Firepower Thread - Conquest of Elysium 3

I wanted to be clear in my own mind what the different firepower available to shooters in the game was. The following two graphs show the results of a preliminary analysis:

A. Damage Per Turn for a sample of firing units, PER FIGURE, WHEN FIRING

B. Damager Per Turn for the same units, including the number of figures in a typical 50 Gold unit (5 archers, 4 longbows, 15 halflings, 7 Barbarians, etc) and divided by the firing rate (where applicable, i.e. Crossbows, Arbalests, etc).

The X axis shows the total defence of the target (Armor plus Fortification). Mostly this will be close to 0, but occasionally it will be higher when assaulting forts and the like. Dwarves defending mines will often have 3 armor, as will HI defending a City or Tower. Above that will not happen THAT often, but it can be arranged.

The Y axis is the number of HP caused PER FIGURE in the first graph, and PER UNIT / PER TURN AVERAGE in the second graph.

Note that this graph clearly underplays the strength of crossbows and Arbalests, because shooting every 2 or 3 turns isn't really as bad as dividing firepower by 2 or 3. They shoot in the first round, and that is the most important round, often deciding the result of the combat.

Examining the first chart:

- Halfling Slingers drop off 50% of their damage at Defence 1. At Defence 3, they do only 10% of their maximum damage.
- Halfling Crossbows by contrast have double the damage capacity of the slingers, and still do 37% of that at Defence 3 (or 7.5x more than the slingers).
- The story is similar but not quite as pronounced for Archers vs Longbows vs Crossbows.

And looking at the second chart, which takes into account the number of figures in the unit and the rate of fire:

- Halfling Crossbows and Slingers start out with the same DPT at Defence 0 (but remember the crossbows are actually doing DOUBLE this and then reloading for a turn, compared to firing twice). As Defence increases, crossbows immediately show their superiority. Conclusion: Never buy slingers, only Crossbows (get iron or trade for it).
- For human type troops, I think it is also sound to only ever buy crossbows. Although SLIGHTLY less damaging against unarmored troops on a Damage Per Turn (DPT) basis, the first shot does more damage, and that will more than compensate for the round of reloading. At Armor 1 the damage is equal, and at higher levels of Armor, Crossbows are markedly better.
- Arbalests are just an extension of that and terrific against heavily armored troops (in any case, they are all you can get as dwarves).

Note: I modelled die results to the 99.90% likelihood in order to come up with the damage numbers. One shot in a thousand was not modeled (but this one shot gives best result, rolling lots of maximum die rolls, and doing heaps more damage than normal).

Any thoughts?

I don't understand what formula are you using to calculate damage but it is inaccurate.
Halfing slingers have average damage 3 against 0 armor (1d2 open-ended)
avg = (1 + 2 + avg)/2 => avg = 3.

Just finished some simulations. I've done 10000 openended rolls for each damage/armour pair.
First graph - average result for one shot

second graph - average stack damage per turn

I was surprised by this results:
Halfings rule the world twice:)

Well, I am not surprised totally by the halflings ruling, their crossbowmen are awesome. But NOT their slingers.

So I say the Halfling slinger averages 2 per shot and you say it is 3. That is quite a difference.

Are you sure you have taken into account that when you have an open ended roll, 1 is subtracted from subsequent rolls?

Oops I wasn't aware of 1 substraction. Such a fail. Your graphs are correct

PS At least got some practice in python graph plotting.

Also there are two units that are missed on your graphs - barbarian bowmen and bakemono archers - they are good unless you are facing defence 3 or greater. than they are still better than archers at def 4-5.

OK, here is the second graph with the Barbarian archers and Bakemono / Goblin archers added in as well...

Indeed, they are quite impressive overall. The Dai Bakemono archer is also there, and is worse than almost anything (being essentially 3 Longbows compared to the normal 4, and costing an additional 15 Iron). They do fight in melee as well, so if you can find a strategy where that works for you, all good.

I have also produced a version just focusing on the three human choices, Bow, Longbow and Crossbow. I think the result is pretty obvious...

This is interested and can be used to tailor your offensive missile needs to your opponent. Druids, for example, typically don't have a lot of armor on their units, so (taking the bottom graph, just for example) it would be most effective to buy simple archers, even when asaulting fortifications that give one extra defence. Or do you think that first round of crossbow firing really makes up for the lower damage against mostly unarmored targets?

I do

Thanks for the graphs! They're great. I guessed that crossbowmen were better but never did the math. Nice to see the difference.

What you also have to take into consideration, if choosing between archers and crossbows is who you're fighting and the max HP.You can only deal damage if health points are left. The extreme example here are 2 HP goblins. The kill rate of archers is a lot better in this case, of course.
"But I don't fear goblins", you say? Well that's certainly a good point, but I just wanted to illustrate that archers might still be useful. Just consider that some heavy infantry that is down to 1HP doesn't mind if it is killed by a crossbow or an archer. The total theoretical damage done is less important than the number of actually killed units. Just think about that when you mix your units.

Crossbows are surely never a bad choice but it should still be useful to put archers in the mix against most enemies. Just think of Hoburg or simple spearmen, too.

I once got the event where lots of disposessed spirits spawn, being ethereal and low on HP, archers were better. BTW. that event really messed up the whole map.

Good points.

I still feel that it is slightly unfortunate that the balance is so skewed in one direction. It would be really nice to think there was a better balance where it was a harder choice to make. This is particularly true for Burgmeister Xbows versus slings.

I definitely agree on the Burgmeister, but I think it is intended that the more iron a unit costs the better it is. The gap between hoburg slingers and crossbows is just too big.

Iron is rare for some classes. You have to decide if you go for iron heavy units or siege engines for example. So there is a strategic decision involved. Archers are a bit of an execption here in my opinion, because in some cases they're even better than crossbows and save you the iron. Though with the Burgmeister I'd give the crossbows the highest iron priority ;-).

The great exception are Zweihanders/Halberdiers that I sadly consider to be worse than spearmen/swordsmen. Why didn't they get 8 hp like the tower guard?