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Offline Zingel
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#185
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AmberSoler;30418

1. What damage value of the units was used for the calculation? For example, the Royal Griffin has 3-6 damage. What do we use - 4.5?
Yes. We use the average damage.
AmberSoler;30418

2. Cyclops King 2.664473684
Manticore 2.662907268
Practically identical characteristics with different attack, defense, and damage values. Coincidence?
No, it's not a coincidence:
-------------------damage---attack--defense--hp
Cyclops King--18.00--17--13--70
Manticore--------17.00--15--13--80
as you can see, 5.8% more damage, 13.3% more attack, but 12.6% fewer hit points
And if we put them in a sparring match, we get:
Manticore deals 18.7 damage to the Cyclops King and "kills" him in 3.743315508
hits, while
Cyclops King deals 21.6 damage and "kills" him in 3.703703704 hits
i.e., Cyclops King is "stronger" than the Manticore (considering only the main parameters).
So, we consider the result acceptable.
AmberSoler;30418

3. If we compare these two units using the specified calculation formula, will the result be close to one?
"-Hello, is this the residence of the Stupid family?"
"-Eee, aaa, I didn't understand the question?"
That's how I feel.
I didn't quite understand the question. :)
AmberSoler;30418

P.S. I think a table would be much clearer if we rounded the numbers to integers. Let's take the Peasant as 1. The Archer would then have a score of 92166 (according to the rounding rules).
Cyclops King - 3466
Manticore - 3463
Yes, yes, that would definitely be better. But! Our benchmark is not the Peasant, so HE (the benchmark unit) should be 1 for now. And after the final result, we can transfer it to the """System S""" :)

P.S.
I wanted to attach a file, but I can't figure out how to do it yet. I'll try to figure it out...
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Offline Zingel
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#186
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Zingel;30463
Yes. We use average damage.
I wanted to attach a file, but it's not working yet; I'll figure out how it's done here in a moment...

Looks like it worked...
Only it's not a Doc file, but an Xls; you need to rename the extension before opening.
The forum doesn't allow saving *.xls files

The file is for those "in the know." It contains the unit table and calculation formulas (Sheet2).
And on the first Sheet, you can copy a unit's parameters into the first cells, and it will automatically compare two units, indicating the damage dealt and the number of hits required to kill the opponent :)

I think not everyone will get it right away, sorry — I made it for myself :-)
Attachments 1
1 file attached • Total size: 71.5 KB
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Offline ***JOKER***
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#187
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Zingel;30463
P.S.
I wanted to attach a file, but I can't figure out how to do it yet. I'll sort it out soon...
You put it in an archive (.zip) and upload it here (button at the top in the form of a paperclip).
Too bad I'm busy right now, otherwise I would help with the discussion of units...
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Offline Zingel
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#188
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***JOKER***;30468
You put it in an archive (.zip) and upload it here (the button at the top looks like a paperclip).
Too bad I'm busy right now, otherwise I would have helped with the discussion about the units...
:)
You could have zipped it :) something must have slowed down :)
The button that looks like a paperclip, you say... :)
I have images disabled in Explorer :)

Come on, share it as soon as possible, we need fresh ideas! :)
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Offline ***JOKER***
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#189
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Zingel;30471
:)
You could have zipped it :) something must have slowed it down.
You're talking about a button in the form of a paperclip... :)\br>I have images disabled in Explorer. :)\br>
Come on, share your thoughts soon, we need fresh ideas! :)
I'll try to keep up with everything...
Can you briefly bring me up to speed? It seems like everything here is calculated with strict mathematical precision... It feels a bit forced. Although... maybe you're right.
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Offline Zingel
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#190
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***JOKER***;30475

Can you briefly bring me up to speed? It seems like everything here is calculated with strict mathematical precision... It feels a bit forced. Although... maybe you're right.
Sorry :(, but honestly, I can't repeat this for the third (or is it fourth?) time. I simply don't have the time. The last 2-3 pages of this thread contain, in my opinion, comprehensive information. Sorry again...
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Offline AmberSoler
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#191
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Zingel;30463
Here I am
I slightly misunderstood the question. :)
Well, maybe I'm getting a bit ahead of myself... My thoughts are outrunning my actions... :)

We will consider two units equal in strength if the ratio of their coefficients tends toward one. The closer it is, the greater the similarity. That's why I divided the coefficients "unknown" to me in my head (since I didn't recalculate them myself, relying on your formula). And I asked whether these coefficients would be equal, but I just overcomplicated things a bit... :) Sorry.

In general, my only concern so far is that the law of transitivity might not work when applied to your research. That is, if two units are equal (when compared to a benchmark), will they be equal if put in a sparring match against each other... So far, it's confirmed. But is it always?
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Offline Zingel
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#192
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AmberSoler;30483

We can consider two units to be equal in strength if the ratio of their coefficients approaches one. The closer the ratio, the greater the similarity. That's what I did – I divided the "unknown" coefficients in my mind (because I didn't recalculate them myself, relying on your formula). And I asked the question – will these coefficients be equal, but I overcomplicated it a bit... :) Sorry.
Something like that :)
AmberSoler;30483

In general, I only have one concern right now, that the law of transitivity will not work in relation to your research. That is, if two units are equal (when compared to a standard), will they be equal if they are put in a sparring match with each other... So far, it is confirmed. But will it always be the case?
Yes, and here, you are right. Unfortunately, it doesn't work! Although it's very close to the truth. But I haven't found another formula yet.
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Offline AmberSoler
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#193
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No problem! The main thing is to find a method... And then we'll fine-tune it! :D The advantage of our approach is that we can independently adjust the foundation (the initial rating without considering abilities) and all the additions (the abilities themselves). And even if, after summing up any intermediate results, we decide to change the basic unit ratings, the system won't collapse; it will just change slightly... Mathematics and systemization are key! ;) So, all that's left is to decide who will go for the Klinsk... :)
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Offline Qwerty
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#194
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2 Zingel
I downloaded the table. Please provide a detailed explanation of each column.
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Offline Zingel
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#195
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Qwerty;31315
2 Zingel
I Downloaded the table. Please explain each column in detail.
I think it is necessary to explain each cell! :)
Just kidding :)

I don't think it's necessary to explain the columns with the main characteristics.

