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Heroes Community > Library of Enlightenment > Thread: A HoM&M Mini-Game, Creature Analysis and Creature Charts
Thread: A HoM&M Mini-Game, Creature Analysis and Creature Charts This thread is 3 pages long: 1 2 3 · NEXT»
Wub
Wub


Responsible
Famous Hero
posted May 20, 2022 08:14 PM
Edited by Wub at 23:29, 12 Jun 2022.

A HoM&M Mini-Game, Creature Analysis and Creature Charts

Here’s a Heroes 3 mini-game. See if you can find the best way to play it:

You and your opponent each have 1 million gold to buy one stack of any Heroes 3 Complete creature you want. For example, one stack of 5000 Nomads. You can buy any resource for 250 gold apiece. Then you fight your opponent’s stack of creatures. You both play to the best of your ability, on Sand terrain, with regular morale and luck, but without any hero skills or spells. Which creature should you buy?

This thread is meant as an ultimate Heroes 3 creature comparison thread. There is analysis, charts, some math, and eventually an answer to my question. You can also download my spreadsheet via this link. If you don’t like long posts, just read these italic parts and check the charts. I’d be curious to read your answer, or what you think of the analysis .

Yes, after 15 years () I decided to briefly drop by again. Ah, great times! Life will be calling again very soon, but I never forgot about Heroes 3 and HeroesCommunity, nor about this creature analysis idea.

I know, we have analyzed the game for over two decades now. And even the idea to juggle creature stats around to make charts is not new. For example, there is this thread, Coyote’s analysis, and most famously Jolly Joker’s (no longer online available?) analysis. I also made an analysis thread for Heroes 4.

Veterans often meet such charts with skepticism. And with good reason. Sometimes the math is hokey, leading to counterintuitive results. Sometimes an attempt is made to even incorporate Creature Specialties. But you cannot accurately express the value of a Creature’s Specialties or even its Speed into one concrete figure.

Take a Black Dragon’s spell immunity: helpful if you face a strong spellcaster, but harmful if you yourself are a strong spellcaster. The value of Creature Specialties is too dependent on the situation. And veterans have far more refined intuitions about these situations than any single formula can express.

My approach is more modest, yet mathematically sound and concrete. I present figures that do not include Speed and Creature Specialties, so it is up to the player’s own intuition to incorporate these. But I do give exact figures of how strong a creature stack is, based on the creatures’ Attack and Defense skill, Health, Damage and number of creatures.

I don’t claim that this will be eye-opening to veterans. If it were, the formulas would probably be wrong . But perhaps, when going over the results, you occasionally feel like ‘hmm, this creature scores a bit differently than I thought’. That may still be an interesting experience after 23 years .

Chart 1: Creature Strength

Heroes 3 Attack and Defense skills are not straightforward, though, so bear with me. Example: It takes exactly 1 hit for an Archangel to kill a Unicorn, and on average exactly 20 hits for a Unicorn to kill an Archangel. So should we conclude then that an Archangel is 20 times as strong as a Unicorn?

Alas, it is not that simple. See, on average, a Unicorn kills exactly 2 Boars per hit, and dies after exactly 45 hits from a Boar, so in that sense is 90 times as strong. It would follow, then, that an Archangel is 90 * 20 = 1800 times as strong as a Boar. But if you pit them directly against each other, you would find the Archangel is actually 1875 times stronger than a Boar. And for other creature fights, you may find even larger differences than 1800 vs 1875.

In other words, a creature’s strength can only be exactly calculated relative to the specific creature it is fighting. The same is true in Heroes 1 and 2 (though not in 4 and 5). That is a pity, but so be it. It means we will just need to find an appropriate creature against which we compare all other creatures.

The creature that I have selected as an appropriate comparison creature is the Demon. It has an Attack Skill and Defense Skill of 10, both of which are precisely the median value of all creatures. Also in almost all other respects it is average. We can then pit every creature against a Demon and calculate their strength against this average creature.

We can calculate this (Demon-relative) Creature Strength by first calculating for each creature how much damage it does against a Demon. Feel free to ignore the math and formulas, but this would be:

Damage to Demon (if Attack Skill < 10) = Average Damage * (1 - 0.025 * (10 - Attack Skill))

Damage to Demon (if Attack Skill >= 10) = Average Damage * (1 + 0.05 * (Attack Skill - 10))

We then calculate how well a creature’s Health and Defense Skill protect it against Demon attacks (compensating in the case of Crystal and Azure Dragons for the maximum Attack-Defense gap):

Demon-adjusted Health (if Defense Skill < 10) = Health / (1 + (10 - Defense Skill) * 0.05)

Demon-adjusted Health (if Defense Skill >= 10) = Health / (1 - (Defense Skill - 10) * 0.025)

Then we just multiply Damage to Demon and Demon-adjusted Health, to get said Creature Strength.

Let’s verify that these formulas work. Remember, the comparison creature is a Demon, which has a Creature Strength of 280. A Zombie has a Creature Strength of 35. This means it is 280 / 35 = 8 times as weak as a Demon. And, surely, a Demon needs exactly 2 attacks to kill a Zombie, while a Zombie needs 16 attacks, so indeed 8 times as many.

Conversely, a Black Dragon, with a Creature Strength of 37800 is indeed 37800 / 280 = 135 times as strong as a Demon (0.444 vs 60 hits for a kill). But, again, we are comparing all creatures against Demons, not against each other, so it does not follow that a Black Dragon, compared to a Zombie, is 37800 / 35 = 1080 times as strong, only that it is 1080 times stronger against a Demon than a Zombie is.

Although, in this case, if a Black Dragon directly fights a Zombie, it is actually precisely 1080 times as strong (0.222 vs 240 hits for a kill). Thus when comparing creatures directly against each other, instead of against Demons, the Creature Strength values can be exact, albeit only occasionally so.

I know, you can criticize my approach. You might say, “Wub, Health protects against magical damage whereas Defense Skill does not, so you cannot incorporate them in one figure”. And you are right: Creature Strength is based on physical damage, not magical damage. But magical damage is rare, and you can still examine a creature’s Health separately from its Creature Strength if you want to know specifically how much magic damage it can take.

