- Units in Heroes 3 Auto-translated

I propose coefficients of 2 for damage on unretaliated strikes and 1.5 for damage on double attacks.
Justification.
In a battle of 4 rounds, an unretaliated striker will deal 8 hits, while a normal unit deals 4 hits. 8 divided by 4 gives 2.
In a battle of 4 rounds, a double-attacker will deal 12 hits, while a normal unit deals 8 hits. 12 divided by 8 gives 1.5.
And this is without considering that the second strike may be dealt by fewer creatures than the first!

Added after 3 minutes
2 Zingel
Alternatively, another approach could be applied: how many pizants in one stack this unit can kill.
If they are in one stack, then one upgraded fairy will kill as many pizants as necessary.

The weighted average attack of all units (including neutrals) is 11, and the weighted average defense is 10 (meaning that, on average, units deal 5% more damage than their base damage). Based on the figures above, we can make an estimate: A Fairy (2;2) receives, on average, 45% more damage than the attacker's base damage, and deals, on average, 20% less of its own base damage. Also, for example, a Phoenix (21;18) receives, on average, 22.5% less damage than the attacker's base damage, and deals 55% more of its own base damage... Based on these calculations, a coefficient can be derived for each unit, taking into account its attack/defense characteristics. This is what I suggested in the previous post. Added 22 minutes later

I suggest coefficients of 2 to damage for an unanswered attack and 1.5 to damage for a double attack.

Yes, that's correct.

I read yesterday's dialogue –
Due to the constant editing of messages, the logic has been somewhat lost. The messages have become somewhat inconsistent and a little unclear.

Yes, a coefficient of 1.5...
At first, it seemed incorrect, but after thinking about it a bit, I agree.

A few more words about compiling the initial table (without considering speed and abilities).
You can simply apply the "Bubble Sort" method, i.e., according to the laws of Heroes, compare 2 units by calculating the number of turns it takes for one unit to "defeat" the other.
But there is also a possible catch here. With practically equal indicators of 3 units (A, B, C), a situation may occur where A defeats B in a smaller number of turns, i.e., A>B, and B>C, but C>A (this is possible, for example, with a high attack skill and damage, but a low defense skill and HP of unit C).

Added 9 minutes later

.... Based on these calculations, a coefficient can be derived for each unit, taking into account its offensive/defensive characteristics.

This coefficient can also be used, but it will only further increase the difference between strong and weak units. Although it is already quite significant.

As for adding any coefficients in an absolute score equivalent, I have serious doubts, because:
Approximately:
Fairy: total score 0.009
Archangel: total score 181.00
And what absolute number can be added for flight?

This coefficient can also be used, but it will only further increase the difference between strong and weak units. Although it is already quite significant.

But agree, you want to abandon an objective coefficient. We discussed this yesterday, and it seems that no one disputes the fact that the defense of a unit significantly affects its power... You justify your refusal by saying that it will increase the difference between units.

From this, I am afraid to ask: are we not going down the wrong path if we are ready to turn a blind eye to the obvious in favor of our internal assessments of units? After all, we should not adjust the formula to fit our assessments... First, we need to take into account everything that we consider significant. And only then will we have to balance the formula.

All units have their strengths and weaknesses!

But agree, you want to abandon an objective coefficient. We discussed this yesterday, and it seems no one is arguing that a unit's defense significantly affects its power... You justify your refusal by saying that it will increase the difference between units.

From this, I'm afraid I have to ask: aren't we going down the wrong path if we are willing to turn a blind eye to the obvious in favor of our internal unit assessments? After all, we shouldn't tailor the formula to our assessments... First, we need to consider everything that we consider significant. And then we'll have to balance the formula later.

Okay. I'll try to recalculate the table, taking into account three correction coefficients.
a)
1 - coefficient from the average attack (at the unit level)
2 - coefficient from the average defense (at the unit level)
3 - coefficient from the unit level
b)
1 - coefficient from the average attack (across all units)
2 - coefficient from the average defense (across all units)

Although, I agree, the previous unit table was also pretty good :)

Added 1 minute ago

All units are good in something... they have strengths and weaknesses!!!

