Some of this may already be obvious but I thought I'd throw out a few combat related observations I've had...
1) Hit Points:
All units in the game have a base 100 "hit points" (well, all the units I've looked at so far...admittedly I didn't check sea going units but I have no reason to think differently for them).
2) Chance of Success:
When a unit attacks another unit a base percentage value is generated between it and the defending unit. For example, a warrior vs. warrior (unpromoted, 2.0 vs 2.0) has a 50% chance of success.
2a) Rounding:
From what I can tell, all the combat success values (or any from the resulting calculations used to determine the victor) are rounded down.
For example, a warrior with the Combat I promtion vs. a normal unpromoted warrior (2.2 vs 2.0) generates a 52.3805% chance which is rounded down to 52.3%
3) Base Damage:
A unit does a base 20 damage, per hit, against an equal unmodified defender (and the defender does the same).
4) Chance Modifiers:
The "success chance" percentage (from above) modifies a units chance to hit and the amount of damage.
5) Combat Rounds:
Essentially a series of combat rounds occur between two units. Each time a random percentile "die" is rolled (1 to 100) and is compared to the success chance determined from above.
5a) To-Hit:
Either one unit or another attempt to hit in any round and will do damage on any round of combat in which they succeed. Effectively the chance to hit uses the "success chance" from above, as far as I can tell. However, I suspect that there is some other unseen factor in play as well that alters the results when a unit from one era fights another. I haven't quite confirmed this but I'm looking at it more to see.
5b) Damage Modifier:
I haven't quite figured out how the damage modifier is determined but I think it is akin too: the percent difference from 50 *2.
For example, a warrior (unpromoted, unmodified) vs. an archer (unpromoted, unmodified) produces a 60% chance of success for the defender. The damage modifier appears to be (60-50)*2, rounded down. In this case, a 20% modifier.
The damage modifier is applied to both the attacker and defender, according to the positive or negative value that results for them. From the above example, the archer would do +20% from the base 20, or 24 damage per hit, and the warrior would do -20%, or 16 per hit.
The result is that the archer needs to land 5 hits (24*5 > 100) and the warrior needs 7 hits.
6) First Strike:
First strike attempts can miss, like any attack. However, they present a very real opportunity to kill an opponent quickly since it can front load 1 or more hits before the opponent gets an opportunity for a first swing.
If nothing else, it can reduce attrition to troops who have a successful run of first strikes, or at least increase attrition to enemy troops even if the battle fails. As a result, it might be ideal to use first strike promotions when you face superior forces that you need to have extra opportunities to hit before your own unit dies...reducing their health for further attackers. It might also serve as a decent way to increase survivability of seige units used for collateral damage, against equal and particularly lesser foes
7) Field Modifiers:
The general modifiers, be they promotions or "field" related (such as being on a hill, fortified, etc.) are additive. That is, if you have the Combat I promotion and are fully fortified, the total modifier is +35%.
8) Defender Selection:
Any time a stack of defender is attacked, the best-fit defender vs. the attacker is always selected for the combat. This is why combined arms is ideal, such as having a spearman as escort with a stack of axemen/swordsmen to counter mounted harry attacks against the group. And yes, it does mention this in the manual
General Combat Observations and Tips
All in all, familiarity and the ability to create situations in which you can stack several bonuses is the key to quick and efficient battles. Using units in a manner that suits their capabilities is also important, such as avoiding the use of mounted troops over slower melee units (combined with seige weapons) to assault cities, and instead, using the mounted troops to move deep into enemy territory, pillaging key resources and hampering enemy reinforcements moving to the main battle.
Overlooking certain promotion types can seriously detract from your ability to carry the battle well to the enemy, especially when the odds are against you. To the contrary, if you are strong and can afford to specialize your force directly against a known objective, by all means you should increase your strength with choice promotions for units playing very particular roles.
Having said that, the Combat I+ promotion should be seen as a "general" promotion, when you are uncertain what enemy types the promoting unit will be facing in the future or when the unit has already been specialized against a particular unit type and is looking to maximize combat effectiveness.
First Strike promotions can be very effective for both offensive and defensive ranged attack unit types (crossbows, archers, etc.) and flanking is most useful for mounted escorts who have other defenders they can retreat into when a battle turns against them. Be sure to leave a few strong/healthy defenders in the stack that make the enemy wary of trying to get to your wounded calvary or immortals.
Highly specialized units can be utterly devestating if you can field them against foes they were designed for. However, versatiity makes the longevity of a unit much more appreciable, particularly if you have designs on upgrading a well promoted unit through the centuries.
Medic units are a must if you plan on carrying on a protracted fight in enemy territory. I often use a mounted unit as a mobile medic (and I rename them as a reminder when I do), who can speed around, comparably, and join stacks of wounded units to speed their ability to press the enemy.
