Amount of artillery to bring?

[VoiceOfUnreason]

Anybody done the math yet on how promotions change survivability of siege units?

OK - I just ran a bunch of world builder experiments, concentrating on catapults versus longbows in cities.

First, a reminder that combat odds aren't what you would expect, because they are based on integer math and small numbers. As a result, you end up with assorted discontinuities ("jump points") when you make what seem like small changes to the inputs.

Also, the law of diminishing returns starts kicking in as you get further from equality. Catapults have a lower strength than longbows to begin with, and on top of that the longbows are pulling in a bunch of defensive bonuses. An unpromoted longbow fortified in a city on a hill has 100% bonus; a CG II longbow fortified on a plains city has 95% bonus.

And that's just about the neighborhood where your two catapult promotions stop making a difference.

The level 3 line assumes CR I + CRII, clearly the best choices for this sort of situation. Yet that only gives you 7% better survival (plus some extra damage on the longbow). By contrast, a level 3 maceman sees his chances for survival improve by about 17% (plus the improved damage).

Note: both of these lines, in real life, have the same shape - the red line is just the blue line shifted 45% to the right. It doesn't quite look that way because of sampling error and excel doing the best it can with the data available.

Now, after you've cracked the top defender, so that you are now facing partially taxed longbows, the math changes a bit. And if the terrain is flat, there's a nice jump point that a CR II catapult can take advantage of.

My basic concern here is that catapults just don't get enough leverage out of that promotion - the bonuses they get are multiplying on a weaker base. You just aren't getting as much oomph from your 6 promoted catapults as you would get from your four promoted swordsmen.


Did we choose the wrong promotion? Not really - Drill is a complete joke; it's nature is such that you get screwed by the same jump points as an unpromoted unit. The combat line is an option if you are meeting stacks in the field, but not so much for city work.

And the barrage line does nothing of interest, thanks to the fickleness of integer math.

 

[zienth]

The level 3 line assumes CR I + CRII, clearly the best choices for this sort of situation. Yet that only gives you 7% better survival (plus some extra damage on the longbow). By contrast, a level 3 maceman sees his chances for survival improve by about 17% (plus the improved damage).

But that extra damage on the longbow is critical. How much better are the second catapult's chances against that damaged longbow? The first cat has a few percent chance, but the extra damage he does because of the CRII lets the second cat have maybe a 25% chance. And the damage he does gives the third cat somewhere around 50%, and after that one it's all good. The percentages are just ballpark of what I typically see, and your mileage will vary depending on the fickleness of the RNG, but you should see something similar most of the time.

Take a stack of 4 CRII cats in WB and send them against a few longbows and see how many cats survive and how strong the longbows are afterwards. Then do the same with unpromoted cats, and barrageII cats. I'm not certain, but I'd be willing to bet that the CRII cats have more survivors and leave weaker defenders (especially the strongest defender).

Zienth

 

[axident]

VoU, he of the xml-delving, thanks.

I concur with the above poster. How many times have we been in a situation where a cat has only CR-I or something and barely scratches--or doesn't even scratch--a heavily-promoted longbow on hilltop?

Personally I almost never use cats vs. longbows if I can help it, just because I hate all the war weariness and wasted hammers from dead cats. Trebs come soon after longbows and I would expect CR-promoted trebs to have a better graph.

 

[Sjaramei]

Tried against protective Civs with CG2/3?

I've started suiciding Drill 2 Cats against them since they are much more likely getting some damage off on a very strong defender.(First strikes are annoying ) A mix of Drill/Barrage Cats at the start then mopping up with CR Cats seems to work best for me. (Sometimes using a heavy promoted attacker to take out a strong defender in between. CR3+C1 Pref)

 

[VoiceOfUnreason]

But that extra damage on the longbow is critical. How much better are the second catapult's chances against that damaged longbow? The first cat has a few percent chance, but the extra damage he does because of the CRII lets the second cat have maybe a 25% chance. And the damage he does gives the third cat somewhere around 50%, and after that one it's all good. The percentages are just ballpark of what I typically see

The extra damage isn't so critical as you suppose, for the simple reason that the the combat algorithm selects the best defender. No matter how strong your first catapult is, the second attack is going to be against a longbow with no fewer than 91 HP. At that point, the CRII promotion improves the survival chance of the second catapult by 8.1% (assumptions: 95% defense bonus for both longbows).


Now, you can make the model much more complicated by weakening the second defender. If the second longbow has only a CG I promotion, now there's a possibility of shifting the odds considerably - because your ability to get at that defender is directly dependent on how much damage you do to the top defender. To make that happen, you need to inflict about 18 points of damage to the top longbow.

Take a stack of 4 CRII cats in WB and send them against a few longbows and see how many cats survive and how strong the longbows are afterwards. Then do the same with unpromoted cats, and barrageII cats. I'm not certain, but I'd be willing to bet that the CRII cats have more survivors and leave weaker defenders

Really going out on a limb there.

Of course the promoted catapults get better math. That's not in question, but it is the wrong question.

Opportunity cost - if you military center is pumping out elite catapults, then it's not pumping out elite something-elses. The choice you actually face is which units get the promotions.

ie - are you better off with 6 elite catapults and 4 swordsmen, or 4 elite swordsmen and 6 catapults? Note that this question differs from "am I better off with a barracks and N promoted catapults or with N+1 unpromoted catapults?"

 

[UncleJJ]

Really going out on a limb there.

Of course the promoted catapults get better math. That's not in question, but it is the wrong question.

I don't think he is. It is a valid question for me in my games. I often wonder if it would be better to go to war now (early) or to wait a few turns for some critical tech. In this case it might be Feudalism or Theocracy to give 2 exp for my catapults.

Opportunity cost - if you military center is pumping out elite catapults, then it's not pumping out elite something-elses. The choice you actually face is which units get the promotions.

ie - are you better off with 6 elite catapults and 4 swordsmen, or 4 elite swordsmen and 6 catapults? Note that this question differs from "am I better off with a barracks and N promoted catapults or with N+1 unpromoted catapults?"

I think we want to know if it is worth switching civics to either Vassalage or Theocracy (or both) to get better catapults against certain types of defender (say Protective longbows). If we're Spiritual it is likely a very good move but if we're not then a valid question is - is it worth losing 2 turns of anarchy switching into and out of the war civic? That is another sort of opportunity cost associated with this problem. Incidently, I find it is somewhat unlikely that I have done enough fighting before the first war with catapults to even get a GG. My first axe rush will get some exp but not enough for a GG. But after this war I expect to get one or even two GGs and that is why I'm particularly interested in getting my catapults to survive some combats and contribute a few GG points

So I think we need to know whether a stack of catapults such as zienth has described will do better with the various sorts of promotion. That question is probably best answered by a small simulation in the WB with say 10 runs with each condition and averaging the results and noting any exceptional outcomes (like all catapults retreating). As VoU is suggesting (I think) an analytical model will soon get very complex trying to deal with the muliplicity of possible outcomes.

 

[VoiceOfUnreason]

If what you are interested in investigating is the value of an extra promotion, take the chart I posted and mentally add a third curve between the two I plotted (ie, take the red curve and shift it 25 units to the left).

So a level 2 catapult is looking at a 21% survival chance when the longbow's bonus is 50% (fortified in a flat city), and falls sharply just after that. Against a CGI longbow fortified in a flat city, the survival odds are about 8%.

Yeah, I really should have plotted survivability against the net defensive bonus.

 

[VoiceOfUnreason]

Yeah, I really should have plotted survivability against the net defensive bonus.