AU mod: Balancing Ground Unit Bombardment

[Dominae]

Originally posted by alexman
After thinking some more about it, I'm a bit uncomfortable about strengthening the Cannon when ground bombard units have been given such a boost in C3C.

So here's a better solution IMHO:

Catapult costs 30 shields
Trebuchet costs 35 shields
No change to Cannon.

Then the Trebuchet is better than the Catapult for defenders of strength higher than 3.

Cannons are better than Catapults for defenders of strength higher than 4, and better than Trebuchets for a defender of strength higher than 6.

Since units are targeted first in sieges, Catapults should be well worth it, even at 30 shields, but the cost increase definitely helps the AI. What do you think?

I like it.

[alexman]

Originally posted by nbarclay
The question is, is the offensive use of catapults in C3C so powerful compared with other modes of combat that it needs to be toned down, or is it just powerful enough to be interesting and useful in some types of situations?

Consider a veteran swordsman attacking a fortified veteran spearman on grass. If the Swordsman wins, you count the HP damage to the spearman and move on the the next battle. If the Swordsman loses, you spend 30 more shields to replace him, and count the HP damage to the spearman. A combat calculator gives:

• Swordsman wins 55.7% of the time (4HP damage)
• Swordsman dies after 3HP damage to spear, 14.7% of the time
• Swordsman dies after 2HP damage to spear, 13.9% of the time
• Swordsman dies after 1HP damage to spear, 10.6% of the time
• Swordsman dies after 0HP damage to spear, 5% of the time

The expected damage to the spearman after one battle is therefore 3.053
The expected damage after n battles is 3.053n, and the expected loss of shields is 30 + (1-0.557)*30n = 30 + 13.29n

Now consider a catapult, which has a 59.7% chance of hitting a fortified spearman. The expected damage after n battles is 0.597n, and the expected shield loss is S, assuming the Catapult doesn't get captured.

In order for the damage per shield investment to be the same for the swordsman and the catapult, we want:
3.053n/(30+13.29n) = 0.597n/S
or n = 0.385S - 2.257

For S=20, n=5.4
For S=30, n=9.3

The break-even point of the Catapult in terms of damage per shield invested comes after 9 battles, when the shield cost of the Catapult is 30 shields. If you plan on doing any kind of fighting, 9 battles will surely be reached, especially given that catapults will live to get upgraded all the way to Radar Artillery.

Incidentally, the odds get better for the catapult when faced with tougher defenders. When you are facing a fortified spearmen with a 50% defensive bonus (city/walls/hills), the break-even point occurs at n=6.5 battles.

Given the above analysis, and considering that the Catapult cost increase favors the AI over the human, I think the 30 shield cost is just right.

[alexman]

Proposals under consideration:
A) No change
B) Catapult=30s, Trebuchet=35s
C) Trebuchet=25s, Cannon/Hwach'a=35s
D) Trebuchet=25s, Cannon/Hwach'a=70s/2ROF

Voting in a week, SoZ style

[Dominae]

B: Yes. Others: No.

[alexman]

The idea is to put the proposals in order of preference (in a week). See the last few posts in the main AU mod thread thread.

[nbarclay]

Originally posted by alexman

The break-even point of the Catapult in terms of damage per shield invested comes after 9 battles, when the shield cost of the Catapult is 30 shields. If you plan on doing any kind of fighting, 9 battles will surely be reached, especially given that catapults will live to get upgraded all the way to Radar Artillery.

There are at least three important elements that you have forgotten to factor into this calculation.

(1) There is the fact that if you take extra time to build catapults before launching a war, you are also giving your enemies more time to build additional cities and to build up their own military. Thus, the number of units that you will have to face in combat will almost certainly be higher if you wait until you have a significant catapult force to start fighting.

(2) There is opportunity cost, which takes at least two forms. First, if you capture enemy cities later because you waited to build catapults, you lose the shields that those cities would have produced during the extra turns in your posession. Note that if that delays building courthouses, there is an additional opportunity cost later from getting the extra shields from the courhouse later. Similarly, delayed libraries, marketplaces, and so forth have their own cost in gold, shields, and in some cases culture. And second, if the catapults don't pay for themselves in the initial fighting, there is an opportunity cost of diverting core cities away from investing in city improvements longer, delaying libraries, marketplaces, and so forth in those cities. Since city improvements are often built back to back, delaying one improvement delays every improvement after that.