Also, don't be afraid to expend several seige units during the course of a battle to take a city. A couple seige units can save the lives, or notably reduce the attrition, of your assaulting melee or gunpowder units. It is far better to lose 1-2 seige units than many more of your regular army. Even further, a well promoted seige weapon can seriously reduce the amount of time it takes to wrap up a battle, especially against a strongly defended city. They can also stump an AI (or possibly PC) landing party on your own territory by wandering out and causing damage to the well stacked invaders. Of all your unit types, you should have several of them available and consider them expendable at all times appropriate.
You might also consider renaming your more experienced units so it serves as a ready reminder. The last thing you want to do is throw away such hardened units in losing battles--use your green fodder or aging and less than ideal units for any such occasion, if you must. Keep those hardened units available for key opportunities when hitting the enemy really counts, and will make a difference for the battles and the war to come. It also makes it easier to figure out which units you will want to upgrade as time passes, and which you will simply replace with fresh recruits.
When possible, I rename my more experienced units to "elite guard" or simply "warmonger", and move them into situations that will help yield them more experience without undue risk, only exposing them to the more serious threats when I really need to kick some heads in. You'll find these specially designated units to become your war's bread and butter, bringing home the key victories when you really need them.
Finally, depending on my gameplay (turtled castle/culture or warmonger...or something in between), I tend to leave only 2 or 3 defenders in any city of mine while spreading out stacks of my more aggressive forces at key locations, enabling them to move toward invaders or to be identified easily when I'm figuring out my own invasions.
Desert locations seem to be good areas, as one example, since they are never developed and therefore make it easy to see your waiting army.
In Summary
I'm not sure the above combat mechanic overview is 100% accurate as it is based on some simple mucking about in the WBS. Any further information some of you may have would be useful, to be sure.
It appears that the first and to some extent second promotions to a unit do not yield that great of an impact. Obviously additional promotions beyond that are when you can really start to see the effect of truly hardened/trained units on the battlefield. For example, the Combat I promotion, while still better than none, really only modifies the chance of success against an equal unit by about 2.5% (actually slightly less). Even still, that small advantage is actually more than it sounds due to the fact that several key mechanics (namely damage, and therefore the number of strikes required to kill an enemy unit) appear to be affected.
Anyhow, hopefully someone found the above useful. So far I've had pretty strong success with my warring strategies (I've played Tokugawa an awful lot, for example) and am now trying to work on more diplomatic and cultural styled victories in an attempt to hone my game before I move into higher difficulties (I've played Noble almost exclusively so far, just a couple at Prince or whatever the next step up is). Still, I'm open ears to any other combat related tips you might be able to offer up!
1) Hit Points:
All units in the game have a base 100 "hit points" (well, all the units I've looked at so far...admittedly I didn't check sea going units but I have no reason to think differently for them).
2) Chance of Success:
When a unit attacks another unit a base percentage value is generated between it and the defending unit. For example, a warrior vs. warrior (unpromoted, 2.0 vs 2.0) has a 50% chance of success.
2a) Rounding:
From what I can tell, all the combat success values (or any from the resulting calculations used to determine the victor) are rounded down.
For example, a warrior with the Combat I promtion vs. a normal unpromoted warrior (2.2 vs 2.0) generates a 52.3805% chance which is rounded down to 52.3%
3) Base Damage:
A unit does a base 20 damage, per hit, against an equal unmodified defender (and the defender does the same).
4) Chance Modifiers:
The "success chance" percentage (from above) modifies a units chance to hit and the amount of damage.
5) Combat Rounds:
Essentially a series of combat rounds occur between two units. Each time a random percentile "die" is rolled (1 to 100) and is compared to the success chance determined from above.
5a) To-Hit:
Either one unit or another attempt to hit in any round and will do damage on any round of combat in which they succeed. Effectively the chance to hit uses the "success chance" from above, as far as I can tell. However, I suspect that there is some other unseen factor in play as well that alters the results when a unit from one era fights another. I haven't quite confirmed this but I'm looking at it more to see.
5b) Damage Modifier:
I haven't quite figured out how the damage modifier is determined but I think it is akin too: the percent difference from 50 *2.
For example, a warrior (unpromoted, unmodified) vs. an archer (unpromoted, unmodified) produces a 60% chance of success for the defender. The damage modifier appears to be (60-50)*2, rounded down. In this case, a 20% modifier.
The damage modifier is applied to both the attacker and defender, according to the positive or negative value that results for them. From the above example, the archer would do +20% from the base 20, or 24 damage per hit, and the warrior would do -20%, or 16 per hit.
The result is that the archer needs to land 5 hits (24*5 > 100) and the warrior needs 7 hits.
6) First Strike:
First strike attempts can miss, like any attack. However, they present a very real opportunity to kill an opponent quickly since it can front load 1 or more hits before the opponent gets an opportunity for a first swing.
