User:Mystickskye/Math

My curiosity leads me to do tests and investigations and these in turn grow and grow and grow. So this page is set for all that I've done on damage in mabi. Most are mathematically sound, would like large number samples to show that it works in-game too.

Calc thingy

http://spreadsheets.google.com/ccc?key=0AmLj3FlMjc9fdDdqLW9ZQUl4REw5VWNRclE5RlJMTkE&hl=en_GB
It's fairly simple to use. Enter the max damage, min damage and critical % as found on your character screen. The resulting graph shows you the "true average damage per hit" complete with critical damage factored in (explained below in the critical hit section). The thing is, effective critical hit (which the spreadsheet caters for) isn't set in battle which is why the graph is there. With it, you can see how protection affects your average damage per hit by lowering your effective critical %.

Please don't muck around with the rest of the spreadsheet, I have a template I can restore from but it's inconvenient for others. If you want to make additions I can gladly supply you with the file to work with. Some notes:

• This spreadsheet isn't designed to be user-specific. It calculates damage based on 80% balance and r1 Critical Hit. I may or may not change this in a future revision (though what people are doing wielding weapons and having really low balance I'm not sure).
• If you want to compare WM damage where protection has no effect on critical chance then just use the left most point of the graph and ignore the rest.
• Direct any questions to my talk page.

Dual Wielding!

Copy pasta from an old post I made. May or may not clear up at a later stage.

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For the purposes of experimentation I smithed a couple of Bastard Swords, Min>Max in order to minimise the damage range.

End result, my main gets [69~75] damage (which means my base is [37~47], this is used later). My smash is rank 9 so the modifier is 300% ie, my damage is tripled. I think we can all agree that with a single Bastard Sword, my smash damage should be [207~225]. I'm smashing Gray Town Rats which have a Def of 1 (so says the wiki) so this is amended to [206~224]. I smashed them 25 times for the sake of records (crits not counted) and the damage came out like so:
216 206 220 212 222
208 213 221 218 224
215 208 224 211 219
218 224 216 209 221
223 219 221 219 208
Upper and lower limits have been bolded for pointing them out.

Now, according to Atma's theory wielding another identical weapon should increase my damage output 50%. [207~225] should thus increase to [310~337] and be amended to [309~336] against Gray Town Rats. Easy enough.

My theory requires a bit more work. Going by [base+weapon1+weapon2], the min~max range comes out to be:
Min = [37+32+32] = 101
Max = [47+28+28] = 103
[Min~Max] = [101~103]
So triple that to get the theoretical Smash data values and it's [303~309] amended to be [302~308] against Gray Town Rats.

So then, [309~336] vs [302~308]:
304 302 307 308 306
302 305 306 304 306
305 303 307 306 307
305 305 306 304 303
308 303 303 304 305
It's fairly clear which data set the samples match better. Have some screenshots while you're at it (that's 8 screens in all).

Not satisfied with this though (when running an experiment you don't stop after you think you've proved yourself right), I tried on my weaksauce proffing mule.

[46~47] damage (meaning base is [14~19]), nice. Smash is rank F (double damage), this is how things turned out against Brown Foxes (keeping in mind that whether young or standard, they have 1 defense).
91 92 91 91 92 92
92 92 91 92 91 91
Oddly enough I didn't get a single 93 but eh. One "mystery" at a time.

According to Atma's "50% boost" theory, I should be looking at [136~138] damage. To use the theory bandied around several foreign server communities... we'll have to do a bit of math first again because it turns out interesting.
Min = [14+32+32] = 78
Max = [19+28+28] = 75
[Min~Max] = [78~75]
That's right, the max is actually less than the min this time. When this happens, you always hit for the lower number. It's why a Min>Max crit build Bipennis is useful for smashing Siren, you don't want to kill her before your luck kicks in.

Anyway! This means that after def, I should be hitting for 149 damage. The results?
149 149 149 149 149
149 149 149 149 149
I'm really not kidding (four screens this time :p)

So there you have it, I'm not going to say that I'm 100% correct but in neither case did the result of wielding a second identical weapon boost the damage by 50%. In the latter case the actual boost was around 61~63% and then has the Min>Max characteristic which is shown by the [base+weapon1+weapon2] formula to the boot which isn't accounted for without said formula. I still should test this more thoroughly but for now? I'm content.

Critical Damage

Badly written for now. Assuming x = damage roll, y = max damage, z = crit modifier as a % (ie, 100% *100 = 100), conventional thought places critical hit damage as x + xz. The supposed theory goes x + yz. This would make maximum damage more important than one would initially think.
(37~50)+(32~28)+(32~28)=(101~106)
Crit r5=110%
Smash r9
Range should be 303~318
Crit range should be?
By conventional thinking, 636.3~667.8?
By theory, 652.8~667.8

Non
312 310 308 317 317 | 314 304 311 310 312
314 305 316 309 307 | 310 313 317 308 314
312 310 302 313 307 |
Crit
660 662 665 663 660 | 661 651 662 662 659
658 653 657 662 659 | 657 664 662 651 656

(53~70)+(27~48)+(27~48)=(107~166)
So smash range is (321~498)
Conventional thought Crit range is 674.1~1045.8
Theoretical is 868.8~1045.8

Non
405 434 379 466 497 | 341 374 469 460 410
361 383 320 443
Crit
979 1033 943 939 961 | 892 964 956 971 907

Average Damage

The current theory (and so far, no one's brought forth anything else) on how balance affects your damage output is that it can be represented as a normal distribution curve with the actual balance being the average point. As the status page puts it

• ((Max Damage - Min Damage) × Balance) + Min Damage.

Where

• Max Damage - Min Damage represents the damage range
• Balance represents the "weight" to find the average
• The Minimum damage on top of that to represent your average damage

So that's pretty easy and represents your average damage over time (ie, over a couple thousand hits, that figure is roughly what you're hitting). A higher number is better! So that's cool and easy. However, this fails to account for how critical damage affects your average. ie, if every 10% of those were noticeably higher, it'd drag your average up too.

Example!
Say you averaged 100 hits, over 10 samples you total 1,000 damage which makes your average 100 but we already know this! However, what if half of those hits were critical hits for 200 damage? The total then becomes 5(100 + 200) which totals 1,500 which would then make the average 150 rather than 100. A rather profound effect!

• Will write rest later

So, the "real" average damage for a defined value of critical hit chance (this bit is important) is
((Max Damage - Min Damage) × Balance) + Min Damage + ((Effective Critical Chance * Critical Modifier)/100) × Max Damage)
Meaning that at most, critical hit can boost your average damage over time by 45% on top of your normal damage (ie, 145% damage total.)

Two Hand vs Dual Wielding

1.2x - x = 0.2x

Max vs Min, Effects on Average Output

Point for point where x is balance as a % (ie, 1* 50% = 0.5)
Max damage = x = balance Min damage = y = 1-x That's right, it's an x/y split of 100% at base level (note that at 80% balance, max damage does four times as much to increase your output then min damage) but then you need to consider crit!. Minimum has no effect on crit, ew. Seeing as effective critical differs in battle it gets a range so this makes max damage's (current) max effective range 0.8~1.25 for increasing your average damage.

How does this relate to strength then? To dex? More to come.