Topic: Slightly increasing atlantean and imperial attack to make defensive promotion more viable
king_of_nowhere Topic Opener |
Posted at: 2017-01-30, 16:02
in the high level play displayed in the latest turns of the 2016 tournament, a few players started to skip the highest level defensive promotion for their soldiers (healtpoints 4 and 3 for empire and barbarians, defence 2 for atlanteans respectively). A bit of math shows the reason: an atlantean or imperial soldier with full attack promotion will kill a fully promoted opponent in 5 hits. lacking the highest level defensive promotion, they still need 5 hits to kill. For example, atlanteans deal at most 48 damages, against an empire with healtpoints 3 (193 hp, 5% defence) they need 193 / (48 * 0.95) = 4.23 so five hits. The only exception to this is against barbarian foes, as barbarians have higher attack and will kill a partially unpromoted soldier with 4 hits - sometimes they kill even a fully promoted opponent with 4 hits, a feat given them to balance their weaker evasion. And high level humans will only use a soldier with full or no attack promotion, as there are micromanaging stragtegies to ensure that all promotions go to full and a fully promoted soldier is more cost-effective than a partially promoted one. So, as it is right now, there is no significant benefit to getting the most expensive defensive promotion when fighting against two of the three tribes. This doesn't look good. I made a bit of math, and I determined that to kill any partially trained soldier with 4 hits, a damage of 50.9 is needed. To make the promotion appealing, it doesn't even need to happen every time, just often enough; an average damage around that value would suffice, while not disturbing the balance significantly. Therefore, I propose that the attack gain per level of imperial and atlantean soldiers is increased by 1.2. This will have no effect at attack level 0, but it will boost level 4 attack at 49.8 to 51.8 for imperials and 48.8 to 52.8 for atlanteans. Still no chance to kill with 4 hits a fully promoted soldier, you need over 55 damages per hit even against the squishier barbarians. The only real difference would be a greater chance for fully trained soldiers to kill unpromoted opponents in 3 hits rather than 4, but i think we can all agree if you are sending unpromoted soldiers against fully promoted ones you are going to lose anyway, and given how expensive fully trained soldiers are, it should stay that way. In general, this small change will make all the healt and defence promotions more useful, as they will increase the survivability against a fully promoted opponent from 3 to 5 hits, while right now they go from 4 to 5, and have a hard time justifying their cost. Top Quote |
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king_of_nowhere Topic Opener |
Posted at: 2017-01-30, 16:19
Oh, and since we're here, a fully promoted barbarian would need to be very lucky to survive the 4th blow of another barbarian (it should take less than 55.2 damages per hit, which is less than one fifth of the damage interval of a barbarian; compound that low damage over four hits, we are in the one-in-severa-hundreds range), again potentially discouraging a barbarian player facing other barbarians to get the last helmet promotion. if the helmet promotion gave +1 hit point per level (bringing the barbarian total from 214 to 217), it would again become more attractive. Top Quote |
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WorldSavior |
Posted at: 2017-01-30, 16:49
-1 Barbarian soldiers are still the weakest. Please don't change too much. I don't see the problem. So in my opinion, you make things very complicated. Anyway, it's rare that there are just fights of fully promoted soldiers. Edited: 2017-01-30, 16:50
Wanted to save the world, then I got widetracked Top Quote |
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king_of_nowhere Topic Opener |
Posted at: 2017-01-30, 17:54
the point is not to change the balance between barbarians and others, as that would not be touched in the slightest (btw, barbarian soldiers have close to 50% chance against others anyway). The point is to make the high end defensive promotions meaningful. As for fights of fully promoted soldiers beign rare, well, in our last game did we ever fight with anything else? Annd anyway, the change I suggest does not affect anything but fights between fully promoted soldiers. Top Quote |
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einstein13 |
Posted at: 2017-01-30, 20:20
Yes, that's right
I am trying to confirm or deny that
What do you mean? We will change max and min attack by 1.2 more? So there will be:
for min_attack? For me it is way too much for barbarians
But I will prove it
Your proposal will change (mean attack) from 46 to 50.8 for Empire and 46 to 50.8 for Atlanteans. Short studyI've made 10^5 (100'000) simulations of fights between soldiers (https://github.com/einstein13/wl_soldiers). The percentage is how many wins have attackers (left) to the defenders (top). Higher percentage means better soldier :).
