Crunbum wrote:

shasho wrote:

I don't like the idea of a multiplicative combat strength system, I think the current one is fine principally. Firstly, because a multiplicative system has its own problem that any flat value modifiers vary in worth depending on the base that is being modified (and if you elect not to use flat values, then it pretty much works like the current system). And secondly, because it has major readability problems (currently a difference of 1 CS means the same thing in all cases, vs. having to do mental math to figure out the strength ratio between two units).

I think the current system will work fine if the damage cap scales well beyond -4 CS to the point that all attacks do 1 damage or none at all.

"Currently a difference of 1 CS means the same thing in all cases, vs. having to do mental math to figure out the strength ratio between two units."

That's the gist of the problem - it does not.

Depending on the matchup, 1 point of CS can mean +20% damage dealt and -0% damage taken. It can mean +12% damage dealt and -6% damage taken. It can mean no change at all. A difference of 1 CS (or even as much as 14 CS) can have literally no impact. It is all matchup dependant. Against Chariots, your Archers might take 20% less damage or even more because of having 1 more CS (more if we are talking hits-to-kill), and against some other unit it could be +3% damage dealt with no change to damage taken, or nothing at all.

On the other hand, a ratio-based formula does exactly what you are praising the current one for - it makes each percentage point worth exactly as much in boost, and yes with percentage modifiers. It makes each and every point matter, and always to the same, predictable and intuitive degree. Percentage modifiers in a fully granular ratio based formula are way more intuitive to understand than flat ones stapled on top of wildly differing damage ranges per point of difference based on an absolute difference in a stat that can cap out and never decrease/increase past a certain point.

Oh sorry I didn't specify what I meant - I don't mean to say that a difference of 1 CS marginally is always the same, nor do I think it should be. But the difference between a unit of 34 CS vs 35, or 19 vs 20 etc. always is. So it's always possible at a glance to tell what the relative difference in strength of units is. Moreover, even with a percentage system points will not all be equal (which, again, I don't think is a problem) because a bonus that puts you over the threshold of, on average, killing or injuring a unit one attack earlier (avg. 49 damage vs avg. 50) will always be more valuable. That is what the system, in my view, should be based around - certain relative differences in CS should push a unit's advantage over a critical threshold.

I haven't bothered to come up with all the necessary values, but pretend a relative difference of 5 CS ought to be considered a critical advantage. So here's a mockup of some of the values you could use:

Crunbum wrote:

In a ratio-based formula, if you see a unit with 20 CS, and a unit with 30 CS, you know how effective they will be, and how much damage they will do to one another. You can just divide one by the other and multiply by four to instantly know how many hits it will kill the other in, doing so in 1 second in your mind, or multiply the ratio by itself to figure out how many units the stronger one will be worth in an "in your face" scenario with everything retaliating. If you receive a bonus of 10%? See, your unit is that much more powerful.

Now, try doing that with the current formula. Tell me, how many CS 20 Warriors can four CS 25 Swordsmen kill at a time? How much damage will a unit with 30 CS deal to a unit with 20 CS, and how much it will take from it, without glancing at the table? How would that change if the opponent had 25 CS instead? 45 CS? How exactly would it change if they got a +4 modifer from that hill, or a -3 modifier from crossing a river? How much value would you get from three soviet districts, and how much would you get from six? Why wouldn't the latter number be twice as good at the former? I hope I got my point across.

Here is the answers by the way:

Ratio formula (done in my head):

- Each CS 25 Swordsman is worth (25/20) ^ 2 = ~1.6 Warriors, so 4 Swordsmen are worth ~6.4 Warriors.

- A unit with 30 CS will deal 3/2 * 25 = ~37.5 average damage to a unit with 20 CS, and it will take 2/3 * 25 = ~16.7 average damage. If you want to do hits to kill, then its even easier as you can just do 3/2 * 4 = 6 hits for CS 20 to kill CS 30, or 2/3 * 4 = 2.67 hits for CS 30 to kill CS 20.