(3) For a Republic, the cost of maintaining a catapult from the ancient era all the way to the mid industrial era is quite high. Further, that cost is also subject to an opportunity cost - gold used for catapult upkeep cannot be invested for research or for rush-building buildings as an investment in getting more gold and shields.

Put those factors together and the only time offensive catapults would seem to make much sense at 30 shields is when fighting a string of ancient wars (for example, a strategy revolving around oscillating warfare and tech extortion). And even then, waiting for catapults would be a bit questionable because it would involve waiting longer to start the process. If your analysis that the break-even point is nine battles is accurate, I think 30 shields is too high a cost.

Nathan

[alexman]

But the attack doesn't need to start later!
Here's an example:

A typical attack might start with, say, 16 Swordsmen and a few Spearmen. You estimate that you have to have that many to sustain the offensive, even though you plan to replace some of your Swordsmen as they die. At the end, because losses came faster than replacements, you are left with 8 Swordsmen.

If you build 6 Swordsmen and 10 Catapults instead, and the war lasts for at least 6-9 battles per unit, you will probably be able to kill more bad guys with that 480-shield investment, or for the same number of bad guys killed, you will lose fewer Swordsmen. Your replacements might even keep up with your losses, so you can sustain the attack for longer. And the attack doesn't need to start later.

Obviously, there are cases where it's better to build Swordsmen: you have extra cash to upgrade Warriors, or you prefer a higher-risk, small-stack attack for example. But that's what makes it interesting.

[nbarclay]

Originally posted by alexman
But the attack doesn't need to start later!
Here's an example:

A typical attack might start with, say, 16 Swordsmen and a few Spearmen. You estimate that you have to have that many to sustain the offensive, even though you plan to replace some of your Swordsmen as they die.

Doesn't happen. If I'm going to attack early, I'm going to do it long before I have 16 swordsmen (unless they're upgraded from warriors) and I'm going to count on new unit builds to replace losses in a reasonably timely manner. Edit: More precisely, if you can sustain an attack with 10 cats and 6 swordsmen, you can probably sustain one reasonably well starting with 10 swordsmen, maybe even a little less, and no cats considering the fact that each city you take leaves the AI weaker.

[nbarclay]

By the way, I'll grant that my thinking is influenced by the fact that I pretty much never fight ancient wars unless either I have a good ancient offensive UU or I can't REX enough to build a lead without fighting. Against a more distant foe, fighting later with larger forces would make more sense if you're going to fight at all, but devaluing catapults makes the kinds of wars where catapults are most useful less worth fighting.

Thinking some more, it is often possible to get at least some cat support without seriously compromising the number of offensive units by having one or more cities forego a barracks in order to build cats earlier. How much difference that would make, I'm not sure.

On the other hand, catapults require an additional tech - Mathematics - before you can even start building them. If the cost/benefit ratio of cat-based military tactics is marginal compared with alternative tactics, that gives players a lot less incentive to make Mathematics a priority.

Nathan

[nbarclay]

How would it work to have

catapult=25
trebuchet=30
cannon/hwacha=40?

An option might be to increase the bombard for cannons and hwachas to 9 instead of 8 if trebuchets would end up too much of a better deal than bombard-8 cannons.

[alexman]

So I think we have agreed that Catapults are useful at cost 30, as long as you have a certain number of Swordsmen to go with them. Depending on your play style this number varies considerably, but at least a couple of Catapults should always be worth it. That's OK with me. Catapults are not supposed to be the main unit in your army anyway, especially since the AI doesn't know how to do that.

By the way, at strength 8, Cannons are always worse than Trebuchets. At strength 9, Cannons are worse than Trebuchets for defenders less than strength 18.

[nbarclay]

Originally posted by alexman
So I think we have agreed that Catapults are useful at cost 30, as long as you have a certain number of Swordsmen to go with them. Depending on your play style this number varies considerably, but at least a couple of Catapults should always be worth it.

