Miscellaneous Maths/Testing II

Iocun

The formula was on the forums once too, I think. If it was accurate at some point, it no longer is. It still tends to get relatively close, but it still often gives me numbers that are off by a slash/stab.

EDIT: Hrm, on closer inspection it's actually slightly different than the formula I was thinking of. So it may be more accurate than I thought, after all.

Sena

Does DSL do more limb damage than two normal weapon attacks? Or does having both chivalry and weaponry transed increase limb damage beyond just weaponry? Because that formula seems to be off by 1 or 2 slashes at almost every point.

Chord

It was accurate for me for everyone but people in dragonform and Tirac (although, that could be because he was so much better than me that he fake applied or something). Also, if it makes a difference (it shouldn't) I had artefact rapiers.

Also, I seem to remember that slash and doubleslash being different for limb damage. I tried to single slash someone and that formula didn't work, but when I dsl'ed them it did. I did not extensively test it, since I was just trying to get something that worked well enough for me instead of for the common man.

Antonius

Observations based on my own testing:

The damage per hit from doubleslash is equal to simply jabbing with that weapon. So one doubleslash with 90 damage rapiers is equal to two jabs with a single 90 damage rapier.

If I've implemented Chord's formula correctly it disagrees with actual, real world data using Soulpiercers. Out of the small sample of recent results I have saved, it only matched on two of them; interestingly those were the two with very high health (9255 and 9535 health). For those it was incorrect about it was consistently too low in its estimations, in some cases off by two slashes.

Iphis

Edited, no longer valid.

Thanks for verifying, Antonius.

Antonius

@Iphis: Yeah, I just went and re-tested it and it doesn't hold up. I've edited it out of my other post. Not sure what happened last time I tried to confirm it.

Chord

Oh.

I forgot to mention.

Uhm. Don't hate me.

This was the amount of hits I needed to PREP someone. I.E., if the hits_to_break was 10, they required ten individual hits to get their limb ready to break on the next DSL. I changed the variable names when I posted them here and got lazy by the end of it, so I made a variable with a misleading name.

Iphis

Well, since everyone else is in a nice mood and sharing information, I guess I can do the same. 

The above link is to the Maldaathi forums where I posted this (my) DSL limb counter. What follows is that post:

---

This is ONLY the assess trigger and function that calculates the hits to break. You'll need to incorporate the actual counting into your variables/triggers, but that's the easy part. The count returned is in number of individual slashes. It is best to use weapons with very close (within 8 pts) damage. To the best of my knowledge, on health ranges from as low as 1200 and up to 9000, and weapon damages from 53 up to 188... this counter is 99% accurate. I can't and wont promise 100% accuracy or that they won't end up changing something in the future, but for the entire time I've been a knight in the Maldaathi; this is the counting script I've used to get up to Blade Lord. al_norm is just a display function. Replace it with your cecho, echo, or display. Happy breaking: Script: (Put this in one of your loading scripts)

-- My current wielded weapons are stored in a table as {['left']='12345', ['right']='532423'} 
-- THP is the target HP 

function assess(thp) 
 local limb_health 
 local weapon_base_damage 
 local weapon_dam_total1 
 local weapon_dam_total2 
 local weapDam1 
 local weapDam2 
 local brkl 

 -- Put your weapon IDs in here exactly as shown in the brackets, using the quotes. The number after the ='s is the weapon damage. 

 local weapons = {['293562'] = 145, ['377847'] = 145, ['264539']=120, ['145115']=120} 

 if table.contains(weapons,wielded['left']) then 
  weapDam1 = weapons[wielded['left']] 
 end 
  
 if table.contains(weapons,wielded['right']) then 
  weapDam2 = weapons[wielded['right']] 
 end 
  
 if not weapDam1 or not weapDam2 then 
  weapDam1 = 74 
  weapDam2 = 74 
  al_alert(string.format("Weapons not registered! Using %i/%i values!",weapDam1,weapDam2)) 
 end 