- If the opponent had 25 CS instead, then its 2.5/2 * 4 = 5 hits to get killed, and 2/2.5 * 4 = just over 3 hits to kill.

- If the opponent had 45 CS instead, then its 4.5/3 * 4 = 1.5 * 4 = 6 hits to kill, and 3/4.5 * 4 = 2/3 * 4 = 2.5 hits to die.

- If you got a +4 CS modifier from a hill (which would always be +25% in a percentage formula), then you would be dealing 25% more damage and taking 1/(1+0.25) = 80%, so 20% less.

- If you got a -3 CS from river crossing (or -20%), then you would be dealing 20% more damage and taking 1/(1+0.2), so 5/6 so 16.7% less.

- From three soviet districts you would get +3, or probably +6% (+2% each) if they were to be balanced to any degree which they can only be in a percentage formula because +1 is the smallest flat increment, and its equal to 2% for up to date CS 50 units. So you would be dealing 6% more damage and talking probably 5% less. From six districts you would be dealing 12% more damage and taking 10% less.

Current formula:

- Each CS 25 Swordsman is worth... looks up table... +5 damage and -4 damage taken.... looks up values... 33.5 damage dealt by swordsman, 15 damage dealt by warrior, so 33.5/15 so.. probably somewhere like 2.2, so 4 of them are probably worth nine warriors or so? Rinse and repeat from every scenario, from simplest to complex. 3 soviet districts to a 30 CS vs 20 CS is 50.5 -> 62.5, or 23.7% more damage, as well as 0% less damage taken because its already 15. 6 Soviet districts, however, is 50.5 -> 100, or 100% more damage, as well as again 0% less damage taken. Can't do the current formula in your head unless you have every entry in damage table memorized.

And in response to the rest of this post: I don't think there should really be "conversion" rates between units. This would mean, using current values, that 2 Crossbowmen are worth about 1 Medium Tank. And that's a problem, because 1,000,000 Crossbowmen should be worth 0 Tanks. You could then modify the base power of units, but then you have the ugly exponential scaling problem if you want a realistic relative strength between tech levels, and that still would not solve the problem that no amount of Crossbows should ever destroy a tank.

shasho wrote:

Oh sorry I didn't specify what I meant - I don't mean to say that a difference of 1 CS marginally is always the same, nor do I think it should be. But the difference between a unit of 34 CS vs 35, or 19 vs 20 etc. always is. So it's always possible at a glance to tell what the relative difference in strength of units is. Moreover, even with a percentage system points will not all be equal (which, again, I don't think is a problem) because a bonus that puts you over the threshold of, on average, killing or injuring a unit one attack earlier (avg. 49 damage vs avg. 50) will always be more valuable. That is what the system, in my view, should be based around - certain relative differences in CS should push a unit's advantage over a critical threshold.

I haven't bothered to come up with all the necessary values, but pretend a relative difference of 5 CS ought to be considered a critical advantage. So here's a mockup of some of the values you could use:

Combat Strength (Defender - Attacker)	Damage (Min)	Damage (Max)	Damage (avg.)	Hits to Kill (avg.)
-20	100	100	100	1
-15	80	100	90	2
-10	42	58	50	2
-5	26	42	34	3
-2	17	33	25	4
0	13	29	21	5
+2	12	26	19	6
+5	7	19	16.5	7
+10	4	16	10	10
+15	1	5	3	34
+20	1	1	1	100

So each "Tier" of relative CS provides a concrete advantage in tempo over the previous. I think balancing unit base power, terrain effects, and other sources of CS around such a system would be healthy and congruent with the current implementation.

The problem is that this difference is not fully granular, and even if you came up with a formula that would make it be so, it is exponential. If you will just look at your values, going from -20 to -15 increases damage dealt to 300% of the previous, yet going for another 5 points up (-15 to -10) increases it to 333%, then -10 to -5 to a mere 165%. The formula should not have non-granular outcomes per point depending on the absolute difference growing larger.

