Pre-Sequel Formula for the Roll to apply Elemental Effect (WIP)

(a.k.a chance to add freeze/corrosive/electric or fire DOT on target. Work in progress since there are a lot more tests that need doing …)

A few observations

  • because the weapon/grenade granted elemental DOTs still DON’T benefit from the greatly enhanced elemental damage multipliers in TPS (so still negligible damage) this is mostly about chance to Freeze (and in Borderlands 2 about chance to slag) ; Crit damage Type A goes up by 200% per number of frozen targets.
  • speaking of freeze, it doesn’t have great odds vs any defense type (unlike electric semi-guaranteed vs shields, fire very high vs health). And three times lower vs shields than vs health and armor.
  • the actual chance used per projectile is hard to put on the weapon’s card because the some of the target’s parameters are factors, thus it will vary depending on what you’re shooting at ( defense type, level difference, ).
  • level difference has a MASSIVE impact on the chance to apply elemental effects.
  • Logging the value used and WHEN such rolls to apply the elemental effect even occur is still game-play VERY Relevant information. A LOT of character skills & Gear (much more than in Borderlands 2) revolve around altering various of those dice rolls to apply the elemental effects - if one doesn’t know how they work - how can they judge and compare their effectiveness relative to say damage related skills ?
  • the chance to apply elemental effect displayed on the weapon’s gun is not a full blown lie, but is just a small factor in the calculation of the chance to apply elemental effects
  • splashes don’t use the % as the main impact
  • other (non-gun) sources of elemental damage such as grenades, nova shields, spike shields don’t take into consideration ALL of player stats/gear/perks that increase the odds to apply the elemental effect
  • ATHENA’s storm Weaving seems to be absolutely, positively capable of achieving 100% freeze chance at level parity (1 shot !) with certain weapons and the chronicler of elpis. (Maybe even without it)
  • Aurelia’s avalanche is quite strong at high levels AND also ups the chance to freeze for shard, grenades, nova, etc …
  • Claptrap’s maniacal laughter doesn’t add that much (especially at 5/5 20% for the much better chronicler COM). Still with the proper weapons he has an easier than Wilhelm time to reach high freeze chance.
  • cold war on Wilhelm with non cold weapon is un-reliable, happy accidents. Maxed cold war (5/5) with Chronicler of Elpis [ takes F9 from 1.49 to 1.59] and high chance cold weapon can bring him close to very short times to freeze times (maybe even 1 shot) vs health and/or armor. Probably not. Doesn’t seem to add that much. I don’t really know yet what the highest chance to freeze (legendary) weapons exist.
  • still to test a lot of skills granting splash like damage (we know Aurelia’s Wintertide can freeze and loves Avalanche/Chronicler)
  • list of Abilities that add splashes that trigger/don’t trigger extra freeze roll check ( YES : Aurelia Wintertide ; NO: Jack : Integrity )

Formula:

Chance To Apply Elemental Effect = CTAEE

CTAEE = F1 * F2 * F3 * F4 * F5 * F6 * F7 * F8 * F9 * F10

That’s right 10 factors ! I don’t know a lot about all of them yet, more tests will explain/edit in more in the future.

F1: (enemy resistance to the application of the elemental effect)

This is usually 1. I’ve seen this at 0.1 when attempting to freeze a glacial enemy. Not impossible, just 10 times harder. I’ve seen it at 0 when using fire dot vs darksiders (immune to fire DOT) .

F2: (base chance to apply effect of element type vs defense type) (TVHM mode tested)

Cold (15 vsHealth, 15 vsArmor, 5 vsShield)
Fire (30 vsHealth, 15 vsArmor, 15 vsShield)
Electric (15 vsHealth, 15 vsArmor, 75 vsShield)
Corrosive (15 vsHealth, 30 vsArmor, 15 vsShield)

F3: (??)

Never seen this other than 1 yet.

F4: A * B

Yup, this one is a bit hard to explain.

A: (Semi-)hidden weapon parameter
In some cases one can sort of infer it reading on the weapon card. (doing some napkin math on it).
Most sniper rifles will have this at 1 and the card will show 30%.
Most Maliwan snipers will have 1.25 . Card shows 30 * 1.25 = 37.5%.
Where is this 30 coming from ? (which is a different value for different weapon classes …) .
F5 might give us an explanation (Card Value / ( 20 * gun class elemental chance application multiplier ) // this is NOT always correct; when the gun has multiple sources of elemental chance modifiers this is wrong).

Laser Railguns tend to have 2 here. Laser Splitters 0.(3). Laser Beams 0.4. Laser blaster (Maliwan) 0.6857… ?? Blaster Hyperion 0.5714 …
Unique weapons can have weird values here : Ex: Moxxi Vibro pulse 0.46
The various weapon parts can have elemental chance application modifiers.