 limb_health = 320 + (thp * .24) 
 weapon_base_damage = 10 + (thp * 0.005) 
  
 weapon_dam_total1 = (weapDam1 + weapon_base_damage) 
 weapon_dam_total2 = (weapDam2 + weapon_base_damage) 

 brkl = ((limb_health / (weapon_dam_total1 + weapon_dam_total2))) * 2 
 echo("\n") 

 al_norm(string.format("lh: %s - bd:%s - w1: %s - w2:%s - brkl: %s",limb_health,weapon_base_damage,weapon_dam_total1,weapon_dam_total2,brkl)) 


 local dam_avg  = ((weapon_dam_total1 + weapon_dam_total2) /2) 
 if tonumber(thp) >=6850 or tonumber(thp) <= 2600 then 
   brkl = math.round(brkl) 
 else 
  
   local point 
   for k,v in string.gmatch(tostring(brkl),"%d.(%d)%d+") do 
    point = k 
   end 

  if point then 
    if tonumber(point) <5 then 
     brkl = math.floor(brkl) 
    else 
     brkl = math.ceil(brkl) 
   end 
  end 
 end 

 echo("\n") 

 al_norm(string.format("%i slashes to break!", brkl)) 

 -- enemy is a table with my enemies current afflicts,limb status, and brkl as shown. 
 if target and string.find(line,target:title() .. " " ) then 
  enemy.brkl = tonumber(string.format("%.f",brkl)) 
 end 
 thp = nil 
end 

function math.round(number, decimals, method) 
    decimals = decimals or 0 
    local factor = 10 ^ decimals 
    if (method == "ceil" or method == "floor") then return math[method](number * factor) / factor 
    else return tonumber(("%."..decimals.."f"):format(number)) end 
end

Copy this to a text file and save as an XML, this is the assess trigger.

Let me know if this is accurate for you. I've had no issues, as stated above. I've used it for everything from rapiers, shortswords, longswords, scimitars. I have not tested it with one handed or blunt weapons. 

Antonius

@Chord: Ahh, ok. Well, that would reduce the need for accuracy in some cases. Telling you that you need 10 hits is still going to be correct, even if that leaves you a single slash away from breaking a limb.

Still seems wildly inaccurate for Soulpiercers, though; with rounding and adding an additional two slashes it's now off in every single case.

Mizik

Anyone have any numbers on Reinforced vs Light Stepper?

Or Rajamala dodge bonus vs stock? Then Rajamala + Light Stepper.

Assume 40% armour stat and 12 Dex.

Tirac

I'm trying to make a UI for sailing because I hate chops. However, the delay in turning and movement is giving me some trouble. As far as I can tell: crew morale and ship type affect turning speed, ship type and wind speed affect movement speed.

Does someone have equations to describe movement speed as a function of wind speed and ship type, and turning speed as a function of crew morale and ship type (or just ship type, assuming fanatical morale)?

edit: Oh, and crew experience is probably somewhere in here as well.

Vadimuses

Not sure about movement speed, but if turning speed is relatively static as you imply, you could have your scripts measure the first turn (or a few) and compute the rest off that data.

Tirac

Tirac said:

I'm trying to make a UI for sailing because I hate chops. However, the delay in turning and movement is giving me some trouble. As far as I can tell: crew morale and ship type affect turning speed, ship type and wind speed affect movement speed.

Does someone have equations to describe movement speed as a function of wind speed and ship type, and turning speed as a function of crew morale and ship type (or just ship type, assuming fanatical morale)?

edit: Oh, and crew experience is probably somewhere in here as well.

Probably nobody has this information, so if anyone has timestamped logs of ship movement speed and turning speeds with the following information attached: wind speed, crew experience, crew morale, ship type. That would be extremely useful to me.

(Or if an admin with the equations wants to make my day, that would be great too. Hint hint.)