The rows >141 are also informative.
141 - characteristics of the standard unit
142 - the weakest unit
143 - the strongest (sort of)

Column 8 - the attacking score of the unit, i.e., how many hits the unit needs to make to "kill" the standard unit.
Column 9 - the defensive score of the unit, i.e., how many hits the standard unit needs to make to "kill" the unit in question.
Column 10 - The General score.
11, 12 - Attacking scores, but now in relation to rows 142 and 143.

13, 14 - Defensive scores for 142 and 143.
15 - Something like the geometric mean :) based on the results of columns 11, 12, 13, and 14. - Nonsense.


P.S. I can't work on further developing the table right now, I have no time :(

We'll wait... :)
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Offline Qwerty
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#196
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I remind you of the theorem by Lord Dmitry and Sir Alax:
the strength of a unit, excluding abilities and speed, is approximately equal to:
((average damage*health)/2)*(1+(attack+defense)/50).
The results calculated using this formula are roughly equal to the results from Zingel's formula, although there are some changes.
Applying abilities will yield the actual result.
We can now proceed to discuss the ability coefficients.
Ranged attack adds approximately 20-25% to a unit's strength, flight - from 10%, double strike increases damage by about 50%, own-turn strike - it is unclear how to evaluate this for now, extended attack increases damage... let's say by 20%, unlikely more. Mass attack - increases damage by 100% (possibly). Vampirism and dendroidism must be evaluated separately, as well as unicorn abilities, manticore abilities, medusa abilities, and other tricks like resurrection.
Magic immunity also provides some bonuses.
Speed apparently gives a boost of 5% per unit.
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Offline Zingel
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#197
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Qwerty;31336
Let me remind you of Lord Dmitry's theorem – Sir Alax:
the strength of a unit, without taking into account abilities and speed, is approximately equal to:
((average damage * health) / 2) * (1 + (attack + defense) / 50).
The results of calculations using this formula are approximately equal to the results using the Zingel formula, but there are also changes.
Hmm...
I apologize for my ignorance, but what is this theorem?

And it's not that there are changes... we have completely different approaches.

Added 10 minutes ago
Qwerty;31336

We can start discussing the coefficients of abilities.
Ranged attack adds approximately 20-25% to the unit's strength, flight – from 10%, double strike increases damage by approximately 50%, retaliatory strike – it is not yet clear how to evaluate it, extended attack increases damage... let's say by 20%, probably no more. Mass attack – increases damage by 100% (maybe). Vampirism and dendroidism need to be evaluated separately, as well as unicornism, manticoresm, medusaism, and other abilities like resurrection.
Immunity to magic also gives some kind of bonus.
Speed gives an increase of 5% per unit, apparently.
Regarding the weight of abilities.

To simplify, it is necessary to divide them into 3 groups:
1. "Significant"
2. "General"
3. "Zero"

1. "Significant" – these are the main ones, the coefficient is calculated individually.
3. Zero – these are abilities whose usefulness coefficient we will consider to be 0%.
2. "All the rest": coefficient = 5-10%
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Offline AmberSoler
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#198
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Perhaps it also makes sense to distinguish between a monster's "strength" and its "utility in the game"...
And thereby determine exactly what we are calculating...

After all, the question of who is stronger implies conducting a sparring match taking into account the unit's primary stats and abilities. But how should we handle, for example, the unicorns' magical aura? This skill does not help the unit directly, yet it is useful for the hero's army... Or the Archangel's ability to resurrect allies? In a sparring match, this ability is useless for the Archangel himself. The same applies to units that increase troop morale (it's unlikely he increases his own morale when acting alone), units with the ability to cast spells during their turn, and so on.

None of this relates to the unit's strength, but sometimes it is a determining factor when choosing one unit or another for battle—meaning, will we think more broadly or not? :)
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Offline Qwerty
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#199
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One must think bigger, or even broader :)))
What is the point of these kinds of tables?
In my view, there are two useful factors here:
1. Calculating the economic viability of a unit. This can be done by dividing its strength by its cost. Thus, in cases where acquisitions fluctuate, one can make a "scientifically grounded choice" and so on.
2. For a better understanding of who to attack and when.

Naturally, sparring is irrelevant — so what if an upgraded fairy hacks down a hydra? That's why abilities must be taken into account!

Regarding this paradoxical theorem.
The formula according to Zingel's table:
((RC[-14]*RC[-11])/2)*(1+(RC[-13]+RC[-12])/50)
Enter the formula and look at the results.
They are, I repeat, very similar, but it seems to me they are closer to my understanding of the game than the previous ones.
If you apply abilities after that, you can arrive at a rather interesting result.
However, I know of at least two exceptions that won't fit the formulas:
the strength of Vampire Lords increases non-linearly as their number grows;
3 different Master Djinns are noticeably stronger than one stack of Master Djinns.
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