Especially the Peasant - it only has strengths :)

Although, I agree, the previous unit table was also pretty good. :)

I don't even doubt that. Do you know how many of these "correct" unit tables I've seen? :) As an option, I have one of the early ones uploaded somewhere, but I don't remember where exactly...

Unit ranking in HMM III

But this hasn't reduced the number of questions, and doubts are only increasing...:cool:

I don't even doubt this. Do you know how many of these "correct" tables I've seen? :) As an option, I posted one of the early ones a long time ago, but I don't remember where exactly I got it from...

Unit ranking in HMM III

But there are no fewer questions, and doubts only increase...:cool:

I immediately noticed that the Centaur Commander is better than the Halberdier! :) And a lot of other things... :)

Okay, it's a flawed table. :)
Although, for comparison and to find other people's mistakes, so as not to make the same ones, it will be useful. :)

Added 6 minutes ago
By the way, I suggest also counting the "Bulkiness" of monsters, but as a negative value.
Approximately: -5%.

:)

Added 3 minutes ago
Ugh....
The table does not correspond to reality.
I wonder if the authors even tested it a little? :)

Added 5 minutes ago

...how many of these "correct" tables I've seen? :)

I suddenly started thinking....
What is the point of all our actions - to create a "Super correct" table?
Or to develop a method, create a scheme for evaluating units?

And does anyone even need it?

Okay, calm down, I'll go home now... It's Friday after all, my brain is already fried after a week :)

Good luck to everyone!

[/U]
Pisante is especially good – he only has strong points :)

you are right about that!!! :)

Okay, it's a flawed table. :)

Yeah, that's true. But it's a beautiful one! :) And seriously, it's just convenient to have a picture and the English name of the unit handy... Everything else isn't worth paying attention to because everyone has their own opinion. This table was created based on some principle. To be honest, I don't remember exactly – I didn't create it, but the website where it was posted mentioned something about it. That is, it's roughly the same as what we're doing – we build a rating in Excel based on an assumption and evaluate how close it is to the truth... As you can see, we're not the only ones who failed... :)

I'm suddenly thinking about something here....
What's the point of all our efforts – to create a "Super correct" table?
Or to develop a method, create a scheme for evaluating units?

I'm for the second one. The method is interesting in itself because it can contain some useful things for quickly evaluating a unit... or comparing several to choose from...

Does anyone even need it?

No. Nobody needs it. It's just a kind of riddle, a puzzle... Which unit is cooler? It's just one of the ways to pass the time... at work. :)

... As you can see, it's not just our pancake that turned out lumpy... :)

Of course... Yeah, right. Our pancake is perfect, no lumps at all :) Smooth, transparent, everything is done properly :)

I'm for the second option. The method is interesting in itself, because it may contain some useful things for a quick assessment of a unit... or for comparing several options...

Ah, I love to exercise my brain, but unfortunately, I've forgotten everything. And I studied... applied mathematics... Eh, but I didn't finish it :)

... Just one of the ways to pass the time... at work :)

At work, you say... :) It's a little scary (as one of my colleagues used to say: "Slightly chicken"). You might get a reprimand :)
Okay, we'll continue next week. According to my plans, there will be 2 more initial tables, on which all the abilities will be superimposed later. And making it look good will take only 20 minutes. :)
I remembered a funny thing from the wonderful table - there, a peasant has 15 points! :)

