the attack stat. When you attack the defense stat is not used at all, the rolles are fixed and will not switch. Same goes for defending. Hello Guards! (This finding supprised me the most, i exspected a switch every new dice roll)
Another important point is the tactics value: The 1.5 is only granted if you have any +tactics at all. Because of this only getting a single point of tactics reduces your casualties by 50%, getting +50% halves your damage recieved.

Some more notes in case you want to check my findings:
I always used 3k vs 3k in a single stack each and recorded the numbers of the first day of combat (all inventions etc removed). This allows to ignore statistics and shows direct results when editing unit values. The only exception for this was when looking for role switching. Setting attack to -10 (=0 casualties inflicted) and letting full battles commence one side is always winning with no damage recieved at all.
One weird observation is caused by tactics; when using values other than 0% there seem to appear rounding errors, after noting this it looked like there is a difference between attacking and defending (by a few %). I did not test this any further, looked like a minor bug to me.

This could probably be formated and explained better, if anyone wants to do it feel free to reformate and add it to the wiki.
 
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Result time! For now im fed up with testing (want to play the new patch) so here is what i found:
/bow...great work Gyorn! Your results seem to explain very well the results I was seeing with the limited testing I did. Thanks for doing some real testing and sharing your results with us. I think this is probably exactly what Cymsdale was looking for to add to the wiki (not to volunteer you Cymsdale). :) This should help tremendously with all the confusion on this topic.
 
And I told you that in the first page of this thread.
 
And I told you that in the first page of this thread.
The problem was your "I can't give a source that's accessible to everyone". Because lots of people say lots of things, and even if you're just a... Smidge more credible, I guess we prefer getting a more in-depth understanding.
 
Flying closer to sun, let's call it. :p But fair enough. Oh, while I'm here - Can you explain the part about tactics, how you arrived at that result?
 
And I told you that in the first page of this thread.
Yes, you were dead on with the attacker/defender roles. I think because of how much weight is allotted to the die rolls vs unit stats it caused some confusion when seeing the results. Before this thread I was under the impression unit stats were far more important than they actually are. Seems to me they are still important when considering attrition over the course of a war, but not as important as I thought for individual battles.
 
Well. Die rolls need to be balanced for the entire game... For low unit stats, and then for way higher unit stats at Tier 5 or Tier 6.
 
[...]Oh, while I'm here - Can you explain the part about tactics, how you arrived at that result?
Same setup as described above (2x 3k, one day of battle) but with the first +tactics invention unlocked for one side. I tried several different values as gain from the tech as well as different unit stats.
Assumption was that tactics reduces casualties by a %, thus i calculated the % of recieved casualties vs. casualties without tactics. When looking at the resulting numbers its obvious that unit stats play no role, same for dice rolls. The % numbers gained however are quite...odd, e.g. about 57% for +25% tactics. However since unit stats get a bonus of +10 it wasnt that hard to assume the same thing happening here and with 150% its a match. There do occur rounding errors (since you cant loose half a soldier) and im not sure whats causing the bug i mentioned above. However the differences are small enough that im convinced its a rounding issue, not a faulty formula.
As for the lack of the 150% (or them beeing 100% to be precise) when having no tactics at all...after finding the formula it was obvious it would not produce the proper results in this case, thats why i did an additional test with +1% tactics, leading to a casualty reduction of ~33% (=1-(1/1.5)).
 
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So basically, all guard armies ARE still usable and will NOT suffer more casualties as long as you are attacking with them? Basically the opposite of what we were told in the dev diaries and AARs.
 
Beta AARs. There's a reason why the word beta is put in the title, they aren't based on the final retail version of the game.

And well, you can put them on the flanks of your army, they can reach farther than infantries in that role, attack diagonally. They just aren't as good at it while not attacking, but still, are solid and useful.
 
So basically, all guard armies ARE still usable and will NOT suffer more casualties as long as you are attacking with them? Basically the opposite of what we were told in the dev diaries and AARs.
Correct, but the increased attack stat on the guard unit isn't going to make a ton of difference, which is probably why the answer to this question wasn't already obviously apparent. You're talking about ~18 for guard vs ~15 for infantry as your modified attack value in the early game. Then you have to consider all the other factors like leader attack/defense, terrain, die roll, etc. which further dilute that gap.