Promotion: general or specific?

[snepp]

Sorry snepp, you're exactly right.

I was reading 5:3/1.5 as (5:3)/1.5 and thought ":3" was a typo.

Both formulas are equivalent when the defender's bonus is 0, aren't they.

That's what I get for cramming things together and not spacing them out. As for the formulas, everything is straight forward and easy to see as long as the defender does not have a negative bonus applied, which is what inevitably causes all the confusion.

 

[Heroes]

Finally figured this out

If the defender's bonus is higher than the attacker's bonus, the effect of the 10% bonus from combat 1 is the same as (100+d)/11.

(again d is the defender's bonus).

With a 10% defender bonus: combat 1 is equivalent to a +10% specific promotion.

With a 25% defender bonus: combat 1 is equivalent to +11%.

With a 50% defender bonus: combat 1 is equivalent to +13%.

With a 75% defender bonus: combat 1 is equivalent to +16%.

With a 100% defender bonus: combat 1 is equivalent to +18%.

Mathematically, it's comparing (1+a)/(1+d) and 1/(1+d-b), where a is the combat promotion bonus, d is total defensive bonus, b is specific promotion bonus. This is assuming d-b>=0, which is in most cases true. To make the 2 things equal, we get (1+a)(1+d-b)=1+d, therefore a(1+d)=(1+a)b, b=a(1+d)/(1+a), or b/a=(1+d)/(1+a). So, the bigger d is, the bigger we need b/a to make specific promotion better. In another word, the smaller d is, the more profitable is specific promotion.

When to begin assign drill promotion (first strike)? I guess it should be after making sure you get a large enough R, then you mainly care about remaining health. As you show, a first strike helps more than combat 1 when R=1.1, but that's because 1.21 from 1.1 doesn't make a jump. And if the defender gets combat 1 rather than drill 1, he will make R=1, thus turn the tide. Before getting large R, I guess it's still wise to add more strength than first strike.

-- The above are copied from my post in Arathorn's thread. And your data are exactly equivalent to mine.

 

[Heroes]

It could be a good idea to assign city raider 1-3 to melee units, then upgrade them to gunpowder units. The reason is gunpowder units can't gain city raider.