For example if you have a 30 CS unit under the current game formula fighting a 20 CS unit, it will do 50.5 average damage. If it receives a +3 CS boost, it will do 62.5 damage, which is close to 25% more. But if it receives a +6 CS bonus, which is twice the previous, it will do a guaranteed 100 damage, which is a 100% damage increase, or four times the damage boost for merely twice the bonus. This is problematic, because it makes weaker, cheaper to produce units inherently better recipients of flat damage modifiers because they benefit more from them, relatively speaking, because it allows them to reach the first crucial threshold (not get damage reduced to near-nothing) and the second (not get one shot), thus making their costs impossible to balance because if you make them balanced at their base values then they will be overpowered if boosted with CS boni. If you try to make them balanced with CS boni, they will be pointless to produce without them. On the other end, it also makes units that are nearing the vital one shot threshold far better recipients of boosts as well, than those fighting equal enemies.

A ratio formula with percentage modifiers just does not have this issue. But you cannot use percentage modifiers in a formula that uses an absolute - rather than relative - difference in CS to determine damage.

Crunbum wrote:

The problem is that this difference is not fully granular, and even if you came up with a formula that would make it be so, it is exponential. If you will just look at your values, going from -20 to -15 increases damage dealt to 300% of the previous, yet going for another 5 points up (-15 to -10) increases it to 333%, then -10 to -5 to a mere 165%. The formula should not have non-granular outcomes per point depending on the absolute difference growing larger.

I mean, yes. It is exponential, but I think that's good. The current system (while the values are somewhat flawed) provides a very narrow band of effectiveness for units with comparable combat strengths, which is the point. Past a certain difference, like 15 or 20 CS, units ought to be utterly ineffective. It shouldn't matter whether an Archer or an Arquebusier is pelting a Helicopter Gunship, it should never do anything besides 1 or 0 damage (depending on whether Amplitude wants 0 damage to be a thing). I think that the absolute difference should matter when assessing the value of a marginal point of CS.

Crunbum wrote:
The problem is that this difference is not fully granular, and even if you came up with a formula that would make it be so, it is exponential. If you will just look at your values, going from -20 to -15 increases damage dealt to 300% of the previous, yet going for another 5 points up (-15 to -10) increases it to 333%, then -10 to -5 to a mere 165%. The formula should not have non-granular outcomes per point depending on the absolute difference growing larger.

For example if you have a 30 CS unit under the current game formula fighting a 20 CS unit, it will do 50.5 average damage. If it receives a +3 CS boost, it will do 62.5 damage, which is close to 25% more. But if it receives a +6 CS bonus, which is twice the previous, it will do a guaranteed 100 damage, which is a 100% damage increase, or four times the damage boost for merely twice the bonus. This is problematic, because it makes weaker, cheaper to produce units inherently better recipients of flat damage modifiers because they benefit more from them, relatively speaking, because it allows them to reach the first crucial threshold (not get damage reduced to near-nothing) and the second (not get one shot), thus making their costs impossible to balance because if you make them balanced at their base values then they will be overpowered if boosted with CS boni. If you try to make them balanced with CS boni, they will be pointless to produce without them. On the other end, it also makes units that are nearing the vital one shot threshold far better recipients of boosts as well, than those fighting equal enemies.

A ratio formula with percentage modifiers just does not have this issue. But you cannot use percentage modifiers in a formula that uses an absolute - rather than relative - difference in CS to determine damage.

I agree that weaker, cheaper units are a problem currently, but I propose that the problem can be solved by just tweaking data. For example, 1) making upgraded units cheaper than they are currently relative to their antecedents, 2) limiting global sources of Combat Strength to make terrain a greater factor and preventing severely outdated (1.5 - 2 eras or so) units from reaching a meaningful relative combat strength by any means, 3) improving the Research system to ensure that unit upgrades are unlocked by a certain point through the tech tree, and in line with the topic of the thread 4) improve the damage scaling formula.

Crunbum wrote:

garethj wrote:

Great thread and excellent work by the OP - thanks for breaking it down so clearly.

