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Post by jonblend on Dec 6, 2022 14:42:33 GMT
Ps: if I understood correctly your second numerical example has a typo, should read 0.63*0.7*0.9*0.8=0.318 You're right, typical copy paste mistake  |
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Post by jonblend on Dec 6, 2022 15:48:58 GMT
My take-aways are as follow: - The more defence bonus is added the less valuable the incremental defence bonus becomes (whether via additional equipment or adding a defence gem) - A defence gem will provide about 4 to 5 times the defence bonus gained from an equivalent level capability gem (and about 8 times for the first equipment added with defence bonus!) - Increasing base defence points of a unit by about 20 is roughly equivalent to one level 3 defence gem - Increasing base defence points of a unit by about 10 is roughly equivalent to 2x level 3 capability gems - At a given unit level, the impact of adding more capability points is more or less linear (ie the impact of the capability added does not decrease as capability goes up) - As unit levels go up, the impact of a capability gem decreases quite significantly So it confirms things we already knew, and also make sense from a game-design perspective: - Unit levels are probably the best way to upgrade overall impact - A "balanced" general is more efficient at using resources vs. a gen focusing heavily on either offence or defence [this is the big news for me, I will probably transfer some equipment and gems around based on this] - Def gems boost defence quite a bit more than capability gems (and presumably similarly for atk gems too) In addition, it would seem that the new rank-boosting level gem would therefore be much more beneficial than a capability gem. Happy to see a fellow numbers enthusiast at work  And I'd like to add a few things: The reduction based on unit def and capabilities
As we can see, it's not linear but might appear so if (combined) def is very high and the scope very small.   Maxed unit def of known mercenaries spans from 64 (0.540) to 277 (0.213), meaning that although we gain more (relatively) from increasing the def of woad raiders, we can never make them as tanky as modao. Thus, starting def of the unit (which takes first spot in the legion) can mitigate most damage.
So far we didn't talk about offense; I wouldn't say that balanced is desirable for the sake of being balanced, it's more a result of gem combinations or limited resources. Having specialists for different purposes is imo a more efficient use of resources.
If we want to build a defensive general then he has to have: (in order of significance)
-unit(s) with high defense -unique weapon with 22% reduction and possibly other item(s) with damage reduction -gems that offer dmg reduction are most useful for this purpose (especially when combining different unit types in the legion). Adding them to the item with highest base dmg reduction offers an additional small bonus compared to spreading them equally. But gem combinations for skills should take priority.
-high title (or if general's title is at least 2-3 levels below emperor: gem of power at corresponding level)
-capability points and gems that match the unit type
Even though we might "optimize" dmg reduction, there is a huge tactical component to taking less damage as well war gear, positioning, attack order, skills such as composure and garrison swap, and of course, damaging opponents before it's their turn to attack.
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Post by lafluth on Dec 6, 2022 17:48:19 GMT
Beautiful graph, really illustrates how unit level is driving most of dmg reduction, much more than capability points.
Trying to come up with practical implications, your list of priorities sums it up well.
What I meant by “balanced” is more efficient, is that given the choice of adding a fifth gem to my cnut with all his equipment geared towards def already, it probably makes more sense to add an attack gem, or capability (or mobility, or regen) rather than a fifth defence gem. The impact of a fifth def gem would be quite negligible.
In other words, if the gem set up on the unique weapons already includes a defence gem, and we have 2 more defensive equipment, then it is probably not worth loading them with defence gems again, or perhaps just one. Having other gems in there will greatly benefit the general.
Same with capability gems. Right now my timur can hold 4 gems. I have put 4 archery gems atm, but these analyses would suggest it would make more sense to have one or two archery gems, 1 atk gem and 1 def gem.
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Post by verily on Dec 6, 2022 22:34:56 GMT
they maybe include lv 7 gems
damage reduction limit is how much you can have it via items and gems.