Aliath

Updated info on augmentation, 100 Darkbows exploded by now, as well as 19 other items

https://docs.google.com/spreadsheet/ccc?key=0Ah2E83E8JLz6dHgtbUN1QkxPMXRFUGF6QWFXck5ULXc#gid=0

Let me know if something doesn't make sense

Eld

Testing endurance/willpower regen with the astronomy tuning for it. For willpower, without it, I was getting 12wp every 4 seconds, and the empowering boosted it to 20. For endurance, I went from 20 per 4 seconds to 36. That's with trans fitness and philosophy. Max ep/wp of 28450/19270, not sure if wp regen is a percentage or just a flat rate.

Yue

@Sena: Saying Drawslash is superior to Staffcast in damage, is that specifically in regards to damage against denizen? (This might be obvious, idk.)

Sena

Yue said:

@Sena: Saying Drawslash is superior to Staffcast in damage, is that specifically in regards to damage against denizen? (This might be obvious, idk.)

Yes, damage against denizens is very different from damage against adventurers.

Xith

Dunno about denizens but I think some staffcasts still get over 1000. Cold being the preferable one.

Xith

So who has done all their alchemist research?

- amount of fluid added by temper, on each level

- amount cured by ginger

- fluid required to temper each humour (how much is consumed upon doing so)

- fluid required/consumed by an inundate

- fluid added by mercury homunc

- rate of natural drain and when

- all wrack/truewrack balances, mana costs

- other relevant values

Need these maths.

Sena

I only did some very basic testing, to get an estimate of fluid values, nothing exact (I don't know how fast the drain tick is or how much is reduced per tick), but here's what I have.

Dropping back to normal fluids naturally (no ginger/antimony or anything else influencing fluid levels) after a single temper takes ~69 seconds.
Dropping back to normal fluids with constant ginger/antimony from a single temper takes ~17 seconds.
Dropping back to normal fluids naturally after a single mercury homunculus attack takes ~10 seconds (although I've heard that it was bugged then, so this might be wrong).

Caladbolg

The Damage formula on Kai Choke?

Sena

If anyone wants to kaichoke me, I'll test it.

Citrus

Some addition numbers for Blademaster stances:  I wanted to figure out what's the best when bashing and what the real difference in the damage vs time of all the stances was, trying to optimize my bashing.  Here are my numbers, with help from Sena and Eld's previous tests.


Assuming 12 strength and nimble trait:
Unbanded:
           DMG    SPEED    DPS
Thyr -   358   -    2.03    -   176
Mir -     404   -    2.72    -   148
Sanya- 450   -    2.24    -   200

Level 1 Band:
           DMG    SPEED    DPS
Thyr -   381   -    1.92    -   198 (+22)
Mir -     427   -    2.58    -   165 (+17)
Sanya- 473   -    2.12    -   223 (+23)

Level 2 Band:
           DMG    SPEED    DPS
Thyr -   404   -    1.86    -   217 (+19)
Mir -     450   -    2.53    -   177 (+12)
Sanya- 496   -    2.03    -   243 (+20)


So according to the data, Sanya comes out on top for the best, way better than Thyr in terms of damage and DPS.  Mir which is much weaker than both Thyr and Sanya, ever weaker than I had thought.  To test if these numbers were accurate I killed a mhun keeper in each stance: Mir, Thyr, and Sanya. Note: I did this test with a level 1 band.

             Hits to kill     -     Time to kill (If no criticals)
Thyr   -       24            -          46 seconds
Mir     -       21            -          54 seconds
Sanya-       19            -          40 seconds

Trevize

Citrus said:

Some addition numbers for Blademaster stances:  I wanted to figure out what's the best when bashing and what the real difference in the damage vs time of all the stances was, trying to optimize my bashing.  Here are my numbers, with help from Sena and Eld's previous tests.