"Worth it" is a very different thing from "possible." Building two cats instead of a barracks and a swordsman, or instead of barracks in two towns to build swordsmen later, provides catapult support up front but reduces the number of swordsman reinforcements over time. That could cause an attack using cats to stall where one using purely swordsmen would not, or to stall earlier than an attack using purely swordsmen would. Foregoing barracks in favor of cats would make excellent sense if a player is sure other towns that do have barracks can produce an adequate supply of swordsmen, but could be rather problematical otherwise.

Of course this assumes the player even has Mathematics to build cats at the time he is preparing his attack. One of the biggest problems with weakening cats is that it reduces the incentive to research (or otherwise obtain) Mathematics early and to delay an offensive until after getting Mathematics and building some cats. If we make the advantage of using cats in an early offensive only marginal, an interesting strategic issue from the default rules becomes a good bit less interesting. (If people who have more experience with ancient warfare than I do think I'm wrong, please let us know; my esperience is somewhat limited in this area.)

Further, the idea that cats can still be useful at cost 30 does not, in my view, even come close to justifying raising the cost that high. In my view, increasing the cost can be justified only if, and only to the extent that, heavy offensive use of catapults under the default rules is significantly overpowered compared with attack strategies that don't use them (or don't use them in any significant numbers). But right now, even granting that cats at cost 20 are probably too good in C3C, I'm inclined to think that a 50% increase in cost compared with the standard rules is overkill. I view that as too radical a change to be justified without compelling evidence that the "big stack of cats" strategy is a significant problem even with a less extreme cost increase.

Regarding cannons, increasing their attack value to whatever it takes to make their cost/benefit ratio a hair better than trebuchets against riflemen fortified in cities should not be unbalancing. The fact that cavalry are available at about the same time as cannons makes the risk of making cannons too powerful smaller than it would be otherwise.

Nathan

[alexman]

Originally posted by nbarclay

Building two cats instead of a barracks and a swordsman, or instead of barracks in two towns to build swordsmen later, provides catapult support up front but reduces the number of swordsman reinforcements over time.

You don't have to build a Catapult instead of a barracks. You can build one in a city with a barracks, or in a city that is never going to build Swordsmen anyway.

If you have enough Swordsmen, chances are that you won't use them all in your attack at any given moment. You just brought them along to ensure that you don't fall victim to an evil RNG roll. In that case, it's far better to bring Catapults instead of the extra Swordsmen. Unlike the extra Swordsmen, Catapults will all get used in each attack, so they will reduce your Swordsman losses (and don't forget the free shot on defense too). In this case 30-shield Catapults are very much worth it.

One of the biggest problems with weakening cats is that it reduces the incentive to research (or otherwise obtain) Mathematics early and to delay an offensive until after getting Mathematics and building some cats.

Yes, but what happens if you already have Mathematics? In the second half of the Ancient Age, you have Mathematics and the AI is stronger. Building some Catapults in that case is a no-brainer, even at cost 30.

But right now, even granting that cats at cost 20 are probably too good in C3C, I'm inclined to think that a 50% increase in cost compared with the standard rules is overkill.

I know that we disagree on this, and that's why we are going to have a vote. I happen to think that a 50% increase is justified because:
1) It still makes Catapults worth building, especially when you are facing strong opposition, or when you want low risk.
2) It helps balance Catapults relative to the other ground bomabrd units. Anything less than about 30 shields for Catapults, and we would have to increase the value of Cannons.
3) It helps the AI

[Myrddin]

Some thoughts on bombardment units

I agree artillery is very powerful at range 2- I was able to roll over AI cities with infantry defenders at Emperor with an artillery stack and cavalry - and should be reduced to range 1

There may be an argument for having light artillery at range 1 and introdusing heavy artillery with range 2 at say Mass Production but adding units is not in the spirit of the mod

Moving artillery from Replacable Parts to Steel might help with the ToE beeline. Most of the techs on the way to Replacable Parts will help you get ToE; not so for steel

[Dominae]

Here's my ranking (despite my dislike of the ranking method!):

1. B, Catapult=30s, Trebuchet=35s.
2. A, No change.
3. C, Trebuchet=25s, Cannon/Hwach'a=35s.
4. D, Trebuchet=25s, Cannon/Hwach'a=70s/2ROF.

What ever happened to Artillery? Just because the game "ends" with Cavalry does not mean Artillery is not the most unbalanced bombardment unit versus the AI.


Dominae