i have fought a lv3 gem dmg reduc plus item on territory and i have hard time defeating. like that one general in timur hero legend
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Post by jonblend on Dec 7, 2022 0:39:32 GMT
Beautiful graph, really illustrates how unit level is driving most of dmg reduction, much more than capability points. Trying to come up with practical implications, your list of priorities sums it up well. What I meant by “balanced” is more efficient, is that given the choice of adding a fifth gem to my cnut with all his equipment geared towards def already, it probably makes more sense to add an attack gem, or capability (or mobility, or regen) rather than a fifth defence gem. The impact of a fifth def gem would be quite negligible. In other words, if the gem set up on the unique weapons already includes a defence gem, and we have 2 more defensive equipment, then it is probably not worth loading them with defence gems again, or perhaps just one. Having other gems in there will greatly benefit the general. Same with capability gems. Right now my timur can hold 4 gems. I have put 4 archery gems atm, but these analyses would suggest it would make more sense to have one or two archery gems, 1 atk gem and 1 def gem. Ah I think we mean different things when talking about balanced. I understand your point about efficiency and we do get less and less additional reduction the more green gems we put in these slots. My line of argumentation is more about roles, e.g. if I need a defensive general that can hold the line/delay the enemy, then an almost pure green gem loadout is the way to go (though I might be a little biased due to recent experiences with John Lackland's treasure). But as we'll see in a few sentences, these points of view will converge when we focus on attacking
When going on the offense, item bonuses being multiplied has a different effect (even though same mechanics but numbers are >1). Here, every additional +5% red gem gives us a little more than 5%.
Example:
dmg increased weapon (+22%) and book+15% and navi.chart+5% -> 1.22*1.15*1.05= 1.473
now we put one +5% red gem into each item -> 1.27*1.20*1.10= 1.676 (which is more than +0.15)
for comparison, if we put all 3 gems into the weapon -> 1.37*1.15*1.05= 1.654 (still more than +0.15 but above distribution is better)
As for capability points, they are divided by 2, then added to the corresponding unit's attack. This sum is then multiplied with all the skill factors, terrain, title, unit's weapon bonus and so on to determine damage.
[unit_atk + 0.5*(general_capa + equipment_capa + gem_capa)]*buffs
So if you want to use Timur as damage dealer, a single green gem that is not part of a (useful) gem combination means that we also forego a little extra damage.
There might be scenarios where it is necessary for him to take less damage, sure. But then it is probably more effective to improve his damage reduction temporarily with war gear (which at 20-25% has a lot higher reduction than a few green gems). I think he will always be kind of a glass cannon (same for charge cav) and we are generally better off playing to its strengths than trying to overcome the weaknesses.
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Post by stoic on Dec 7, 2022 9:53:41 GMT
Beautiful graph, really illustrates how unit level is driving most of dmg reduction, much more than capability points. Trying to come up with practical implications, your list of priorities sums it up well. What I meant by “balanced” is more efficient, is that given the choice of adding a fifth gem to my cnut with all his equipment geared towards def already, it probably makes more sense to add an attack gem, or capability (or mobility, or regen) rather than a fifth defence gem. The impact of a fifth def gem would be quite negligible. In other words, if the gem set up on the unique weapons already includes a defence gem, and we have 2 more defensive equipment, then it is probably not worth loading them with defence gems again, or perhaps just one. Having other gems in there will greatly benefit the general. Same with capability gems. Right now my timur can hold 4 gems. I have put 4 archery gems atm, but these analyses would suggest it would make more sense to have one or two archery gems, 1 atk gem and 1 def gem. Ah I think we mean different things when talking about balanced. I understand your point about efficiency and we do get less and less additional reduction the more green gems we put in these slots. My line of argumentation is more about roles, e.g. if I need a defensive general that can hold the line/delay the enemy, then an almost pure green gem loadout is the way to go (though I might be a little biased due to recent experiences with John Lackland's treasure). But as we'll see in a few sentences, these points of view will converge when we focus on attacking
When going on the offense, item bonuses being multiplied has a different effect (even though same mechanics but numbers are >1). Here, every additional +5% red gem gives us a little more than 5%.
Example:
dmg increased weapon (+22%) and book+15% and navi.chart+5% -> 1.22*1.15*1.05= 1.473
now we put one +5% red gem into each item -> 1.27*1.20*1.10= 1.676 (which is more than +0.15)
for comparison, if we put all 3 gems into the weapon -> 1.37*1.15*1.05= 1.654 (still more than +0.15 but above distribution is better)
As for capability points, they are divided by 2, then added to the corresponding unit's attack. This sum is then multiplied with all the skill factors, terrain, title, unit's weapon bonus and so on to determine damage.
[unit_atk + 0.5*(general_capa + equipment_capa + gem_capa)]*buffs
So if you want to use Timur as damage dealer, a single green gem that is not part of a (useful) gem combination means that we also forego a little extra damage.
There might be scenarios where it is necessary for him to take less damage, sure. But then it is probably more effective to improve his damage reduction temporarily with war gear (which at 20-25% has a lot higher reduction than a few green gems). I think he will always be kind of a glass cannon (same for charge cav) and we are generally better off playing to its strengths than trying to overcome the weaknesses.