Assuming 12 strength and nimble trait:
Unbanded:
           DMG    SPEED    DPS
Thyr -   358   -    2.03    -   176
Mir -     404   -    2.72    -   148
Sanya- 450   -    2.24    -   200

Level 1 Band:
           DMG    SPEED    DPS
Thyr -   381   -    1.92    -   198 (+22)
Mir -     427   -    2.58    -   165 (+17)
Sanya- 473   -    2.12    -   223 (+23)

Level 2 Band:
           DMG    SPEED    DPS
Thyr -   404   -    1.86    -   217 (+19)
Mir -     450   -    2.53    -   177 (+12)
Sanya- 496   -    2.03    -   243 (+20)


So according to the data, Sanya comes out on top for the best, way better than Thyr in terms of damage and DPS.  Mir which is much weaker than both Thyr and Sanya, ever weaker than I had thought.  To test if these numbers were accurate I killed a mhun keeper in each stance: Mir, Thyr, and Sanya. Note: I did this test with a level 1 band.

             Hits to kill     -     Time to kill (If no criticals)
Thyr   -       24            -          46 seconds
Mir     -       21            -          54 seconds
Sanya-       19            -          40 seconds

What about Arash and Doya, just for completeness?

Citrus

Trevize said:

What about Arash and Doya, just for completeness?

I've only got the numbers with a level 1 band:
           DMG    SPEED    DPS
Doya  -   496   -    2.61    -   190
Arash -   519   -    2.02    -   256

But as you can see Doya is only slightly less damaging than Thyr.  Arash is very strong, giving about 15% more DPS than Sanya, however at that large cost of decreased defense.

Eld

My numbers from the last time I tested, with nimble and no band:

Stance  Trials  Mean    Std dev
neutral  400     2.228   0.091  
Thyr      338     2.033   0.079  
Mir        605     2.724   0.100  
Sanya   600     2.241   0.080  
Doya    600     2.752   0.084  
Arash   604     2.129   0.086  

For DPS, assuming 12 str, that gives:
neutral: 191
Thyr: 176
Mir: 149
Sanya: 201
Doya: 172
Arash: 238


I'm a bit surprised that Sanya comes out so much better than Thyr/Doya, but other than that it's about what I'd expect.

Edit: aaand just realised I'd already posted these numbers.

Eld

And just for completeness, finally got around to testing with a level 3 band:

Stance    hits    mean    std dev
neutral    300        1.928    0.091
Thyr    250        1.727    0.061   
Mir        300        2.427    0.076
Sanya    430        1.924    0.060
Doya    306        2.419    0.082
Arash    312        1.823    0.060

Looks to me as though things are consistent with a base time of 2.5s, with a 10% reduction for Thyr, 5% for Arash, and 20-25% increase for Doya and Mir, and a 5/10/15% reduction for a band, all stacking multiplicitavely.

Caladbolg

Also consider the faster you attack the better chance you have of critting and finishing the mob.

Eld

So I got curious about the effect of crits in translating from straight DPS to average time required to kill a thing. Caladbolg's statement above seems to be true, at least up to a point: at the low damage/high speed end, getting slower and stronger hurts up to a point, and then starts getting better again. It's all very dependent on crit rate, of course (faster attacks being more favoured at higher crit rates), and I suspect dependent enough on your damage rate compared to the health of the mob you're fighting to make it difficult to make blanket statements. Some numbers, though, spoilered to spare those who don't care:
[spoiler]
Assuming a denizen with 10000  max health, with a crit rate of 20% (~level 84):

250 damage at 1.00 seconds per attack: base DPS 250.00
30.39 +/- 0.14 seconds per kill

500 damage at 2.00 seconds per attack: base DPS 250.00
31.15 +/- 0.16 seconds per kill

750 damage at 3.00 seconds per attack: base DPS 250.00
33.07 +/- 0.19 seconds per kill

1000 damage at 4.00 seconds per attack: base DPS 250.00
32.02 +/- 0.20 seconds per kill

1250 damage at 5.00 seconds per attack: base DPS 250.00
31.91 +/- 0.22 seconds per kill

1500 damage at 6.00 seconds per attack: base DPS 250.00
33.81 +/- 0.23 seconds per kill

1750 damage at 7.00 seconds per attack: base DPS 250.00
34.38 +/- 0.24 seconds per kill