More serious is that, in a similar vein, Damage and Attack Skill are quite different from Health and Defense Skill. Would a Sharpshooter be equally valuable if it would do halve Damage but have double Health? Probably not. But here, too, there is a solution. You can calculate the average number of hits a creature needs to kill itself, and use that in combination with the Creature Strength value to analyze a creature.

This leads, then, to the first chart: I have sorted creatures per Shooter vs Melee and per Level, and calculated their Creature Strength. As noted, this allows you to see how strong a creature is compared to one Demon (with its Creature Strength of 280), assuming combat with simultaneous attacks and no Creature Specialties. I have also added a creature’s required number of Hits to Kill Itself:        

                                  Chart 1: Creature Strength



We can see that the creature needing the fewest hits to kill itself – namely 1 – is the Peasant, while the Level 8 Dragons from Armageddon’s Blade need the most, all more than 11 hits. On average shooters need fewer hits to kill themselves than melee units do, and Level 1 creatures need fewer hits to kill themselves than Level 4, 5 and 6 creatures do, which in turn need fewer hits than level 2, 3 and 7 creatures.

The median value of Hits to Kill Self is 4.375, and the creature with this value is…the Demon. An average creature indeed!

The Creature Strength data show how strong each creature is relative to a Demon, which has a Creature Strength of 280. Again, it does not say exactly how strong a creature is compared to other creatures than Demons. For example, Griffins score a bit higher than Hell Hounds (97.1591 vs 93.75) and indeed fare better against Demons than Hell Hounds do, but if Griffins would fight Hell Hounds directly, their strength is actually exactly equal: both have 25 Health and do precisely 4.95 Damage against each other.

Of course, the reported strengths of Griffins and Hell Hounds are still quite similar, so Chart 1 does give a fair estimate (albeit not exact) of how strong all creatures are relative to each other.
   
Chart 1 also shows that for Level 2 to Level 6 creatures, Creature Strength increases with around a factor 3 per level. The increase in Creature Strength from Level 1 to 2, however, is around factor 5, and the increase from Level 6 to upgraded Level 7 creatures is even a factor 10.

You can use this chart to already meaningfully compare some creatures against each other, mostly creatures of the same level. Imps and Goblins, for example: same growth, same speed, neither have specialties. But Goblins are 20% cheaper and 28% stronger against Demons (and 31% stronger against Imps in a direct fight). So the chart further quantifies what we already know: Imps suck .

The problem with this chart is that neither Heroes 3, nor our Heroes 3 mini-game is about creatures fighting 1 on 1. Creatures fight in stacks, which can be as large as the number of creatures available to you (or the gold you have to buy them, but that is for later). So we would like to answer questions such as whether 2 weeks’ growth of Iron Golems are stronger than 2 weeks’ growth of Diamond Golems.

Chart 2: Creature Growth, and Size and Strength of Creature Stacks

Unfortunately, determining the strength of creature stacks is not straightforward. A stack of 10 Demons is not 10 times as strong as a single Demon. For starters, it has both 10 times the number of Health and 10 times the number of damage as a single Demon. So would that mean it is 100 times as strong?

No, that too is incorrect. The stack actually only does 10 times more Damage than a single Demon at the beginning of a fight. Once the first Demon dies, the stack does only 9 times more Damage, once the second Demon dies, it does only 8 times more damage, etc. In other words, if the fight demands the Demons’ full strength until they have all died, the 10 Demons do on average (10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1) / 10 = 5.5 times more Damage than a single Demon. So with 5.5 times more Damage and 10 times more Health, a stack of 10 Demons is in this sense 55 times stronger than a single Demon.

In a similar vein, a stack of 4 Demons is (4 + 3 + 2 + 1)/4 * 4 = 10 times as strong as a single Demon. And since we are first dividing and then multiplying by 4, we might as well state it is 4 + 3 + 2 + 1 = 10 times as strong. That means a stack of 2 Demons is 2 + 1 = 3 times as strong as a single Demon, a stack of 3 is 3 + 2 + 1 = 6 times as strong, etc.

We can also write this in a formula:

Number of Single Creatures = 0.5 * Stack Size^2 + 0.5 * Stack Size

Or the other way around:

Stack Size = SQRT(2 * Number of Single Creatures + 0.25) – 0.5

With these formulas we can also quickly compare larger stacks against each other. For example, a stack of 20 Demons is twice as strong as a stack of 14 Demons (i.e., 210 vs 105 single Demons).

Don’t believe me? Let’s look at a fight between a stack of 3 Titans vs a stack of 2 Titans. We already established that a stack of 3 Titans is exactly twice as strong as a stack of 2 Titans (i.e., 3 + 2 + 1 = 6 single Titans vs 2 + 1 = 3 single Titans). Here is how the fight would go (again assuming simultaneous attacks):

• Round 1: 3-Titan stack receives 2 * 50 = 100 damage, topmost Titan ends with 200 Health;
                 2-Titan stack receives 3 * 50 = 150 damage, topmost Titans ends with 150 Health
• Round 2: 3-Titan stack receives 100 damage, topmost Titan ends with 100 Health;
                 2-Titan stack receives 150 damage, 1 Titan left with 300 Health
• Round 3: 3-Titan stack receives 50 damage, topmost Titans ends with 50 Health;
                 2-Titan stack receives 150 damage, 1 Titan left with 150 Health
• Round 4: 3-Titan stack receives 50 damage, topmost Titan dies, 2 Titans with full Health left;  
                 2-Titan stack receives 150 damage, last Titan perishes.

Thus, the stack of 3 Titans survives with 2 full Titans left, precisely enough to take on another stack of 2 Titans, meaning a stack of 3 Titans is indeed exactly twice as strong as a stack of 2 Titans.

Still skeptical? You may have a point. Even if we assume average Damage, like here, fights rarely play out so neatly as above, with all creatures perishing sufficiently gradually, and without overkill.

Ok, example: 10 Peasants fight 9 Peasants. The fight would last only one round, and 1 Peasant would be left. That is quite a difference from the exactly 4 Peasants that the above formulas predict would be left. The formula predicts the outcome of 10 vs 9 Zombies better, a fight that lasts not 1 but 11 rounds. And here, indeed, 4 Zombies would be left (albeit that the topmost has only half Health).