I want to consult with knowledgeable people. Regarding the calculation method: First: it is impossible to evaluate a single unit. At a minimum, another unit is needed. I don't think I need to explain why. Therefore, to get a complete picture, it is necessary to take into account ALL units. Second: to assess how significant certain unit parameters are, it is necessary to know the algorithm for calculating damage, etc., that is embedded in the program. We know this, so this method will be based on it. The basis of each unit in Heroes is the DAMAGE dealt by the unit, as well as the unit's LIFE. DAMAGE is a combination of the attack parameter (at.skill) and the original damage. Life is a combination of the defense parameter (def.skill) and HP. Since the damage dealt in battle directly depends on the unit's survivability (and vice versa) (let me explain: the longer a unit lives, the more damage it will deal), these two components are directly proportional. That is, they must be multiplied during the calculation. Various unit abilities are nothing more than relative or absolute coefficients for DAMAGE or LIFE or the OVERALL result. Relative coefficients (double strike, vampirism, retaliatory strike, etc.) are quite easy to calculate, as they directly depend on the four main parameters of the unit. Absolute coefficients (flight, the ability to cast spells, increased morale, etc.) are quite difficult to calculate. Most likely, they will have to be converted into relative ones accordingly. Now, a little about the calculation. For calculations, we will take (or obtain) an average unit. That is, a unit with average four main characteristics. (I believe that neutral dragons with their unrealistic indicators should be excluded from the calculation, since the overall score of weak units will tend to 0, and the score of strong units will be significantly less affected.) We get a standard. ---at---dam---def----HP--- ---12----11----10----56--- I believe that it is not advisable to calculate correction factors for each level of units, since the assessment is made in relation to all units, and the result will be presented in a single general table. 1. DAMAGE: the exact number of hits required for the unit to "destroy" the standard unit. 2. LIFE: the exact number of hits from the standard unit required to "destroy" the unit being studied. The following table is obtained, on which additional coefficients can be applied. Archangel 70.861678 Titan 56.21693122 Black Dragon 54.08653846 Gold Dragon 51.61830357 Archdevil 32.60869565 Ancient Horror 32.36607143 Angel 28.80184332 Chaos Hydra 23.52150538 Red Dragon 21.84709821 Green Dragon 20.45454545 Phoenix 19.57070707 Ghost Dragon 19.03886555 Giant 18.49489796 Devil 16.11111111 Horror 15.12605042 Hydra 14.36237374 Firebird 13.25757576 Bone Dragon 12.55580357 Death Knight 6.818181818 Naga Queen 6.719924812 Black Knight 5.969387755 Champion 4.974489796 Naga 4.479949875 War Unicorn 4.424066924 Cavalier 4.133597884 Sultan - Efreet 3.764478764 Unicorn 3.61969112 Efreet 3.571428571 Magic Elemental 3.13283208 Scorpikora 2.844272844 Cyclops King 2.664473684 Manticore 2.662907268 Cyclops 2.403846154 Psychic Elemental 2.202772556 Monarch Wyvern 2.162162162 Wyvern 2.162162162 Mighty Gorgon 1.75 Minotaur King 1.653439153 Gorgon 1.576576577 Minotaur 1.465201465 Roc 1.334821429 Thunderbird 1.334821429 Diamond Golem 1.263736264 Spawn of Evil 1.215930451 Hell Spawn 1.215930451 Dendroid - Soldier 1.160714286 Dendroid Guardian 0.982142857 Master Genie 0.973748474 Genie 0.973748474 Sorcerer 0.865384615 Powerful Lich 0.847505669 Ogre Mage 0.770089286 Troll 0.744047619 Gold Golem 0.721153846 Lich 0.586734694 Great Basilisk 0.537240537 Fanatic 0.514455782 Ogre 0.513392857 Crusader 0.499465812 Horned Demon 0.453514739 Monk 0.45014881 Basilisk 0.4375 Swordsman 0.400641026 Demon 0.396825397 Magma Elemental 0.375 Vampire Lord 0.368480726 Archmage 0.357142857 Earth Elemental 0.340136054 Medusa Queen 0.297619048 Silver Pegasus 0.290178571 Mage 0.27173913 Pegasus 0.264945652 Vampire 0.263798701 Energy Elemental 0.249094203 Medusa 0.230823864 Fire Elemental 0.226449275 Iron Golem 0.217633929 Sniper 0.210459184 Water Elemental 0.201955782 Ice Elemental 0.201955782 Stone Golem 0.176977041 Storm Elemental 0.164874188 Air Elemental 0.164874188 Nomad 0.151397516 Royal Griffin 0.148386769 Cerberus 0.145574534 Griffin 0.138295807 Mummy 0.13764881 Hell Hound 0.133928571 Evil Eye 0.113871636 Specter 0.10639881 Dragonfly 0.094246032 Snake 0.087594697 Guard 0.082589286 Ghost 0.082589286 Orc - Chief 0.073302469 Battle Dwarf 0.068824405 Dwarf 0.066964286 Elf 0.066964286 Great Elf 0.066964286 Lizardman 0.061141304 Orc 0.054976852 Zombie 0.050080128 Obsidian Gargoyle 0.045882937 Stone Gargoyle 0.042857143 Magog 0.039765212 Gog 0.038690476 Boar 0.038633242 Raider 0.038060897 Living Dead 0.037560096 Harpy - Witch 0.0375 Lizard 0.036458333 Harpy 0.036458333 Wolf Rider 0.03176511 Thief 0.030293367 Halberdier 0.025755495 Archer 0.023915816 Bowman 0.023915816 Centaur Commander 0.023915816 Pikeman 0.019459707 Centaur 0.01860119 Gnoll - Marauder 0.015178571 Gnoll 0.014165522 Skeleton - Warrior 0.012857143 Skeleton 0.011574074 Hell Troglodyte 0.011574074 Troglodyte 0.009034864 Hobbit 0.006978654 Hobgoblin 0.006975446 Goblin 0.006542488 Imps / Familiar 0.005621693 Gremlin - Leader 0.005621693 Gremlin 0.00526148 Imp 0.005102041 Fairy 0.004926108 Small Fairy 0.003694581 Peasant 0.000768849 It can be seen that a value close to 1 is possessed by the unit "Dendroid Guardian". This is the unit whose parameters are closest to the parameters of the standard unit. (which means that everything is calculated correctly :) ) However, even in this table, there are some discrepancies (but there are very few of them, and they are mainly observed at the level of the standard). In short! Should we use this table to apply coefficients for abilities, speed, etc.? P.S. To be honest, I spent half a day trying to build a mathematical model using combinations of calculations based on the average arithmetic, average geometric from the standard unit, from the weakest unit and the strongest unit. In any case, the most accurate picture is observed in my initial and in this version.