2000 damage at 8.00 seconds per attack: base DPS 250.00
33.01 +/- 0.24 seconds per kill

Same setup, but a crit rate of 42.5% (dragon with L1 pendant):

250 damage at 1.00 seconds per attack: base DPS 250.00
17.17 +/- 0.20 seconds per kill

500 damage at 2.00 seconds per attack: base DPS 250.00
18.96 +/- 0.23 seconds per kill

750 damage at 3.00 seconds per attack: base DPS 250.00
21.08 +/- 0.26 seconds per kill

1000 damage at 4.00 seconds per attack: base DPS 250.00
21.34 +/- 0.26 seconds per kill

1250 damage at 5.00 seconds per attack: base DPS 250.00
21.78 +/- 0.28 seconds per kill

1500 damage at 6.00 seconds per attack: base DPS 250.00
24.38 +/- 0.29 seconds per kill

1750 damage at 7.00 seconds per attack: base DPS 250.00
25.80 +/- 0.29 seconds per kill

2000 damage at 8.00 seconds per attack: base DPS 250.00
24.85 +/- 0.29 seconds per kill
[/spoiler]

Applied specifically to the blademaster stance question, this effect isn't large enough to make up for the difference in DPS between Thyr and Sanya, though at high levels and high damage the difference isn't nearly as large:
[spoiler]
10000 health denizen, 20% crit

No band, Thyr, 12 str
358 damage at 2.03 seconds per attack: base DPS 176.35
43.78 +/- 0.20 seconds per kill

No band, Sanya, 12 str
450 damage at 2.24 seconds per attack: base DPS 200.89
39.88 +/- 0.20 seconds per kill

L3 band, Thyr, 12 str
427 damage at 1.73 seconds per attack: base DPS 246.82
32.01 +/- 0.17 seconds per kill

L3 band, Sanya, 12 str
519 damage at 1.92 seconds per attack: base DPS 270.31
29.94 +/- 0.16 seconds per kill

No band, Thyr, 14 str
403 damage at 2.03 seconds per attack: base DPS 198.52
39.14 +/- 0.19 seconds per kill

No band, Sanya, 14 str
507 damage at 2.24 seconds per attack: base DPS 226.34
34.72 +/- 0.19 seconds per kill

L3 band, Thyr, 14 str
481 damage at 1.73 seconds per attack: base DPS 278.03
28.05 +/- 0.15 seconds per kill

L3 band, Sanya, 14 str
584 damage at 1.92 seconds per attack: base DPS 304.17
26.83 +/- 0.15 seconds per kill

10000 health denizen, 42.5% crit rate

No band, Thyr, 12 str
358 damage at 2.03 seconds per attack: base DPS 176.35
25.73 +/- 0.31 seconds per kill

No band, Sanya, 12 str
450 damage at 2.24 seconds per attack: base DPS 200.89
23.48 +/- 0.29 seconds per kill

L3 band, Thyr, 12 str
427 damage at 1.73 seconds per attack: base DPS 246.82
19.38 +/- 0.23 seconds per kill

L3 band, Sanya, 12 str
519 damage at 1.92 seconds per attack: base DPS 270.31
18.28 +/- 0.22 seconds per kill

No band, Thyr, 14 str
403 damage at 2.03 seconds per attack: base DPS 198.52
22.84 +/- 0.28 seconds per kill

No band, Sanya, 14 str
507 damage at 2.24 seconds per attack: base DPS 226.34
21.23 +/- 0.25 seconds per kill

L3 band, Thyr, 14 str
481 damage at 1.73 seconds per attack: base DPS 278.03
17.21 +/- 0.21 seconds per kill

L3 band, Sanya, 14 str
584 damage at 1.92 seconds per attack: base DPS 304.17
16.61 +/- 0.21 seconds per kill

[/spoiler]

Sena

Tested kai choke a bit, it looks like it's simply 25% of max health (before int bonus and other modifiers).

I'm not 100% certain, though. Seeing choke at 12 int without a scimitar would help a lot.