Fortunately there is a solution to the above inaccuracies in the prediction: We should use the formulas not to estimate how many creatures would be left when 2 stacks fight, but how many more creatures we should add to the weaker stack to make the fight even. For example, how many Air Elementals are an equal match to 1000 Wyvern Monarchs?

Wyvern Monarchs are exactly 16 times stronger than Air Elementals, so we use the above formula to calculate that one stack of 1000 Wyvern Monarchs is equal to 500500 single Wyvern Monarchs, we multiply that by 16, and then use the reversed formula to calculate the stack size corresponding to that amount, which is 4001.5 Air Elementals. Then we test that fight.

And, sure enough, when 1000 Wyvern Monarchs fight 4001 Air Elementals, they win with 19 Wyvern Monarchs left, but when they fight 4002 Air Elementals, they lose with 42 Air Elementals left. Also worth pointing out for our Heroes 3 mini-game is that the size of these stacks are not that far off from what 1 million gold can buy, so the formula can calculate such battles pretty accurately.

In fact, the formula even becomes exact when stack sizes are infinite, when we would find that infinite Wyvern Monarchs are as strong as 4 times infinite Air Elementals. I admit, it is a bit theoretical. But I promised exact formulas, so there . Though also for small fights, it only rarely happens that the formula is off by more than one unit.

This means we can make a chart displaying how strong stacks of different creatures are. Most insightful would be examining the Stack Strength of one week worth of creatures, or two weeks, or infinite weeks, and we can include Castles and Horde Buildings as we please. We will keep using Demons as comparison creatures.

And so we arrive at Chart 2, which expresses the strength of a stack of creatures as the equivalent number of Demons in one stack.

For example, a Necropolis Castle with Horde Building can produce in one week one stack of 2 * 12 + 6 = 30 Skeleton Warriors, which we can see in the chart is basically equally strong as one stack of 5 Demons (i.e., 4.9903). Indeed, when simulating this battle, again assuming simultaneous attacks and average damage, the Demons win with 1 Health left(!), so the calculation is indeed very close.

The chart also shows the stack strengths of infinite weeks of Castle growth (i.e., double growth), both with and without Horde building. So recruiting 6 Gold Golems from two dwellings for an infinite number of weeks would yield a stack that is basically as strong as infinite times 8 Demons (i.e., 7.9963). This number is exact, not an approximation.


                                  Chart 2: Creature Growth and Size and Strength of Creature Stacks



Chart 2 shows, not surprisingly, that when Growth is taken into account, the strength gap between creatures of different levels becomes much smaller. One on one, a Demon is over 500 times as strong as a Peasant, but 1 Demon vs 25 Peasants is a closer fight, which the Demon handily wins. However, interestingly, the chart shows that 10 Demons lose against 250 Peasants. Why is that?

Well, when 1 Demon fights 25 Peasants, the Demon will keep doing the same amount of damage from beginning to end, while the 25 Peasants will start perishing and therefore be doing less damage as the fight progresses. When 10 Demons fight 250 Peasants, however, the 10 Demons will also start doing less damage after the first exchange of attacks, allowing the Peasants to win.

This also explains why only a few higher level units can fight very effectively against lots of lower level creatures, and why it was necessary to make different columns for different growth numbers in Chart 2.

Basically, Chart 2 helps to find out which creatures are available in sufficient quantities at which stages in the game to make a good power stack, especially if you would take into account building order and Heroes’ starting armies. And if your point is that it is especially important for a power stack to deal good damage, you can again use the Hits to Kill Self statistic from Chart 1.

What Chart 2 does not show as directly is the strength-wise cost efficiency of different units. It may not sound very impressive that you need as much as 250 lowly Peasants to narrowly beat 10 Demons in a fight with simultaneous attacks, but it becomes (somewhat) more impressive when you realize both stacks cost the exact same amount of gold. Not too bad for a Level 1 creature!

Thus, higher level creatures tend to make for strong stacks, but how cost-efficient is their strength? That is an important next question, at least for our Heroes 3 mini-game.

Chart 3: Strength of Creature Stacks for Various Amounts of Gold

Fortunately, we already did most of the groundwork to determine how strong a stack of creatures you can buy for the Gold you have available. All we need to do is calculate how many creatures you can buy, and then calculate the strength of that stack with the formulas used for Chart 2.

In doing so, I will assume that one Mercury, Sulfur, Crystal or Gem costs 250 Gold. Based on Marketplace rates, the amount should be 500 Gold, and based on Hero Specialties 350 Gold, but both amounts seem high because it is not uncommon to actually sell resources later in the game for up to 250 Gold. I know, you rarely have that many Marketplaces, but then again you don’t always have an abundance of rare resources either, so 250 Gold seems a fair amount.

In Chart 3, therefore, I have again expressed the strength of various creature stacks in the equivalent number of Demons, but now all creature stacks are equally expensive. I have done this for three different amounts of Gold:

• 6,000 Gold – Enough to buy even the most expensive Level 7 creature. Level 8 Dragons are more expensive and therefore omitted here: no point in presenting data for a quarter of a Dragon.
• 40,000 Gold – Enough now to also buy an Azure Dragon, and to see how multiple Level 7 creatures do.
• 1,000,000 Gold – The amount of Gold used for our mini-game, and enough for our calculations to be very precise.
 
I have not rounded off the number of creatures bought. After all, 6000 Gold would allow you to buy one Archangel or one Angel: not a fair comparison!

For easy comparison, it made most sense to sort Chart 3 by Shooter vs Melee and by Speed.


                                  Chart 3: Strength of Creature Stacks for Various Amounts of Gold



Chart 3 shows that when stack sizes are limited not by growth (as in Chart 2) but by creature cost, certain low-level creatures suddenly seem more viable. In terms of strength, growing 25 Peasants per week is negligible to growing 1 Azure Dragon, but when you realize that one Azure Dragon costs as much as 3,500 Peasants, you will find that the angry little buggers actually one-hit kill the fearsome beast (if they can ever catch it).

Similarly, when single creature stacks worth 6,000 Gold fight each other, you would find that Gremlins beat Earth Elementals, Halberdiers beat Diamond Golems, Centaurs beat Magma Elementals, and Pixies beat Wyverns, even if they don’t get the first strike.