I noticed that Timur with high lvl IBC is not such a glass cannon as it could be supposed. I was attacked today by Richard leading lvl 15 Templars and Timur survived a triple charge.   With all these war drums at our disposal we can ignore defence most of the time concentrating all our efforts on offense. What doesn't kill us - makes us stronger Another example. I admit it is not the strongest team in the world but I can't say it is a complete pushover either     Yet    |
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Post by lafluth on Dec 7, 2022 11:09:32 GMT
jonblend , yes I think we broadly agree I always liked having specialists any way. I guess what these discussions have changed for me are the following 2 things (which I believe more or less encompass what we have both been saying): 1. All other things being equal, a red or green gem will have more impact than a capability gem. Or as is often the case (eg for gold equipment), one red and one green is better than 2 capability gems. So for instance I had 4 yellow on my timur, and I now switched to 3 yellow / 1 red. Once I get more gems I might even swap another yellow for another red. It feels weird to see his archer capability go down, but according to these numbers he should be quite a bit stronger in attack, while losing only a little in def (to your point of specialists, which I agree with!) 2. The word “balance” is probably wrong to use here. My thought is merely once a gen is set up with a very strong specialty (atk or def), it is worth considering swapping the nth specialty gem (atk or def) for something that can bring a major boost in one go, as the nth specialty gem is quite weak in incremental value. So for instance in the case of my timur, if I give him another equipment with a gem slot, I might inlay a mobility gem if it gives me one more attack, as opposed to adding yet another red gem if he already has 2. Another example would be my basil who runs full varangians. If I already gave him 2 or 3 reds and 2 capability gems, I can see the benefit of giving him 1 green instead of yet another red or capability. Varangians have actually a good def to start with, so with an extra red he might become 9/10 in attack and 4/10 in defence, but if instead I give him a green, he would become 8/10 in attack and 6/10 in defence… which could be a good hybrid gen. But these types of scenarios I will admit are quite seldom. Your list of priorities will need to be covered first in the right order any way, and if there is still a vacant gem slot at the end then this type of reasoning can be considered - it is more about marginal decisions on gems than fundamental gem and upgrade strategy. And thanks for sharing the atk equations! I might do some calcs on these some day too…
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Post by lafluth on Dec 7, 2022 11:13:49 GMT
stoic , I could be wrong but timur’s high dodge has a lot to do with its resilience, no? I seem to have noticed that timur is almost immune to damage for a few attacks, and then (because of morale drop?) as soon as he starts taking damage he is gone in 1 or 2 attacks… but perhaps my ibcs need to be higher level too, just lvl 7 atm. But yeah I always disliked war drums, also for this reason. It kinda skews the game heavily towards attack. The sole purpose of hi def gens, regen gems and tents is pretty much just saving war drums, which is a shame. It limits the game’s variety and overall interest quite a bit imo. Case in point, I just passed the gao epic battle… it seemed tough, but I just spammed war drums and it was a breeze. I pretty much did not pay attention to general placement, positioning, war gears (except when clashing with the 3 op enemy gens, I will admit). I just moved my guys forward and got them to full health every turn… not exactly a strategy game. It is still fun to see a tanky cnut taking virtually 0 dmg from archers though
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Post by stoic on Dec 7, 2022 11:45:58 GMT
stoic , I could be wrong but timur’s high dodge has a lot to do with its resilience, no? I seem to have noticed that timur is almost immune to damage for a few attacks, and then (because of morale drop?) as soon as he starts taking damage he is gone in 1 or 2 attacks… but perhaps my ibcs need to be higher level too, just lvl 7 atm. But yeah I always disliked war drums, also for this reason. It kinda skews the game heavily towards attack. The sole purpose of hi def gens, regen gems and tents is pretty much just saving war drums, which is a shame. It limits the game’s variety and overall interest quite a bit imo. Case in point, I just passed the gao epic battle… it seemed tough, but I just spammed war drums and it was a breeze. I pretty much did not pay attention to general placement, positioning, war gears (except when clashing with the 3 op enemy gens, I will admit). I just moved my guys forward and got them to full health every turn… not exactly a strategy game. It is still fun to see a tanky cnut taking virtually 0 dmg from archers though Yes, I agree that war drums are a "weak link". I usually play without them and stockpiled 800+ big war drums, but, for sure, it is very tempting to use them, because it is usually the shortest way to victory. There are few players who are willing to restrain themselves when there is a key to all doors. |
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Post by jonblend on Dec 8, 2022 7:10:01 GMT