All values has measurement uncertainty of 0.4%, so "54.6%" and "54.7%" can be the same value. Current situation
Proposal + 1.2 per level
ConclusionThere is new imbalance between Barbarians and other tribes. Edited: 2017-01-30, 20:22
einstein13 |
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king_of_nowhere Topic Opener |
Posted at: 2017-01-30, 21:58
I did specificaly say to give bonus only to atlanteans and imperials, not to barbarians. Barbarians are fine. I specifically said that the problem only concerned atlanteans and imperials. And your simulations back me up. Strongly so. Current situation, there is no difference between level 9 and 10, as i say. With my proposal, there is again a difference between level 9 and 10 - ignore the barbarian part of it, as it is based on a flawed premise. Feel free to run again the simulation after fixing the barbarian issue. Finally, do add the +1 for helmets; current situation, barbarians have no benefit from helmet against other barbarians, and they would not be touched by my attack modification; let's see if my second change there works. Also, your simulation back me up on all soldiers being really close at the moment. Actually, imperial ones are a little behind, but we're talking 5% or less. Finally, I see no reason you may need more simulations. As it is, they are accurate enough, to within a fraction of %. We don't need any more finesse to discuss balance. By the way, for those wondering why a soldier can have a greater than 50% chance against himself: that's because the guy on the left attacks first. Top Quote |
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einstein13 |
Posted at: 2017-01-30, 22:17
A bit longer studyThe same situation, just 10^6 simulations Current state
King's proposal
Uncertainty is 0.1% My pointsWhat I need from you is to think about barbarians too. If you add attack bonus for Empire and Atlanteans, you will give less chance for Barbarians. They need tweaking too. Give me any specific rules and I will make simulations to prove your point. I agree that making more difference between lvl 9 and lvl 10 soldier will be better, but I disagree that we should leave only +1.2 attack for E & A. Last thing is about lvl2 and lvl0 soldiers. I need to check if they have any chance for winning against lvl10. I remember that in B18 I was able to defend/attack with my lvl2 soldiers in early game. Even if other player had a few lvl7 soldiers. Swarm of lvl2 soldiers should be better than one or two lvl10 soldiers. If we change that balance, we will add benefit for very advanced players who are able to produce first lvl10 soldier in a short time. Other players will be in bad situation EDIT: Maybe I made mistake about Barbarians? Their lvl 10 soldiers are almost the same as before. But their lvl9 soldiers are very weak against lvl10 soldiers from other tribes: atl_10 56.8% -> 72.7% / 50.5% -> 34.5%, emp_10 55.3% -> 71.7% / 52.3% -> 35.6%. Edited: 2017-01-30, 22:29
einstein13 |
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king_of_nowhere Topic Opener |
Posted at: 2017-01-30, 23:20
-- To simplify (hopefully) the post, I will use a sort of matematical notation to refer to soldiers: (At), (Em), (Bb) (S) refers respectively to atlantean, imperial, barbarian, and soldiers of any tribe. (S/Bb) refers to a soldier of any tribe except barbarian. 10(At) refers to an atlantean soldier of level 10. 10(Bb)vs2(X) refers to a level 10 barbarian fighting a level 2 soldier of any one tribe. I think, scientist to scientist, that we'd both find it clearer than referring to this or that soldier -- Yeah, as you already noticed, with my change 10(Bb) would be just as strong as they are right now, even if 10(S/Bb) were buffed. What changes is that there is a difference between 9(S) and 10(S). Before, it was like 9(S)vs10(S/Bb)=50%, now 10(S/Bb)vs9(S)=40% which is the desirable result. Barbarians became much weaker when fighting 9(Bb)vs9(S/Bb). Apparently strange, but easily explained: now 9(Bb)vs9(S/Bb) both need 4 hits to kill, and barbarians have a lower evade, so they have lower chance. With 10(Bb)vs10(S/Bb), barbarian will die with 5 hits, but some half the times it will still kill with 4 hits, and this compensates the lower evade. In other words, 9(Bb) are weaker, but they get a greater benefit form the last promotion: they always get to survive one more hit from (S/Bb), while (S/Bb) will only get to survive one more hit some times. By the way, I see that even with my proposal, 9(Bb)vs10(Bb)=50%. Did you give the slight buff to barbarian helmet I suggested? If you did, and it didn't affect the chances much, then try doubling it (so that 10(Bb) have 220 hit points). I'd like to get 9(Bb)vs10(Bb)=45% or less. As for 2(S)vs10(S), I don't think your simulation will give meaningful data there, because you don't need the likelyhood of 2(S) defeating 10(S) (1 in a million, maybe), but you need to know how many 2(S) it takes to kill a 10(S). Maybe you can tell your simulation to look not at the victory chance, but rather at the damage taken by 10(S), in % of its hit points? That way, if we see a shift from 20% to 15% hit points lost, it means that it took some 5 2(S) to defeat a 10(S), and afterwards it would take 7 2(S). That would offer meaningful data. I agree with your concerns, but I believe they would not affect the balance; if player A has 10(S) and player B has only 2(S), then player A will win, regardless of how we tweak the suble differences. Well, unless player B also gets 10(S) soon, in which case he'll have to use some stalling tactics, which are not really affected by my slight change. Either way, I don't see this affecting the overall balance of the game. Top Quote |
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SirVer |
Posted at: 2017-01-31, 07:14
I am really enjoying this discussion and the analysis!! Here is how I read the situation right now:
I agree that we want to address the viability issue, but hopefully without affecting lvl9 barbarians as strongly. einstein, what do you use to make those tables? Also, could you show (+- %) in the same cell for new values easily? Top Quote |
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WorldSavior |
Posted at: 2017-01-31, 18:09
It looks like Einstein shows you some arguments Still there would be many things to do which I consider as much more important.
Yes: I've been fighting against many soldiers which have not been at a toplevel. And concerning your soldiers: You just surrendered before we could kill all of your elite-troops
I don't know... Edited: 2017-01-31, 18:10
Wanted to save the world, then I got widetracked Top Quote |