That doesn’t mean that creatures scoring low in this chart are necessarily bad, just that purely in terms of strength they are expensive. Conversely, some creatures that do very well in this chart – Halflings, for example – are rarely available in large enough numbers to be a force to reckon with. This is especially true because large creature stacks are more cost-efficient than small ones: when creature stacks double in size, their strength actually triples to quadruples.

This is also one of the reasons why Level 7 creatures show in the chart as less cost-efficient than you might expect: in practice, lower-level creatures often come in too small numbers to create stack sizes that may effectively challenge Level 7 creatures, so they reign superior in actual games. The other reason is that Level 7 creatures often have high Speed and powerful Creature Specialties, which are not taken into account here.

Creatures such as Vampire Lords, Marksmen and Grand Elves of course also suffer from their Creature Specialties not being factored in. In fact, if we would consider the “Shoots Twice” ability as identical to doing double damage, then the values for Marksmen and Grand Elves in this chart would be around 42% higher.
 
Chart 3 already goes a long way to answer our million-dollar question, but let’s produce one final chart to help solve the puzzle of which creature we should choose to win our Heroes 3 mini-game.

Chart 4: Solving the Heroes 3 Mini-Game

In Chart 4, I have calculated for every creature the exact number of creatures you can buy (rounded down) for one million gold, and then arranged them according to their Strength, again expressed as the equivalent number of Demons in one stack.

                                  Chart 4: Solving the Heroes 3 Mini-Game



Remember, Chart 4 is based on the assumption that creature stacks attack simultaneously and do not use Creature Specialties. But in our Heroes 3 Mini-Game we can let all these assumptions go and instead play with our creature stack to the best of our ability. Thus, we can outwait our opponent’s stack to have a double first strike, use Creature Specialties in any way possible, benefit from Morale bonuses, etc. With this in mind, which creature should we choose?

Chart 4 helps answer this question. It shows how well creatures do against Demons, which is a good indication of how well they do against each other. The chart can therefore be read as that lower-ranked creatures will normally not beat higher-ranked creatures, unless maybe they strike first or have a redeeming creature specialty.

Thus, we can just start looking at the highest ranked creatures of Chart 4 and then work our way down the chart to see if any lower-ranked creature stack may nevertheless defeat them, in particular by striking first or with their creature specialty. Often, the answer is evident from the chart, but in case of doubt we can simulate the battle.


On places 1, 2, and 3 we find Stone Golems, Dendroid Guards and, yes, Peasants - all very slow creatures. This is to be expected if creature costs are any balanced: you pay only for their strength, not for high speed or any game-changing creature specialties, so strength-wise they should be very cost-efficient. None of these creatures excel in our mini-game, though. While they may not lose many battles, any reasonably fast shooter or no-retaliation creature will easily defeat them.

Moving further down the list, we find on place 4 our first real contender: Behemoths. Not a huge surprise, as Behemoths are Level 7 creatures, relatively slow, and designed as cheap brawlers in the Stronghold town plan. With 6 Speed and positive Morale, Behemoths are fast enough to deal with shooters and with their 40% Defense reduction they cleave through almost anything.

As such, Behemoths can outwait Stone Golems, Dendroid Guards and Peasants, then get two crushing first strikes in and thus defeat these strength-wise more cost-efficient creatures. Against slower creatures lower on the list (Demons, Gremlins, Ogres…), we don’t even need to simulate the battle: Behemoths are stronger and get two first strikes, so win easily. Against Horned Demons and Minotaurs, which are equally fast, Behemoths are strong enough to walk in, tank the first hit, and still win the battle.

But Behemoths are not almighty. They are vulnerable to first strikes and powerful creature specialties. As such they actually lose to Pixies, which have 7 Speed and are hardly affected by the Behemoths’ specialty. Moreover, Behemoths are completely torn apart by Sprites, who get two non-retaliation hits in. For the same reason they also lose to Magic Elementals and Psychic Elementals. And while Behemoths can defeat Ancient Behemoths and Vampire Lords, they fall easily to Mighty Gorgons’ death stare.

So Behemoths lose to a handful of creatures. Are these creatures equally convincing in other match-ups? Evidently, Pixies and Psychic Elementals are both inferior to their upgraded versions, so this brings us to the next two contenders: Sprites and Magic Elementals.

Both Sprites and Magic Elementals are dirt cheap – just see how far down the list similar creatures are, such as Naga Queens or Chaos Hydras, which are slower, too. Sprites and Magic Elementals can outwait most units and then do two critical non-retaliation strikes, enough to deal with Mighty Gorgons, for example. So only faster units might present a challenge.

As it turns out, though, only Firebirds are fast and strong enough to defeat Sprites and Magic Elementals. Silver Pegasi, Phoenixes and other faster units further down the list all lack strength. The same is true for strong stacks with equal Speed, such as War Unicorns, Ancient Behemoths and Vampire Lords. Interestingly, when Sprites fight Magic Elementals, it is a stand-off: neither can allow the other the first strike, so it’s a draw!

This brings us to Firebirds, clearly an overpowered creature given how much higher it is on the list than other fast units, not to mention how it dominates Chart 2 due to its infamously high growth. And, indeed, they burn through almost anything. Still, as noted, they lose to Behemoths with their 40% damage reduction, as well as to Mighty Gorgons with their death stare. Firebirds also lack the strength to overcome Stone Golems and Dendroid Guards. They can infinitely avoid these stacks, though, so technically it is a draw or, with tool-assistance, potentially a win if good Morale can be predicted.            

Mighty Gorgons, finally, beat Behemoths, Firebirds and everything else  they can effectively stare to death (or just outright defeat). This excludes Sprites and Magic Elementals, though, with their high Strength and no-retaliation. Peasants and Pixies are also too numerous for death stare to really matter. Stone Golems are immune and also too strong, so Mighty Gorgons can at best only try to infinitely avoid them. And Vampire Lords, who are similarly immune, easily wipe them out too, so in that sense Mighty Gorgons are more of a kingmaker than contender.

The winners, then, are Sprites and Magic Elementals, with only one draw – against each other – and one defeat, namely against Firebirds. So Firebirds would still be part of the meta, albeit that they have a few more losing match-ups. Also, all these creature are from the Conflux town. Coincidence?