If nothing else, it can reduce attrition to troops who have a successful run of first strikes, or at least increase attrition to enemy troops even if the battle fails. As a result, it might be ideal to use first strike promotions when you face superior forces that you need to have extra opportunities to hit before your own unit dies...reducing their health for further attackers. It might also serve as a decent way to increase survivability of seige units used for collateral damage, against equal and particularly lesser foes
7) Field Modifiers:
The general modifiers, be they promotions or "field" related (such as being on a hill, fortified, etc.) are additive. That is, if you have the Combat I promotion and are fully fortified, the total modifier is +35%.
8) Defender Selection:
Any time a stack of defender is attacked, the best-fit defender vs. the attacker is always selected for the combat. This is why combined arms is ideal, such as having a spearman as escort with a stack of axemen/swordsmen to counter mounted harry attacks against the group. And yes, it does mention this in the manual

General Combat Observations and Tips
All in all, familiarity and the ability to create situations in which you can stack several bonuses is the key to quick and efficient battles. Using units in a manner that suits their capabilities is also important, such as avoiding the use of mounted troops over slower melee units (combined with seige weapons) to assault cities, and instead, using the mounted troops to move deep into enemy territory, pillaging key resources and hampering enemy reinforcements moving to the main battle.
Overlooking certain promotion types can seriously detract from your ability to carry the battle well to the enemy, especially when the odds are against you. To the contrary, if you are strong and can afford to specialize your force directly against a known objective, by all means you should increase your strength with choice promotions for units playing very particular roles.
Having said that, the Combat I+ promotion should be seen as a "general" promotion, when you are uncertain what enemy types the promoting unit will be facing in the future or when the unit has already been specialized against a particular unit type and is looking to maximize combat effectiveness.
First Strike promotions can be very effective for both offensive and defensive ranged attack unit types (crossbows, archers, etc.) and flanking is most useful for mounted escorts who have other defenders they can retreat into when a battle turns against them. Be sure to leave a few strong/healthy defenders in the stack that make the enemy wary of trying to get to your wounded calvary or immortals.
Highly specialized units can be utterly devestating if you can field them against foes they were designed for. However, versatiity makes the longevity of a unit much more appreciable, particularly if you have designs on upgrading a well promoted unit through the centuries.
Medic units are a must if you plan on carrying on a protracted fight in enemy territory. I often use a mounted unit as a mobile medic (and I rename them as a reminder when I do), who can speed around, comparably, and join stacks of wounded units to speed their ability to press the enemy.
Also, don't be afraid to expend several seige units during the course of a battle to take a city. A couple seige units can save the lives, or notably reduce the attrition, of your assaulting melee or gunpowder units. It is far better to lose 1-2 seige units than many more of your regular army. Even further, a well promoted seige weapon can seriously reduce the amount of time it takes to wrap up a battle, especially against a strongly defended city. They can also stump an AI (or possibly PC) landing party on your own territory by wandering out and causing damage to the well stacked invaders. Of all your unit types, you should have several of them available and consider them expendable at all times appropriate.
You might also consider renaming your more experienced units so it serves as a ready reminder. The last thing you want to do is throw away such hardened units in losing battles--use your green fodder or aging and less than ideal units for any such occasion, if you must. Keep those hardened units available for key opportunities when hitting the enemy really counts, and will make a difference for the battles and the war to come. It also makes it easier to figure out which units you will want to upgrade as time passes, and which you will simply replace with fresh recruits.
When possible, I rename my more experienced units to "elite guard" or simply "warmonger", and move them into situations that will help yield them more experience without undue risk, only exposing them to the more serious threats when I really need to kick some heads in. You'll find these specially designated units to become your war's bread and butter, bringing home the key victories when you really need them.
Finally, depending on my gameplay (turtled castle/culture or warmonger...or something in between), I tend to leave only 2 or 3 defenders in any city of mine while spreading out stacks of my more aggressive forces at key locations, enabling them to move toward invaders or to be identified easily when I'm figuring out my own invasions.
Desert locations seem to be good areas, as one example, since they are never developed and therefore make it easy to see your waiting army.
In Summary
I'm not sure the above combat mechanic overview is 100% accurate as it is based on some simple mucking about in the WBS. Any further information some of you may have would be useful, to be sure.
It appears that the first and to some extent second promotions to a unit do not yield that great of an impact. Obviously additional promotions beyond that are when you can really start to see the effect of truly hardened/trained units on the battlefield. For example, the Combat I promotion, while still better than none, really only modifies the chance of success against an equal unit by about 2.5% (actually slightly less). Even still, that small advantage is actually more than it sounds due to the fact that several key mechanics (namely damage, and therefore the number of strikes required to kill an enemy unit) appear to be affected.
Anyhow, hopefully someone found the above useful. So far I've had pretty strong success with my warring strategies (I've played Tokugawa an awful lot, for example) and am now trying to work on more diplomatic and cultural styled victories in an attempt to hone my game before I move into higher difficulties (I've played Noble almost exclusively so far, just a couple at Prince or whatever the next step up is). Still, I'm open ears to any other combat related tips you might be able to offer up!
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