lafluth, stoic, probably the main reason why ranged units and Timur in particular are so strong is attack order. Even on the opponent's turn, when a non-ranged unit attacks a ranged one, the latter attacks first and reduces troops of the attacker (or outright kills them) before their damage is even calculated. Number of troops is considerable part of a unit's damage output, so there might not be much left that actually hits our legion and the tent recovers these minor injuries. This Timur has a lot of good skills to increase triple IBC damage and also never suffers from loss of unit dmg bonus from unique weapon. And if ranged units attack then he simply dodges (though dodging ship attacks is no longer possible)
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Post by jonblend on Dec 8, 2022 7:36:12 GMT
jonblend , yes I think we broadly agree 1. All other things being equal, a red or green gem will have more impact than a capability gem. Or as is often the case (eg for gold equipment), one red and one green is better than 2 capability gems. So for instance I had 4 yellow on my timur, and I now switched to 3 yellow / 1 red. Once I get more gems I might even swap another yellow for another red. It feels weird to see his archer capability go down, but according to these numbers he should be quite a bit stronger in attack, while losing only a little in def (to your point of specialists, which I agree with!) 2. The word “balance” is probably wrong to use here. My thought is merely once a gen is set up with a very strong specialty (atk or def), it is worth considering swapping the nth specialty gem (atk or def) for something that can bring a major boost in one go, as the nth specialty gem is quite weak in incremental value. So for instance in the case of my timur, if I give him another equipment with a gem slot, I might inlay a mobility gem if it gives me one more attack, as opposed to adding yet another red gem if he already has 2. Another example would be my basil who runs full varangians. If I already gave him 2 or 3 reds and 2 capability gems, I can see the benefit of giving him 1 green instead of yet another red or capability. Varangians have actually a good def to start with, so with an extra red he might become 9/10 in attack and 4/10 in defence, but if instead I give him a green, he would become 8/10 in attack and 6/10 in defence… which could be a good hybrid gen. But these types of scenarios I will admit are quite seldom. Your list of priorities will need to be covered first in the right order any way, and if there is still a vacant gem slot at the end then this type of reasoning can be considered - it is more about marginal decisions on gems than fundamental gem and upgrade strategy. And thanks for sharing the atk equations! I might do some calcs on these some day too…
The mobility gem is definitely the single most valuable gem (not just in price  ). It's probably the biggest improvement to my team that infantry can now move once and attack twice (welcome back Hardrada, would you like this helmet, power gem lv3 and Cnut's axe?). And Timur with 11 mobility can now move 4 tiles with constantine's hammer3/country's technology or get in 4/3/2 attacks after moving 0/1/2 tiles with rhino3.
And yes, there is certainly an optimum to be found between capability gems and red ones, especially if units (such as campaign generic ones) have not reached 200 atk yet (with capability from general and equipment already taken into account).
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Post by lafluth on Dec 8, 2022 20:14:08 GMT
Yeah timur is the one I had identified as potential recipient for the mobility gem. If I am not mistaking timur with mob gem, ibc + mamluk + mongolian raiders gives 3 attacks. In theory because I still dont have mamluk or raider lol. But that is the plan.
Not sure about infy with mob gem, will think about it.
How do you get 4 attacks with timur though!?
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Post by conkueror on Dec 8, 2022 21:28:46 GMT
mob gem always gives another attack to inf. you should always have forest and mountain moving skills so you can move and still attack twice with it 3+6+1
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Post by jonblend on Dec 8, 2022 22:53:26 GMT
Yeah timur is the one I had identified as potential recipient for the mobility gem. If I am not mistaking timur with mob gem, ibc + mamluk + mongolian raiders gives 3 attacks. In theory because I still dont have mamluk or raider lol. But that is the plan. Not sure about infy with mob gem, will think about it. How do you get 4 attacks with timur though!? I'm using IBC, mamluk and woad raider as well as rhino3. 11, 8, 5, 2 is how mobility is reduced with each attack in this case. For me, lv18 woads are still better than lv6 mongolian raiders and forest movement is very useful. You could substitute mamluks with ravennas but then forced march via gems is necessary or you end up with 9 (+1 with mobility gem). Or just triple IBC, it's very effective as stoic showed.
I did not buy a lot of gear from territory shop but bought selected 16 coin fragments (mamluk, ibc, templar, hengdao). Not sure if it was the best decision but that's what it lead to. Once you have a high level t6 unit there is always a way to use it.
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Post by stoic on Dec 10, 2022 14:03:39 GMT
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). It's probably the biggest improvement to my team that infantry can now move once and attack twice (welcome back Hardrada, would you like this helmet, power gem lv3 and Cnut's axe?). 