Thus, the Heroes 3 mini-game is solved, but more importantly I hope you enjoyed the creature charts – it is probably just me, but I find such charts mesmerizing. Curious to hear what you think


Edit June 5, 2022: reuploaded data and charts to correct Angel cost-efficiency plus some minor inaccuracies.
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baronus
baronus


Promising
Legendary Hero
posted May 22, 2022 01:01 PM

I like question like these. Real power calculstions. Ive made my topic with mathematical calculstions b&#281;d&#281;:

H3 unit calculation

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fanofheroes
fanofheroes


Famous Hero
posted May 22, 2022 03:29 PM

Would it be accurate to state that halflings are the top shooter in chart 4?

I guess the next comparison is based on an average number of external dwellings.  I mean, how easy is it to accumulate that many neutral creatures?  The ones recruited in a town are somewhat fixed since you can build the dwellings, but finding them on a map?  you might be lucky to find 1 frozen cliffs dwelling, so on average, the azure isn't really worth it if you can only accumulate 1/week.  Million gold or not.

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Wub
Wub


Responsible
Famous Hero
posted May 22, 2022 10:59 PM
Edited by Wub at 22:37, 26 May 2022.

Thanks, baronus! I don’t visit the WoG forum often, so was unfamiliar with your thread, but your approach seems more ambitious, because you also incorporate Speed and Creature Specialties in your figures. My approach is less ambitious, but this does allow for precise estimations of Creature Strength. I leave the rest of the picture to the player’s expertise .

Yes, fanofheroes, Halflings are strength-wise the most cost-efficient shooter, at least against Demons. Ratings may vary slightly against other creatures, but Halflings normally end a bit ahead of the runner-up, Cyclopes. In a direct fight Cyclopes would typically win, though, because they get the first shot. Note that Halflings do the most Damage of any shooter, more than Grand Elves and Marksmen, even when not factoring in their Luck specialty. They also do more Damage than Sharpshooters, except when the range penalty applies.

You are right that Creature Growth is a key limiting factor. But once you know how many dwellings (internal or external) you have available, Chart 2 gives you an idea of how strong a stack you can generate.
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NimoStar
NimoStar


Honorable
Legendary Hero
Modding the Unmoddable
posted May 22, 2022 11:24 PM
Edited by NimoStar at 06:43, 23 May 2022.

I would like to see this analysis applied to the next version of Heroes 4 Ultimate (v7)

Anyways, I always said that Magic Elementals are extremely OP

As HotA realized for once, they are very undercosted to begin with.

And as I sem to read, since it's single stack of creature vs creatures with no heroes or spells, you are not even taking into account their ultra strong abilities:

- Attacks all around
- Immune to magic
- Unliving (cannot have bad morale, vampires don't drain)
- AND Magic Elementals and Sprites don't need to have "wait to have two first strikes" at all. They already have No Retaliation, another OP ability.

Fortunately tho H4 resolved te "speed equals initiative" issue by having two diferent values, Movement and Speed (wich I renamed Drive)
and thus  decoupling battle/wait order from high movement.
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baronus
baronus


Promising
Legendary Hero
posted May 25, 2022 04:04 PM

For Heroes IV Ive calculations too. I was made in 2015 for my mod 'Restoration of her4athia'.
But past year I was made better method using unit vs unit tests. I was done sucessfully lvl 1,2 and I was stopped on lvl 3 because domek units are very hard to rate. Especially cyclops...

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Wub
Wub


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Famous Hero
posted May 25, 2022 10:29 PM
Edited by Wub at 22:35, 25 May 2022.

Agreed, NimoStar, Magic Elementals come out on top in the mini-game even without being able to use their powerful Attacks-All-Adjacent-Creatures specialty, so in that sense they are even more underpriced than the mini-game suggests. Their spell immunities are in certain situations also more powerful than the mini-game suggests, even if it helps them significantly in the War Unicorn match-up. To be fair, though, No Retaliation is probably stronger in the mini-game than in the real game.

Fun fact: Even if stack sizes in the mini-game would be equal to 50 weeks of Castle Growth instead of 1 million Gold, we would still find that 200 Magic Elementals beat 100 Hydras, and that 100 Hydras, in fact, cannot even beat 200 Psychic Elementals.

Baronus and NimoStar: I'm afraid I have only played vanilla Heroes 4. Creature Strength there is easier to calculate than in Heroes 3, though, because it is simply a matter of multiplying Damage, Attack Skill, Defense Skill and Health - no comparison creature like Demons needed. In fact I posted a Creature Strength chart for vanilla Heroes 4 in this thread, third post long ago. Stack sizes could be implemented with the same formulas I use here in this thread.
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NimoStar
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posted May 25, 2022 10:44 PM
Edited by NimoStar at 22:45, 25 May 2022.

Well, I specifically said about mod strenght. Your H4 chart also doesn't take into account expansions, in which case, in H3 chart there woudn't be Sprites or Magic Elementals

In fact as in H3, some overpowered creatures were added in H4 expansions. The most powerful of which is probably the Gargantuan.

Which leads me to question something in your methodology. Not only did you not take into account Marksmen and Grand Elves double attacking, but also, you didn't take into account ranged at all. I know it is hard but this make evaluations of all ranged units invalid with this method, so far as I have understood.

I'd wager Titans are a very powerful creature, more than your chart suggest. Even if they aren't as cost efficient as Magic Elementals, they can probably kill many Sprites with their ranged attack, so that they will beat the on growth, and probably beat many more creatures on growth than in seems.
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Wub
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Famous Hero
posted May 26, 2022 10:35 PM
Edited by Wub at 21:04, 28 May 2022.

NimoStar, I realize you were talking about Heroes Ultimate (v7), I just meant to say that I am familiar only with vanilla Heroes 4 for which I made only said basic Creature Strength chart, so mods and expansions go a bit over my head .

You are right that the figures in my charts do not take into account whether a creature is Melee or Ranged (nor its Speed or any Creature Specialties). The reason is that I cannot do this in a way that is  straightforward, yet at the same time eye-opening to experienced players like yourself. You have a much better idea of under which circumstances Ranged creatures perform well than I could ever express with a single formula.