Instinctively I agree with a lot of the counterpoints, archers just don't feel that powerful in normal play. But I think the difference is you're not talking about "normal" play, you're outlining an OP strategy that flows from an underlying game mechanic, and to make it work you need to commit to it 100%. 3 archers aren't going to beat a tank but 300 archers are going to beat any number of tanks that an opponent could realistically field, and 300 archers are very achievable.

I think this mainly applies to multiplayer or single-player conquest games. If you're playing the AI and you're mostly peaceful you don't need a huge military to achieve your goals, just a few stacks that you only upgrade when they are needed. In that case having 300 researchers or traders would be more useful than a ton of archers. [I know that's not how food/population works and it's not a straight trade off but you get the idea]. Also if the opponent attacks first you are going to lose potentially as many archers as your opponent has troops which is a cost, that you might not have to pay if you have fewer but better troops. If you're fighting constantly I get that the food to replace archers is probably cheap vs. the industry/gold to build/upgrade better ones, but if it's just a skirmish or fighting greys it's not really going to affect your game much.

A left-field idea that would fix it pretty easily would be to increase tech dependencies so that you can't advance without taking techs like War Summons. I think the game has slightly too many opportunities for beelining as it is so this would be good for gameplay overall. That way you could field your Bronze Age swarm but only with legacy units that you actually built during the Bronze Age, and you wouldn't be able to field overwhelming numbers.

In fact, 3 longbowmen will already beat a tank, especially since they have the same range but are not bound by line of sight rules, and it used to be that 3 ancient era archers would do just that prior to the anachronism penalty change. They can deal 15 damage per hit to it, so round 1 means the tank is already at 55/100 hp, turn 2 one longbow is dead and the tank is at 25/100 hp, and turn three the tank is at 10/100 hp with the last longbow dead - but that is only if the tank can fire every round which it cannot since it is concerned about line of sight. As outlined, said 3 longbows will cost the same amount of pops, half the upkeep and 30 times less industry to make as a tank does. And if you pick soviets then you can make them be on par with actual contemporary units - if you construct just a few weapons districts, then they will only die in 2 hits from tanks and other such units, and as such 2 longbowmen will be able to defeat a tank reliably even if they are shooting back and forth.

Updated my first post with an Armor Class idea mentioned just above, since I think it is a concept worth exploring and could solve several issues, notably with melee units and more armored units like battleships or tanks being just as vulnerable to obsolete weaponry like arrows or melee weapons as contemporary infantry in uniforms is.

From a gameplay point of view I don't think there's anything wrong with 3 longbows beating a tank, as long as the empire with longbows is genuinely in the Medieval Era. If this was changed too much it could easily go too far the other way - where suddenly tech is king and a single tank could conquer entire continents. Beating the 3 longbows is simple for the empire with tanks, but they do have to bring some reasonable number of tanks. The real issue is that an empire that can build tanks should not have the option to build any new longbows.

Crunbum wrote:

If that is what you are aiming at, then perhaps units should use a ratio formula BUT each unit should come with an Armor Class or Armor Rating value, which would reduce the damage they receive by half if the Combat Strength of the enemy unit is below the unit's Armor Class or by 75% if it is below half of its value. That way you can differentiate tankiness between units of the same era without making their relative strengths to one another too out of whack, which would work just fine from both your so-far stated perspective, and mine, I think?

It would make the formula still simple and intuitive to understand, still granular and still not exponential in most matchups - while allowing melee units to be tankier than ranged ones for example, without artificially inflating their combat strength, which could easily give them a place in combat. Same for tanks, helicopters and whatnot.

I'm all for Armor Class, this is starting to sound like DnD lol. Actually that would be interesting, some of my favorite damage systems are the classic RTS ones. Damage = Attack - Armor. It's simple but allows for many nuances between big-hitter units and ones that are weaker but attack quickly or can be massed easily.

If I could do whatever I wanted with the game, I'd probably like a system with a lot more unit counters, special damage rules, etc. But as a rule, I usually try to propose solutions that are as close as possible to the base game, unless the base system is totally unworkable or it's just a really good idea. I actually like your system a lot - it's elegant in its simplicity, and I think it would have been great in Endless Legend or Endless Space (I particularly didn't like how attack/defense worked in Endless Legend). But for this game they chose a system very close to Civ, because hey, if it ain't (entirely) broke...