Aurelia’s Bitter riposte has 100 * F9 here. (1 point freeze wonder).
Athena’s Prismatic Aspis has 100 here for all elements!! (pretty much guaranteed to apply elemental effects unless severe level difference , high resistance to the element)
Cold Jumping betties 1.2 ; vladoff cold 1.5.
Cold Spike shields have 3 here.
Cryo Novas from cryo nova Shields have 100 here …
Claptrap Rainbow Coolant novas have 999 here.
Elemental barrels have 100 here (pretty much guaranteed to apply elemental effects unless high resistance to the element)
Wilhelm’s Cold war used with Non-cold weapon types forces 100 here if separate dice roll to apply this succeeds.
ZX-1 legendary Has an extra dice roll per hit made with 100 !! value here.
Splash damage usually has some weird numbers here (don’t know formula …)

B: (1 + sum of +element chance effects) ) . This only works for guns ! (MAIN HAND ONLY WHEN GUNZERK)
The BAR elemental effect chance is added here. And the effects of skills such as ATHENA’s storm Weaving and Claptrap’s Maniacal Laughter.
COMs, Oz kits and skills that boost the chance to apply a SPECIFIC element type aren’t used here but make up F9.

F5: (gun class elemental chance application multiplier)
Sniper Rifle 1.5, Laser Beam 1.15 , Laser Splitter & Railgun & Blaster 1, Rocket Launcher 1, Pistol 0.6, SMG 0.5, Shotgun 0.4, Assault Rifle 0.3

F6: (Level Difference HUGE IMPACT!!)

lvl diff Attacker - Target and chance multiplier
-5 *0.1; -4 *0.3; -3 *0.5; -2 *0.7; -1 *0.9;+3 * 1.1; +4 *1.2 ; +5 *1.4 … +9 *2

F7: (??)

Bitter riposte has this <1.
Also splash-es usually have this <1 but in a in-consitant manner

F8: (??)

Never seen this other than 1 yet.

F9: (1 + sum of specific element chance bonus). This ALSO APPLIES TO NON-gun sources of elemental damage (aurelia’s shard, grenades, skill and shield granted novas & spike shields, …)

From COMs, Oz kits and skills.

Examples:
Chronicler or Elpis extra freeze chance, Claptrap’s Short Circuit extra electrocute COMs (overkill much ?).
Aurelia’s Avalanche skill. Wilhelm’s ColdWar skill ALWAYs ON ice damage (grenades, novas etc …).
Dual Oz kits can have extra Specific Elemental chance.

F10: (??)

Never seen this other than 1 yet.

Some test numbers

//cold war test. Sadly I don't have the Chronicler of Elpis for Wilhelm yet. Might get it tonight and edit the test.
// The machine (legendary SR ice version, used vs health, appropriate level, 8% extra chance to apply elemental effect BAR)
# Chance to trigger effect 1.0000 * 15.0000 * 1.0000 * 1.0800 * 1.5000 * 1.0000 * 1.0000 * 1.0000 * 1.0000 * 1.0000 = 0.2430 
//turn on cold war 10/10  Skill says +20% to cold weapons ; 50% on the other elementals. The 20% adds to F9.
# Chance to trigger effect 1.0000 * 15.0000 * 1.0000 * 1.0800 * 1.5000 * 1.0000 * 1.0000 * 1.0000 * 1.2000 * 1.0000 = 0.2916  

// using non cold weapon 
# Normal Hit = 1867.56189 using             TMP ; Scaled Base Gun Damage (CARD) = 1236.23608 ; Sum of Additive Gun Damage Multiplier    0.51068 (beware exceptions!! & AMP SHIELD)  
# Damage Type =     CORROSIVE ; ElementalMul = 1.00000; ( GrenadeMul = 1.08372 ); address =    9DBE018 
# vsShieldsMul 0.4; Intermediary Damage Value 1867.56189  
        110  9281113.000 Max   9280366.000 Cur  9281113.000 Prev      747.000 Damage   3CA37318 baseaddress   Captured Lost L     vsShield 
# Chance to trigger effect 1.0000 * 15.0000 * 1.0000 * 1.0800 * 0.6000 * 1.0000 * 1.0000 * 1.0000 * 1.0000 * 1.0000 = 0.0972  
# Chance to trigger effect 1.0000 * 5.0000 * 1.0000 * 100.0000 * 1.0000 * 1.0000 * 1.0000 * 1.0000 * 1.2000 * 1.0000 = 6.0000  