Even the “Shoots Twice” specialty of Marksmen and Grand Elves is not straightforward to incorporate, because damage is not always doubled. Think Lucky shots or Retaliation. However, I did write in my post that if we would “consider the “Shoots Twice” ability as identical to doing double damage, then the values for Marksmen and Grand Elves in [Chart 3] would be around 42% higher”.

However, while I cannot insightfully incorporate Speed and Creature Specialties, I do claim that the Creature Strength calculations in my four charts are substantially more precise than the intuitions of experienced players (albeit under the assumptions of simultaneous attacks and average damage). Moreover these figures are readily interpretable and thus helpful for refining one’s intuitive grasp of Creature Strengths, or even for use as a decision-making support tool.

The latter is basically what I try to illustrate with the Mini-Game: the figures can serve as a basis for making gameplay decisions, which experienced players can then build upon by applying their own superior knowledge of how Speed and Creature Specialties may affect, interact with, or even circumvent Creature Strengths.

Put simply: it is better to keep precise calculations precise and to clearly delimit their scope, than to substantially muddle them in an overzealous attempt to formulate a ‘grand theory of HoM&M3 .
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NimoStar
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posted May 26, 2022 10:51 PM
Edited by NimoStar at 19:30, 27 May 2022.

I appreciate that your attempt is statistical and idealized, however in such a statistical attempt to not count the double attack as a certain % higher damage is misleading.

Of course ranged changes many things: Grand Elves actually do a quarter damage when retaliating in melee (damage value divided by two because of melee penatly) than they do when attacking ranged with good aim (double attack and full damage).

In any case, I believe it is more honest to exclude ranged creatures than to take them as melee creatures where range doesn't apply.

I also think that your calculations did not differ really from the "intuition of experienced players". For example, without the calculations we already knew Magic Elementals, Sprites and Firebirds were the most OP units, thus why HotA took the unusual step of nerfing basically only those three units (while Necro still has skeleton transformer...)

Behemoths are good when fighting but their relative low mobility acts as a strong nerf as level 7 units, thus why they are not OP.
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Wub
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Famous Hero
posted May 28, 2022 09:02 PM
Edited by Wub at 21:03, 28 May 2022.

Quote:
in such a statistical attempt to not count the double attack as a certain % higher damage is misleading.

True, I don’t want to suggest that Archers or Wood Elves are in the same league as their Upgrades. Still, I stand by my approach of emphasizing that Creature Specialties are not included and to add a sentence explaining how Marksmen and Grand Elves would rank if their damage would be doubled, but if you find that misleading, I certainly understand.

Quote:
In any case, I believe it is more honest to exclude ranged creatures than to take them as melee creatures where range doesn't apply.

Creature Strength is also a useful concept for Ranged creatures, and I did list them separately from Melee creatures especially in Charts 1, 2 and 3 to make it easier to compare Melee vs Melee and Ranged vs Ranged.

If your point is that Ranged creatures are at a disadvantage in the Mini-Game, that could be true. I don’t mean to imply that says a whole lot about their value in the actual game. The Mini-Game was meant more as a bit of fun and as a demonstration of how players can build on my figures with their own expertise to make gameplay decisions.

Quote:
I also think that your calculations did not differ really from the "intuition of experienced players".

You’re right, I should have said that the calculations in my charts are “even more precise” rather than “substantially more precise” than the intuitions of experienced players. My charts are indeed not needed to realize that, say, Firebirds are overpowered, and I think very highly of the intuitions of Heroes 3 veterans (which I am not). I leave it to the reader how much more precise these figures are than their own intuitions about Creature Strength.

Quote:
Behemoths are good when fighting but their relative low mobility acts as a strong nerf as level 7 units, thus why they are not OP.

My thoughts exactly when I was doing these analyses. Anyway, thanks for the feedback NimoStar
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angelito
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posted May 30, 2022 08:59 AM

Great and very informative as ususal Wub
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Wub
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Famous Hero
posted May 30, 2022 07:49 PM

Angelito, the Legend, is still here! How epic! Your message made my day
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LouWeed
LouWeed


Adventuring Hero
posted June 02, 2022 03:10 AM

Fascinating

I'm doing this instead of the next project euler problem, using the wiki https://heroes.thelazy.net as a primary source.

Couple of questions, not sure who has the answers:

https://heroes.thelazy.net//index.php/Enchanter
The spell percentages given on this page don't add up to 100, and seem weirdly precise. Don't suppose anyone knows what the chances of each spell actually are? Also doesn't mention that bloodlust is only cast if there's a melee ally

https://heroes.thelazy.net//index.php/Leprechaun
"Doubles friendly unit luck chance" - anyone know what this means? What if you have zero luck? What if you have negative luck? Does it decrease your luck?

And I don't know if anyone needs this, but here's the formula for Mighty Gorgon's death stare (the wiki only gives odds for killing at least one enemy creature)
G = Mighty Gorgon stack size divided by 10, rounded up to nearest whole
K = number of enemy creatures killed (0 <= K <= G)
0.9^(G - K) * 0.1^K * G! / (K! * (G - K)!)
https://imgur.com/1NPQJqg




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LouWeed
LouWeed


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posted June 09, 2022 04:51 AM
Edited by LouWeed at 05:43, 09 Jun 2022.

OK
I have similar results, although the magic elemental does not do so well because I used HoTA creature stats, and they cost a bit more:

creature                         #  win   score
sprite                   x   33333  158  128.14
behemoth                 x     666  154  105.47
ayssid                   x    3076  150   93.45
war unicorn              x    1052  148   95.18
leprechaun               x   10000  147   85.17
halfling                 x   25000  146  109.95
stone golem              x    6666  146   90.40
horned demon             x    3703  146   86.14
pixie                    x   40000  145   89.01
haspid                   x     222  143   87.79
dendroid guard           x    2857  143   87.57
unicorn                  x    1176  142   85.80
demon                    x    4000  141   80.35
dendroid soldier         x    2352  138   76.94
gorgon                   x    1904  138   73.64
minotaur king            x    1739  136   81.29
zealot                   x    2222  134   91.33
mighty gorgon            x    1666  133   75.44
iron golem               x    5000  133   73.30
efreet                   x    1111  133   71.24
cyclops                  x    1333  131   90.34
minotaur                 x    2000  130   67.11
pit lord                 x    2000  129   70.51
silver pegasus           x    3636  127   78.38
pegasus                  x    4000  127   70.68
ancient behemoth         x     307  125   66.75
satyr                    x    3333  124   68.88
cerberus                 x    4000  123   74.74
black knight             x     833  122   64.09
naga                     x     909  121   59.87
stormbird                x    3636  120   66.04
magic elemental          x     833  119   70.93
medusa queen             x    3030  119   68.73
master gremlin           x   25000  118   81.06
efreet sultan            x     909  118   69.83
devil                    x     338  118   68.30
cavalier                 x    1000  116   64.26
bone dragon              x     555  114   59.74
ogre                     x    3333  113   60.57
pikeman                  x   16666  112   58.58
ogre mage                x    2500  112   55.49
firebird                 x     500  111   64.76
nomad                    x    5000  111   54.44
peasant                  x  100000  107   63.96
gnoll                    x   20000  107   58.93
gremlin                  x   33333  106   59.68
naga queen               x     625  105   61.57
oceanid                  x   22222  105   55.53
champion                 x     833  105   55.42
dread knight             x     666  105   52.39
pit fiend                x    2000  105   51.79
mage                     x    2857  103   64.14
sea serpent              x     408  103   50.17
swordsman                x    3333  102   48.46
thunderbird              x    1428  101   45.45
sorceress                x    1941  100   71.36
storm elemental          x    3636   99   56.49
medusa                   x    3333   99   53.63
halbedier                x   13333   99   48.28
monk                     x    2500   98   63.31
arch devil               x     200   98   55.92
enchanter                x    1333   95   61.35
roc                      x    1666   95   45.27
dwarf                    x    8333   93   48.32
manticore                x    1176   93   44.35
hell hound               x    5000   93   43.67
greater basilisk         x    2500   92   41.84
grand elf                x    4444   91   64.60
scorpicore               x     952   91   42.64
sharpshooter             x    2500   90   64.31
centaur                  x   14285   87   39.95
nymph                    x   28571   85   42.42
giant                    x     444   85   38.51
lizard warrior           x    7142   84   50.52
red dragon               x     363   83   36.99
wyvern                   x    1250   82   37.63
sea witch                x    1941   81   53.02
hydra                    x     454   81   37.48
black dragon             x     222   80   43.68
griffin                  x    5000   80   38.49
vampire lord             x    2000   77   36.09
basilisk                 x    3076   77   35.34
arch mage                x    2222   75   45.07
gold dragon              x     222   75   40.47
centaur captain          x   11111   75   34.49
green dragon             x     377   75   34.22
crew mate                x    9090   75   31.72
power lich               x    1666   74   46.64
angel                    x     307   74   33.04
crusader                 x    2500   73   36.83
goblin                   x   25000   73   32.50
orc chieftain            x    6060   72   39.34
genie                    x    1818   71   32.09
lizardman                x    9090   70   38.80
titan                    x     181   70   37.67
chaos hydra              x     266   70   32.16
walking dead             x   10000   70   31.72
cyclops king             x     909   67   39.77
wolf raider              x    7142   66   31.08
master genie             x    1666   66   28.45
corsair                  x    3636   65   37.50
gog                      x    8000   63   33.21
pirate                   x    4444   61   36.39
troll                    x    2000   61   28.65
nix                      x    1000   61   27.66
wolf rider               x   10000   61   26.36
orc                      x    6666   60   34.39
archer                   x   10000   60   33.58
marksman                 x    6666   58   38.61
harpy hag                x    5882   58   33.56
archangel                x     173   57   30.01
royal griffin            x    4166   57   24.38
nix warrior              x     769   56   25.24
hobgoblin                x   20000   53   22.33
air elemental            x    4000   53   20.37
lich                     x    1818   52   32.20
zombie                   x    8000   52   23.33
beholder                 x    4000   49   27.41
battle dwarf             x    6666   48   20.09
evil eye                 x    3571   47   25.33
psychic elemental        x    1052   47   19.14
vampire                  x    2777   46   23.96
ghost dragon             x     307   46   23.42
troglodyte               x   20000   46   22.31
phoenix                  x     307   44   21.40
seaman                   x    7142   43   19.08
sea dog                  x    2666   42   23.91
wood elf                 x    5000   42   22.66
rogue                    x   10000   42   20.56
magma elemental          x    2500   40   18.91
wyvern monarch           x     909   40   18.45
skeleton                 x   16666   39   18.74
steel golem              x    2500   39   18.58
dragon fly               x    4166   37   18.37
gold golem               x    2000   34   15.29
gnoll marauder           x   14285   31   14.44
stone gargoyle           x    7692   27   13.01
fangarm                  x    1666   27   11.67
infernal troglodyte      x   15384   26   11.65
ice elemental            x    2666   25   12.07
skeleton warrior         x   14285   25   11.31
diamond golem            x    1333   19    7.85
harpy                    x    7692   19    7.61
water elemental          x    3333   19    6.99
magog                    x    5714   17    8.37
obsidian gargoyle        x    6250   17    7.80
earth elemental          x    2500   17    6.84
serpent fly              x    4545   17    6.72
wight                    x    5000   14    5.42
fire elemental           x    2857   13    4.42
crystal dragon           x      44   12    5.68
boar                     x    6666   12    4.32
imp                      x   20000   10    4.60
energy elemental         x    2500   10    3.71
azure dragon             x      28    9    3.38
wraith                   x    4347    8    3.46
mummy                    x    3333    6    2.86
familiar                 x   16666    5    2.71
faerie dragon            x      83    5    1.08
rust dragon              x      54    4    1.37


The "win" count is how many other stacks that stack will win against, on average. To determine this, each stack fought every other stack at least once. The score is based on how many battles were required to declare a stack an outright winner against another. So ranged units tend to have a higher score because when they do win, they win comfortably.

Obviously I didn't actually fight these battles in the game itself, I wrote a script to simulate the battles, including all of the special abilities etc. There's probably still some bugs though.