As for this game, I just don't see the utility in such a large overhaul because it's historical fiction. As I see it, the current damage system is supposed to account for the fact that different empires shouldn't be so far ahead or behind each other in tech, hence why there are only a narrow range of values accounted for in combat strength difference. Getting a stronger unit before another player is supposed to be something of a timing attack, but it shouldn't take the defender too long to adapt to the new technology supposing they can hold out with their defenses. The problem is that the game does not actually provide safeguards for the fact that you can indeed mass horribly outdated units far past their obsolescence, and they actually work. If it were up to me, as @garethj said, I would make way more tech dependencies, and make 0 rolls on damage inevitable past a certain deficit in strength, among other things. The availability of outdated units is probably a bigger problem than their effectiveness.

Crunbum wrote:

Furthermore, if terrain and situational modifiers (such as dug-in, being wounded and so on) can significantly change the Combat Strength of an unit, then in a formula based on a ratio the case where clever use of terrain does afford your units the possibility of dispatching enemies with fewer hits than normal or lets them tank more hits before dying becomes quite common...

Ah that reminds me, a much wider-scoped balance change I would make (if it were up to me) would be to increase the strength impact of units being wounded or maimed (and probably lower the thresholds to something like 50 or 60% and 25 or 30% health, respectively), lower damage slightly across the board, and allow for in-battle retreats. I would much prefer it if battles resulted in strategic victories of forcing the enemy to retreat and spend time or money healing, gaining ground, getting to sack that outpost/district, etc. than the entire obliteration of the enemy force 100% of the time. 4X games almost universally have this problem, since, being turn-based, the attacker gets to focus fire on one unit and snowball the battle a-la Lanchester's laws.

shasho wrote:

Ah that reminds me, a much wider-scoped balance change I would make (if it were up to me) would be to increase the strength impact of units being wounded or maimed (and probably lower the thresholds to something like 50 or 60% and 25 or 30% health, respectively), lower damage slightly across the board, and allow for in-battle retreats. I would much prefer it if battles resulted in strategic victories of forcing the enemy to retreat and spend time or money healing, gaining ground, getting to sack that outpost/district, etc. than the entire obliteration of the enemy force 100% of the time. 4X games almost universally have this problem, since, being turn-based, the attacker gets to focus fire on one unit and snowball the battle a-la Lanchester's laws.

Not sure that having armies be able to constantly retreat instead of being destroyed PLUS the ability to pay to heal will favor aggressive play in multiplayer. It's already a gamble to attack someone knowing that they'll start pumping out units every turn right nex to your armies, if you have to actually beat their forces twice in a row while being injured and they can heal instantly every turn.

Yes, I can't believe they added an extra parameter based on era to faff with in the damage formula, when there is the extremely glaring problem of a formula capping at -4 in a game where high ground gives +4 and one era difference is around +10.
Sorry to sound heated but it is so... stupid! I can't believe it passed a code review, could the developer not be bothered to hardcode more than 4 values?
Let's create a nice modern 4x (went back to civ 6 and the core mechanics feel so much smoother in humankind), lots of complex geography and fortifications to make the map feel alive, and then invalidate everything because a legion is going to take the same damage from an archer on open ground, on high ground with fortifications, and only 5 damage of difference on average when attacking an archer with the same strength on equal ground.
And the solution would be so easy too, no need to reinvent the wheel: civ 6 formula mostly works, and I don't think it is copyrighted, Then it can be improved and tested, but just this would be so much better and easier to implement than arbitrary extra parameters in a broken formula.

I guess units for money is sorta what hiring mercs is all about though... isn't it?

I do agree though that money is too easily ignored. With flat costs for trade, and flat upgrade costs, and unit upkeep not really mattering terribly much (and finding goodie huts with gold all the time), its pretty easy to ignore. But I digress and this is getting offtopic.