// ice vladoff grenade on Aurelia ; Frostbyte debuff integrated in the vs element multiplier; lvl 49 vs lvl 40
# Damage Type =          COLD ; ElementalMul = 1.36400; ( GrenadeMul = 1.08372 ); address =    9DBE018 
# vsHealthorArmorMul 1.56; Intermediary Damage Value 2556.62061  
         16  6781426.500 Max   6777438.000 Cur  6781426.500 Prev     3988.500 Damage   36E49B18 baseaddress   Captured Lost L vsHealthOrArmor 
# Chance to trigger effect 1.0000 * 15.0000 * 1.0000 * 1.3000 * 1.0000 * 2.0000 * 1.0000 * 1.0000 * 1.3735 * 1.0000 = 0.5357  

// aurelia's shard ; Frostbyte debuff integrated in the vs element multiplier ; lvl 49 vs lvl 40
# Damage Type =          COLD ; ElementalMul = 1.36400; ( GrenadeMul = 1.08372 ); address =    9DBE018 
# vsHealthorArmorMul 1.56; Intermediary Damage Value 1844.59729  
        360  6781426.500 Max   6778549.000 Cur  6781426.500 Prev     2877.500 Damage   36E49B18 baseaddress   Captured Lost L vsHealthOrArmor 
# Chance to trigger effect 1.0000 * 15.0000 * 1.0000 * 0.6867 * 1.0000 * 2.0000 * 1.0000 * 1.0000 * 1.3735 * 1.0000 = 0.2830  


// aurelia's bitter riposte 1/5 shard ; seems to Double dip F9.
# Damage Type =          COLD ; ElementalMul = 1.36400; ( GrenadeMul = 1.08372 ); address =    9DBE018 
# vsHealthorArmorMul 1.00; Intermediary Damage Value 4150.34375  
     119703    38035.766 Max     33885.422 Cur    38035.766 Prev     4150.344 Damage   4166C458 baseaddress    Lil' Darksider vsHealthOrArmor 
# Chance to trigger effect 1.0000 * 15.0000 * 1.0000 * 137.3500 * 1.0000 * 0.7000 * 0.9014 * 1.0000 * 1.3735 * 1.0000 = 17.8551 


//Claptrap with Purple Maliwan Sniper Rifle. 5/5 Maniacal laughter; Splash % is inconsistent.
# Normal Hit = 1697.50342 using      Corinthian ; Scaled Base Gun Damage (CARD) = 1801.31982 ; Sum of Additive Gun Damage Multiplier   -0.05763 (beware exceptions!! & AMP SHIELD)  
# Damage Type =          COLD ; ElementalMul = 1.00000; ( GrenadeMul = 1.08372 ); address =    9DBE018 
# vsHealthorArmorMul 1.00; Intermediary Damage Value 1697.50342  
      86828    16338.499 Max     14640.996 Cur    16338.499 Prev     1697.503 Damage   433BD5D8 baseaddress       Lil' Madman vsHealthOrArmor 
# Chance to trigger effect 1.0000 * 15.0000 * 1.0000 * 1.6000 * 1.5000 * 1.0000 * 1.0000 * 1.0000 * 1.0000 * 1.0000 = 0.3600  
# Damage Type =          COLD ; ElementalMul = 1.00000; ( GrenadeMul = 1.08372 ); address =    9DBE018 
# vsHealthorArmorMul 1.00; Intermediary Damage Value 848.75171  
         16    16338.499 Max     13792.244 Cur    14640.996 Prev      848.752 Damage   433BD5D8 baseaddress       Lil' Madman vsHealthOrArmor 
# Chance to trigger effect 1.0000 * 15.0000 * 1.0000 * 2.4000 * 1.0000 * 1.0000 * 1.0000 * 1.0000 * 1.0000 * 1.0000 = 0.3600  

...
# Chance to trigger effect 1.0000 * 15.0000 * 1.0000 * 2.4000 * 1.0000 * 1.1000 * 0.5982 * 1.0000 * 1.0000 * 1.0000 = 0.2369 

// aurelia's winter's veil nova 
TODO

Also I should take a look at the freezing slam damage chance to freeze.

Chronicler of elpis, Cold war, Avalanche … these things can maybe raise that slam freeze chance to very nice levels. Maybe Wilhelm’s extended slam range isn’t such a joke skill after all :slight_smile:

# Damage Type =          COLD ; ElementalMul = 1.00000; ( GrenadeMul = 1.45272 ); address =    DAAE018 
# vsHealthorArmorMul 1.00; Intermediary Damage Value 1792.75977  
       4531    18165.602 Max     10751.459 Cur    12544.219 Prev     1792.760 Damage   58D31A58 baseaddress       Lil' Madman vsHealthOrArmor 
# Chance to trigger effect 1.0000 * 15.0000 * 1.0000 * 4.0000 * 1.0000 * 1.0000 * 0.2250 * 1.0000 * 1.0000 * 1.0000 = 0.1350  
# Damage Type =          COLD ; ElementalMul = 1.00000; ( GrenadeMul = 1.45272 ); address =    DAAE018 
# Chance to trigger effect 1.0000 * 15.0000 * 1.0000 * 4.0000 * 1.0000 * 1.1000 * 0.7434 * 1.0000 * 1.0000 * 1.0000 = 0.4906  
# Damage Type =          COLD ; ElementalMul = 1.00000; ( GrenadeMul = 1.45272 ); address =    DAAE018 
# vsHealthorArmorMul 1.00; Intermediary Damage Value 1792.75977  
         31    20760.688 Max     18967.928 Cur    20760.688 Prev     1792.760 Damage   498E4758 baseaddress            Madman vsHealthOrArmor 
# Chance to trigger effect 1.0000 * 15.0000 * 1.0000 * 4.0000 * 1.0000 * 1.0000 * 0.4709 * 1.0000 * 1.0000 * 1.0000 = 0.2826  

there is a *4 in F4 but huge variance of F7 sort of kills hope. Perhaps jumping height ? Yes elpis could add *1.5 ; *1.6 Wilhelm ; * 2.3? Aurelia but even then the odds aren’t that great :frowning: . And where is this huge variance coming from , extra layer of RNG ??

EDIT: Holy Crap 100% chance to freeze slam (could higher altitude be the answer ?) No elpis no nothing
*8 in F4, high roll? in F7

 # Damage Type =          COLD ; ElementalMul = 1.00000; ( GrenadeMul = 1.45272 ); address =    DAAE018 
# vsHealthorArmorMul 1.00; Intermediary Damage Value 2694.04004  
       5594    18672.570 Max     15978.530 Cur    18672.570 Prev     2694.040 Damage   14B1FA18 baseaddress            Madman vsHealthOrArmor 
# Chance to trigger effect 1.0000 * 15.0000 * 1.0000 * 8.0000 * 1.0000 * 1.0000 * 0.8545 * 1.0000 * 1.0000 * 1.0000 = 1.0254  

// sadly no consistency
hit 3 guys on the same slam . Same damage , same  *8 in F4 YAY !  But F7 all over the place :(
# Damage Type =          COLD ; ElementalMul = 1.00000; ( GrenadeMul = 1.45272 ); address =    DAAE018 
# vsHealthorArmorMul 1.00; Intermediary Damage Value 4534.14160  
       3578    16792.535 Max     12258.394 Cur    16792.535 Prev     4534.142 Damage   58D36698 baseaddress            Madman vsHealthOrArmor 
# Chance to trigger effect 1.0000 * 15.0000 * 1.0000 * 8.0000 * 1.0000 * 1.1000 * 0.2650 * 1.0000 * 1.0000 * 1.0000 = 0.3498  
# Damage Type =          COLD ; ElementalMul = 1.00000; ( GrenadeMul = 1.45272 ); address =    DAAE018 
# vsHealthorArmorMul 1.00; Intermediary Damage Value 4534.14160  
         32    15100.007 Max     10565.865 Cur    15100.007 Prev     4534.142 Damage   58D37818 baseaddress            Madman vsHealthOrArmor 
# Chance to trigger effect 1.0000 * 15.0000 * 1.0000 * 8.0000 * 1.0000 * 1.2000 * 0.8997 * 1.0000 * 1.0000 * 1.0000 = 1.2955  
# Damage Type =          COLD ; ElementalMul = 1.00000; ( GrenadeMul = 1.45272 ); address =    DAAE018 
# vsHealthorArmorMul 1.00; Intermediary Damage Value 4534.14160  
         15   189362.625 Max    180588.250 Cur   185122.391 Prev     4534.141 Damage   58D34618 baseaddress       Fair Dinkum vsHealthOrArmor 
# Chance to trigger effect 1.0000 * 15.0000 * 1.0000 * 8.0000 * 1.0000 * 1.0000 * 0.3680 * 1.0000 * 1.0000 * 1.0000 = 0.4416  
# vsHealthorArmorMul 1.00; Intermediary Damage Value 1173.36658   

Could cryogenic exhausting manifold perform in a more predictable manner ?
Sadly much, much worse :frowning: *1 F4 ; same F7 variance.

Frozen shields nova HAS >100% chance to freeze.

# Damage Type =          COLD ; ElementalMul = 1.00000; ( GrenadeMul = 1.53372 ); address =   44D08018 
# vsHealthorArmorMul 1.00; Intermediary Damage Value 6081.64063  
      13812    14693.469 Max      3536.381 Cur     9618.021 Prev     6081.641 Damage   2BD34D98 baseaddress    Lil' Darksider vsHealthOrArmor 
# Chance to trigger effect 1.0000 * 15.0000 * 1.0000 * 100.0000 * 1.0000 * 1.1000 * 0.7817 * 1.0000 * 1.0000 * 1.0000 = 12.8974