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alexman
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Hunt Valley, MD
Jan 1970
time: 00:32
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quote:
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.
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Dominae
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B: Yes. Others: No.
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nbarclay
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Huntsville, Alabama
Dec 1999
time: 23:32
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quote:
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
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alexman
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Hunt Valley, MD
Jan 1970
time: 00:32
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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.
Last edited by alexman on 17-01-2004 at 03:37
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nbarclay
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Huntsville, Alabama
Dec 1999
time: 23:32
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quote:
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.
Last edited by nbarclay on 17-01-2004 at 05:26
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nbarclay
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Huntsville, Alabama
Dec 1999
time: 23:32
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quote:
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
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alexman
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Hunt Valley, MD
Jan 1970
time: 00:32
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quote:
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.
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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.
quote:
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.
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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.
quote:
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
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Dominae
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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
Last edited by Dominae on 21-01-2004 at 20:28
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donZappo
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quote:
Originally posted by Dominae
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 |
I'll agree with that! Especially since the game won't (hopefully!) end at cavalry anymore this could become a large issue.
-donZappo
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nbarclay
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Huntsville, Alabama
Dec 1999
time: 23:32
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quote:
Originally posted by alexman
By the way, how does Artillery seem, now that we have a little more experience with the new ground unit bombardment? Too powerful, or in line with air power? |
In a recent game, I made very extensive use of both artillery and bombers. I had a big enough tech lead that I didn't have to worry about having my bombers shot down, so both types of units were able to attack with impunity.
Against targets out in the open, bombers worked wonderfully. Comparing the stats, bombers have the same bombardment attack value as artillery but their rate of fire is one higher. (And since I wasn't playing with the AU Mod, bombers could kill.)
Bombers could also kill AI ships in places that artillery couldn't even reach. That is definitely a nice advantage.
Against cities, bombers have both advantages and disadvantages. Bombers have a longer reach than artillery do, so where artillery usually have to spend every other turn repositioning to get in range to fire (and sometimes two turns repositioning), bombers have to waste a turn only when the front has advanced enough to take them out of range. On the other hand, the new "target units first" algorithm does not apply to bombers. Bombers often destroy buildings and kill civilians instead of damaging enemy units. (At least that was true with the 1.12 patch, and I've seen no indication that it's been changed since.) If a player wants to knock a metropolis down to a city to reduce the effective value of its defendes, bombers are useful, but since I more typically want to take cities intact, I find it highly annoying. Further, unless bombers reduce a city's size enough to undercut its defense bonus, the attacks that don't hit units are wasted. Mostly, I used bombers against cities only when it let me attack them sooner than I could have using artillery (either because it would have taken two turns to move artillery into position or because all my artillery were busy elsewhere).
Bombers operating out of captured enemy cities face an additional risk in that a culture flip could cost a player an entire huge stack of them. That didn't actually happen to me in my game, but it was something I had to worry about a bit (and I tended to keep more units in cities with bombers than I would have otherwise to help reduce the risk of flipping). I don't know whether that risk could be countered by spending workers to build airbases or whether an airbase that suddenly found itself within enemy cultural borders after a flip would be destroyed and all its bombers with it. If bombers at airbases that find themselves within enemy borders after a culture flip would be destroyed, the only really safe option for a player in a weak cultural position (short of having truly massive numbers of units sit around as MPs) would be to bring settlers along and build cities in between captured AI cities to serve as airbases. That would be a bit messy and would add to the cost of bomber operations. (Also note that under Communism that late in the game, the loose city build pattern AIs favor can actually be a very good thing since fewer, larger cities mean less corruption.)
Another drawback to bombers, one that I didn't face in that particular game but which players often would face overall, is that bombers can be shot down. In contrast, properly protected artillery face no real danger of being killed when they are used. Thus, once enemies have a significant ability to shoot down bombers (which they may or may not have when the human player first gets bombers, depending on the status of the tech race), the balance of advantage shifts a bit more in favor of artillery.
All in all, I think the balance between bombers and artillery is good enough that no change is really needed purely from that perspective. On the other hand, artillery provide a powerful bombardment capability quite a few techs before bombers (and with enemies more likely to be still using riflemen), which has nasty implications for the AIs. Artillery/cavalry stacks with appropriate defensive support can eat up territory against riflemen with very few losses, as can artillery/tank stacks against infantry (and artillery can be built before tanks so artillery production need not compete with tank production the way bomber production almost inevitably does).
Reducing the bombardment strength of artillery from 12 to 10 would undercut the power of such tactics a bit (and thus help the AIs), and I don't think it would make the choice of how much to use artillery and how much to use bombers less interesting than it is currently in the AU Mod. Compared with cannons, artillery would still have a slightly higher bombardment strength, and their longer range and higher rate of fire would easily justify their cost. (For offensive use, artillery often have to spend only half the time repositioning that cannons need, and being able to attack every two or three turns instead of every three or four is a huge advantage all by itself.) So I see no risk of balance problems between artillery and cannons either.
Conclusion: I would support reducing the bombardment strength of artillery from 12 to 10. Yes, it would undercut a strategy I really enjoy using, but isn't that the idea? 
I also very strongly endorse the idea of having AIs never build bombardment land units. It seems to me that any losses that such units cause me are easily repaid and then some when I capture them and turn them against the AIs. Consider the fact that even if a trebuchet tips the balance between a MedInf's losing or winning, capturing the trebuchet repays all but five shields of the MedInf's value with our revised costs. And a lot of the time, the trebuchet's shot won't tip the balance, either because the trebuchet misses or because the extra hit point of damage to the attacking MedInf won't change the outcome of the battle.
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13-01-2004 10:02
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