Mathematical aproach for damage calculation of combos
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Mathematical aproach for damage calculation of combos
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posted11/06/2006 09:45 PM (UTC)by
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07/03/2005 10:54 AM (UTC)
Uranius Wrote:
Mathematical aproach on enhancing damage calculation of combos
For Damage Calculating of Combos I propose the following formula, with the variables: C = combo damage; z = damping exponent; a,b,c,... = single hit damage:
C = z√az+bz+cz.....
In this formula the root of the function reduces damage growth, when the Combo already has high damage.
The exponent makes strong hits count more than weak ones in the combo, and makes the formula valid for a one hit combo.
holy god, great stuff dude
Consequences when using this formula for damage Calculation.
From the combo damage to the damage of a hit in the combo.
To get the damage that a new hit adds to the combo (and subtract it from the opponents health) the console will have to calculate the following way:
Remember a sum of Hits: S = az+bz+.... ; and remember the damage the combo has already caused: C ; as well as the new combo damage: D.
Lets say, z = 1,3 and all hits have a base damage of 5.
Examples:
For z = 1,3 a Combo of all 5-damage hits would look like this:
For this value of z, a 20 hit Combo has the damage of 10 single hits.
for a Combo consisting of 7- Hit moves it would look like this:
Mathematical aproach on enhancing damage calculation of combos
For Damage Calculating of Combos I propose the following formula, with the variables: C = combo damage; z = damping exponent; a,b,c,... = single hit damage:
C = z√az+bz+cz.....
In this formula the root of the function reduces damage growth, when the Combo already has high damage.
The exponent makes strong hits count more than weak ones in the combo, and makes the formula valid for a one hit combo.
holy god, great stuff dude
Consequences when using this formula for damage Calculation.
- A "one hit combo" has the same damage as the hit itself. For one Hit, the exponent and the root compensate each other.
- Juggle Hits and on-ground hits are treated the same
- Performing the same hits in different order will not change combo damage. If you swap the hits in that sum it won't have effect. In MKD damage changes when hits are done before a popup instead of afterwards.
Example: Ermac Choy¡Lay¡Fut
1 1 ←2 .. 1 1 2 .. CS↑3 = 25% compared to
←2 .. 1 1 .. 1 1 2 .. CS↑3 = 33% - If you insert an extra hit anywhere into any combo the resulting combo will have higher damage. Insert a dz in the sum and it is obvious that damage must get more. In MKD second popups as well as hits before the popup can decrease combo damage.
Examples: Baraka Blades
↑3 ↑3 .. 3 3 2 1 .. →→3 = 39% compared to
↑3 .. 3 3 2 1 .. →→3 = 43%
Kenshi Thai Chi (several hits inserted)
2 2 2 CS 4 ←2 .. CS↑2 .. CS 2 2 2 3 .. ←→3 = 25% compared to
Katana ↑2 .. CS 2 2 2 3 .. ←→3 = 38% - Moves consisting of two hits or parts of combos can be considered as one hit. One power hit with the same damage as the combo damage of two weak hits will have the same effect in a combo than the two weak hits. So you can calculate combo damage based on "combo snippets"; for example (a hit + popup), (three punches), power Move.
I'll show the Mathematics behind this:
Lets say A stands for hit and popup: A = z√az+bz
And B represents the punches: B = z√cz+dz+ez
Finally there is a power move left called f.
Combo damage would be: C = z√Az+Bz+fz
But Az = az+bz because the root and the exponent compensate each other. Bz = cz+dz+ez.
We can insert those and get the formula based on single hits: C = z√az+bz+cz+dz+ez+fz - The highest Combos shouldn't surpass 49% Damage and should be in the same range of damage for all characters. The root function does a damage degradation to make it harder to get more damage when you already have much. This can be fine tuned with the damping exponent z. If you pick a value of 1.3 or 1.35 for z, it simulates damage reduction behavior for MKD ground combos quite good. Secondly gameplay needs tiny corrections.
- Gameplay issues: to prevent getting too high combos there schouldn't be extreme long ground combos ending on popups, letting you do very many hits, like Shujinko 22 hits or something. I would recommend two hits before a popup and long combos ending on a power move, that can be used for the juggle. This way combos consisting of two times the same glued together would be avoided automatically.
From the combo damage to the damage of a hit in the combo.
To get the damage that a new hit adds to the combo (and subtract it from the opponents health) the console will have to calculate the following way:
Remember a sum of Hits: S = az+bz+.... ; and remember the damage the combo has already caused: C ; as well as the new combo damage: D.
Lets say, z = 1,3 and all hits have a base damage of 5.
- We start with Hit number one: S = 51,3 = 8 ; C = 0 ; D¡=¡z√S ; Damage for this hit is D-C¡=¡5
- Hit number 2: We add 5z to S and override the value for S: S = 8+51,3 = 16 ; D = z√S = 9 and D-C = 4 ; D overrides C (so C is the old Combo damage for the next step).
- Hit 3: S = S+5z = 24 ; D = z√S = 12 ; D-C = 12-9 = 3 ; C = D.
- and so on ... If the combo doesent connect spit out Combo "D"% and reset S and C to 0.
Examples:
For z = 1,3 a Combo of all 5-damage hits would look like this:
For this value of z, a 20 hit Combo has the damage of 10 single hits.
| hit adds 5 4 3 3 2 3 2 3 2 2 3 2 2 2 2 2 2 2 2 2 |
| Combo 5 9 12 1517 20 22 25 2729 32 34 36 3840 42 44 46 4850 |
for a Combo consisting of 7- Hit moves it would look like this:
| hit adds 7 5 4 4 4 4 3 4 3 3 3 3 3 3 3 3 3 3 3 3 |
| Combo 7 12 16 2024 28 31 35 3841 44 47 50 5356 59 62 65 6770 |
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Well, I have to calculate supersonic airflow of jet engines and stuff,
I guess this is a reason why my mind somtimes needs to relax on a simpler matter....
I guess this is a reason why my mind somtimes needs to relax on a simpler matter....
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