Please provide the formula used for the calculation.

Attack Score
=IF(RC[-3]>R141C6;R141C7/(RC[-4]*(1+0.05*(RC[-3]-R141C6)));R141C7/(RC[-4]*(1-0.025*(R141C6-RC[-3]))))
Defense Score
=IF(R141C5>RC[-3];RC[-2]/(R141C4*(1+0.05*(R141C5-RC[-3])));RC[-2]/(R141C4*(1-0.025*(RC[-3]-R141C5))))
General Score
=RC[-1]/RC[-2]

:)

Well, if we describe it in algorithmic language, we can break it down into 3 steps.
1: Calculating the attack score (how many hits a unit needs to make to "kill" a reference unit)
If A>D
then Ascore=H/(D*(1+0.05*(A-D)))
otherwise Ascore=H/(D*(1-0.025*(D-A)))
2: Calculating the defense score (how many hits the reference unit needs to make to "kill" the unit being tested)
If Aref>D
then Dscore=H/(Dref*(1+0.05*(Aref-D)))
otherwise Dscore=H/(Dref*(1-0.025*(D-Aref)))
3: General score (The closer to 1 and the further from 2, the better, so 2 is directly proportional, and 1 is inversely proportional)
Gscore=Dscore/Ascore

Where
A - Attack skill of the unit
D - Defense skill of the unit
H - HP of the unit
D - Damage of the unit

Aref - Attack skill of the reference unit
Dref - Defense skill of the reference unit
Href - HP of the reference unit
Dref - Damage of the reference unit

A few questions:

1. What unit damage was used for the calculation? For example, the Royal Griffin has damage of 3-6. Do we use 4.5?

2. Cyclops King 2.664473684
Manticore 2.662907268

Practically identical characteristics despite different attack, defense, and damage values. Is this a coincidence?

3. If these two units are compared using the specified calculation formula, will the result be close to one?

P.S. I think a table would be significantly clearer if it were converted to whole numbers. Take the Peasant as one unit. In that case, the Archangel would have a score equal to 92166 (according to rounding rules).

Cyclops King - 3466
Manticore - 3463