If you present such cases (20% on attacker vs. -20% on defender) make it more clear for unexperienced readers that you only do it for illustrating, in practice the comparable CR unit would have -45% (CR2).
Back on topic, as Feyaria pointed out, promotions do not exist in a vacuum.
Later available promotions (and those that are not like CR for gunpowder after the uprgrade) are a huge factor.
I was a bit rushed with my previous posts so I was a lot less clear than I could/should have been. I used the CR1 and C2 praetorians because it was the easiest way I could think to get exactly equal bonuses but where one was applied to the attacker and where one was subtracted from the defender. It was not meant to serve as any sort of comparison for the two promotions - just to illustrate the effect of where the bonus gets applied.
10% increase to the attacker is equivalent to -9.09% (-1/11) to the defender in this case.
2.2 / 1 = 2.2
2 / 0.909 = 2.2
Like Oyzar pointed out, it's the ratio that determines combat odds, not the absolute difference.
Agreed. Oyzar already pointed it out and I agreed. However it is more complicated than examples like yours suggest.
First define what you mean by a term before you use it. What is this R value? Is it the ratio between attacker and defender?
If you look at promotion by a case by case basis then combat will be worse except when you are attacking a defender with very strong defensive bonuses. For example where combat frequently outpreform CR or counter promos are during amphibious assults. Here it is not uncommon for the defender to get up to 200%+ defensive bonus. When fighting a war from boats you'll hardly ever want to pick up counter promos(or even CR if that is an option).
R = attacker's modified strength over defender's modified strength. Essentially it's the one ratio that determines everything for combat except damage per hit which can also be affected by unit damage. Of course, number of hits to kill is the other thing affected by unit damage.
The reason it's good to use R is that it's just the ratio of the two numbers that are actually presented to you on screen. On screen you are given the attacker's and defenders modified strengths, whether you use the game's odds display or the one in Advanced Combat Odds.
simple explanation:
Combat usually has better odds than the drill line does. Drill allows you to get XP quicker, is resistant to siege damage, and has better odds when defending against weaker/disadvantaged units successively.
I have a question for piece of mind; do you know if the ingame combat odds are correct for units with a lot of first strikes? It feels to me that they aren't.
The game combat odds are correct to good accuracy for all combat except rare cases of using siege units to attack. Drill promotions work absolutely correctly but because of the way they alter combat they give very different statistics to what other promotions give. Think what happens if I tell yold you the average age of civfanatics was 18 and the average age of Grade 12 students was 18. Both may be correct but civfanatics would have a wider spread of ages compared with the grade 12s, and so a single statistic - the mean - only gives you a little bit of information. A single combat odds statistic is a bit the same way - it only gives you a little bit of information and not the whole story of how the combat is likely to turn out. Drill units tend to "spread" the results more - unit is both more likely to die and more likely to survive with high health compared with using combat. Using combat is more likely to usually give the average HP result which might be 70HP or so. Using drill you might get half with 12HP and half with 100HP - it depends.
Back to my point about the effect of high base strength on choice of promotions for attackers...
Now oyzar has pointed out that the good use of combat promotions on attackers is due to defender having high number of defensive bonuses and nothing to do with the base strength of the attacker. I agree with that partly. The fact is, a high base strength unit is more likely to be able to use a combat promo to overcome one of the jump points using combat promos than a lower strength unit.
In the following picture example, the praetorian will get an additional 0.8 each time he uses a combat promo, and the archer would lose 0.3 each time he got an extra 10% defense. For the swordsman, it's 0.6 per combat promo and again 0.3 each time the defending archer gets another 10% defense. So if one of the attackers is in a situation where he is very close to a jump point like the significant R=1 jump point (R = 1 is when attacker's modified strength equals the defender's modified strength) then taking pretty much any promotion will drastically improve the odds.
Spoiler :
NOTE: 1 small correction. In the box on the right where I have said the archer's modified strength is 7.95, it should be 8.55
Because the praetorian's strength is closer to the defender's modified strength, using the combat promo (or the CR promo) sends him over the jump point and gives him cosiderably better odds, but not so for the weaker swordsman.
Interestingly, if you give the archers another +5% fortify, the CR on the praet is not enough to send his strength through the jump point and will only have 37% odds. If he takes C1 in that situation he'll have 63% odds.
Now the R=1 case is usually the most extreme jump point so any promotion that takes the ratio through 1 (in the attacker's favour of course) is always going to be an effective promotion. I would contend that this happens more often for higher base strength attackers than lower base strength attackers when using combat promos due to the simple fact that it is adding on a greater piece of strength each time.
There are other jump points which are less obvious to spot because their effects are smaller, but they are there, and again higher base strength units are more likely to be able to use combat promos to send themselves over those points.
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Let me give a couple more examples. I'll try to be as clear as possible this time...
Suppose there is a defender with base strength 8 and tile defense 50%, so total modified strength is 12.
Let us compare two possible attackers - a cataphract (str12) and a praetorian (str8). Assume the praetorian already has an attack bonus of 50% for that battle.
So we have cataphract v defender as 12 vs. 12, and the praet vs defender is 8 vs. 8. So both units have exactly 50% odds.
Now, as oyzar would correctly point out, using combat 1 on either of these attackers leads to exactly the same effect: 13.2 vs. 12 (for R = 1.1) for the cataphract, and 8.8 vs. 8 (also R=1.1) for the praetorian.
So it would seem the combat promo does just as well on either unit right? Well, technically yes but not compared with other promos they could take.
What happens if we give each of the attacker's a +25% ordinary bonus instead of the combat promo. Then we have 12 vs. 10 for the cataphract giving R=1.2, and we get 8 vs. 6.4 for the praetorian giving R = 1.25. So the weaker base strength unit comparitively benefits more from a non-combat promo. The higher base strength unit has his other promotions having a weaker effect and so indirectly making his combat promo seem better.
Is the effect here only because R is close to 1? Let's try the same example but with R as 2/3 or 0.67.
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Defender base strength 9 (a musket for example). Attacker's are cataphract and pikeman. This time the defender has +100% vs. the cataphract but not the pike. So the ratios come from 12:18 and 6:9. (Both are R=2/3).
Both attackers start with odds 9.94%. Giving both attackers combat 1 leads them both to get odds of 20.91% (as predicted by oyzar).
But giving each of them a +25% vs defender bonus (eg. Pinch promotion), the numbers change...
Cataphract gets 22.66% vs. the defener. The pike gets 27.23% vs. the defender. This again means the higher base strength attacker does comparitively better by using a combat promo than using an ordinary counter-flavoured promo.
This example is interesting because the battle where the defender has more defensive bonuses is the battle where the combat promo is the least effective. This goes against the intuition oyzar suggested.
I am fairly certain the real explanation here is that combat just works better on higher base strength attackers than it does for lower base strength attackers when compared with alternative promotions like city raider, pinch etc.
This is why I sometimes dish out the advice that combat promos work better on higher base strength units. It would be more correct of me to say counter-type promos work less effectively on higher base strength units and so combat promotions look better. Perhaps most importantly, the combat promotion obviously has the advatange of being general so if you are attacking a city where the defender could change based on what promo you take, taking the combat promo will often be more effective than taking a specific-counter promo.
I still would argue, for example, that using combat instead of CR on praetorians is a far more effective strategy when compared with doing the same thing on swordsmen. The extra defensive ability of the praet vs. any type of unit is valuable, and the reason it works better for praetorians is their higher base strength.