Here's the sprites fighting the behemoths (sprites win easily):

% test_battle sprite behemoth  33333 666 sand
                       sprite  V  behemoth
                  33332x3 + 3    665x160 + 160
-----------------------------------------------------------------
                            2 ATT 17
                            2 DEF 17
                        1 - 3 DMG 30 - 50
                            9 SPD 6
                        99999 HEA 106560
                              STA

Round 1 begins
sprite's turn
Distance to enemy is 13
sprite waits
behemoth's turn
Distance to enemy is 13
behemoth moves 6 cells from 13 to 7
sprite's turn
Distance to enemy is 7
sprite moves 6 cells from 0 to 6
sprite melee attacks behemoth:
-Base damage is 59999: x33333 @ (1 - 3)
-Min = 33333, Max = 99999, Expected = 66666
-Attack 2 vs enemy defense 17
-Negative attack differential: base reduction of -37.50% to damage = 37499
-Net damage is 37499 (min = 20833, max = 62499, expected = 41666)
-37499 damage has killed 234 units; top unit's health is 101/160
                       sprite  V  behemoth
                  33332x3 + 3    431x160 + 101
-----------------------------------------------------------------
                            2 ATT 17
                            2 DEF 17
                        1 - 3 DMG 30 - 50
                            9 SPD 6
                        99999 HEA 69061
                              STA

Round 2 begins
sprite's turn
Distance to enemy is 1
sprite melee attacks behemoth:
-Base damage is 69999: x33333 @ (1 - 3)
-Min = 33333, Max = 99999, Expected = 66666
-Attack 2 vs enemy defense 17
-Negative attack differential: base reduction of -37.50% to damage = 43749
-Net damage is 43749 (min = 20833, max = 62499, expected = 41666)
-43749 damage has killed 273 units; top unit's health is 32/160
behemoth's turn
Distance to enemy is 1
behemoth melee attacks sprite:
-Base damage is 6328: x159 @ (30 - 50)
-Min = 4770, Max = 7950, Expected = 6360
-Attack 17 vs enemy defense 2
-Behemoth lowers enemy defense to 1
-Positive attack differential: base increase of +80.00% to damage = 11390
-Net damage is 11390 (min = 8586, max = 14310, expected = 11448)
-11390 damage has killed 3796 units; top unit's health is 1/3
Enemy retaliates
sprite melee attacks behemoth:
-Base damage is 50212: x29537 @ (1 - 3)
-Min = 29537, Max = 88611, Expected = 59074
-Attack 2 vs enemy defense 17
-Negative attack differential: base reduction of -37.50% to damage = 31383
-Net damage is 31383 (min = 18461, max = 55382, expected = 36921)
-31383 damage has killed behemoth
sprite wins


Edit: found a bug with the Ayssid's ferocity, they drop down the list a bit to 144 wins and a score of 88

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admin
admin

Tavern Dweller
posted June 09, 2022 06:21 AM
Edited by admin at 06:24, 09 Jun 2022.

Interesting table. Shows how important upgrading your elves, air elementals and psychic elementals is, and how unimportant upgrading your cyclopses is.

Small typo: Pit Lord quantity should be 1428 not 2000.

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NimoStar
NimoStar


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Legendary Hero
Modding the Unmoddable
posted June 09, 2022 06:14 PM
Edited by NimoStar at 18:18, 09 Jun 2022.

Quote:
how unimportant upgrading your cyclopses is.


Probably because Cyclops King was meant to have a spellcast, which wasn't implemented but remains in the anim.

Quote:
The "win" count is how many other stacks that stack will win against, on average. To determine this, each stack fought every other stack at least once. The score is based on how many battles were required to declare a stack an outright winner against another. So ranged units tend to have a higher score because when they do win, they win comfortably.



I like your table better. And it does show a more realistic set of results. Validating what I have been saying about ayssids being OP, too  ; )

However, your script will not be 100% accurate unless it takes into account waiting... (which autocombat does)

Mummy is way overcosted, sadly.Add to that it gives your army -2 morale. I wish it was more viable, for example always Cursing, like the H4 one.
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LordCameron
LordCameron


Hired Hero
Veteran of the Succession Wars
posted June 09, 2022 06:31 PM

Wow, Demons aside, inferno really sucks doesn't it? And that's with assuming they can buy as many units as they want, even though low numbers is another problem of theirs.

I've been playing with town portal banned and it makes them way better. I wonder at what point the spell was added to the game? Kind of throws the rest of the game design out the window.

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NimoStar
NimoStar


Honorable
Legendary Hero
Modding the Unmoddable
posted June 09, 2022 06:57 PM
Edited by NimoStar at 00:18, 10 Jun 2022.

Quote:
Wow, Demons aside, inferno really sucks doesn't it? And that's with assuming they can buy as many units as they want, even though low numbers is another problem of theirs.


Well Inferno has other problems here. To boot:

- Pit Lords reviving Demons is extra power but that doesn't work much in these conditions. (even without demon farming this can be used as a resurrection)

- Magog is made to damage more than a single stack, which doesn't work here either

- Archdevil -2 luck (in hota) is more important when it afects many enemy stacks thus weakening their whole army

But also Castle gate, yes, is much more useful with TP banned, as it probably should be. i believe many spells would have been better is introduced as campaign-only by design, much like heroes.

Sir Mullich being available by default for Castle was also a huge oversight... probably the most OP hero in the whole game
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LouWeed
LouWeed


Adventuring Hero
posted June 09, 2022 11:45 PM
Edited by LouWeed at 23:45, 09 Jun 2022.

NimoStar said:
However, your script will not be 100% accurate unless it takes into account waiting... (which autocombat does)


Well ackshually, it does. That was the easiest AI "trick" to hard-code, so the script does do that. Not all waiting scenarios, but specifically the scenario where there one enemy is faster, and the enemy can't attack them yet.

I'm putting in some other tricks like:
- Melee units will avoid entering a ranged unit's penalty area. E.g boar vs halfling, the boar will first round wait, then move only two cells; second round wait, move six cells; third round move the final six cells and attack - thus taking only two ranged attacks at half damage before engaging the enemy in melee

-Faster melee units won't move inside a slower melee unit's reach, will instead move to just outside their reach

-Slower melee units will defend instead of moving, if they can't reach a melee enemy, and the faster (melee) enemy can reach them. This actually negates faster enemies who wait

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