LC Rolls explained

Used links :
http://www.smogon.com/bw/articles/bw_complete_damage_formula
http://pokemonshowdown.com/damagecalc/

EDIT : ok i'll be clear this time, i call this a math post bc this is about calculations but if you are unable to multiply something by 1.5 and to take the entire part you are dumb af so don't run away from this thread please

Damage Calc Thread said:
BaseDamage = ((((2 × Level) ÷ 5 + 2) * BasePower * [Sp]Atk) ÷ [Sp]Def) ÷ 50 + 2
= 4*BP*Atk/Def/50 +2 = BP/12.5 * Atk/Def + 2

Apply the multi-target modifier
Apply the weather modifier
In case of a critical hit, double the value
Alter with a random factor
Apply STAB modifier
Alter with type effectiveness
Alter with user's burn
Make sure damage is at least 1
Apply the final modifier
This is the same in XY except that critical hits do x1.5

As i know nothing about math language in english and this is a translation (edit : +upgrade now) of my french thread in english i'll define here the words i use:
ROUND DOWN = take the entire part : 2,4 -> 2 (edit : apparently it's "truncate")
ROUND = take the closest entire number : 2,4 -> 2 ; 2,7 -> 3

And i don't know smogon codes either so this will be an ugly black on white thread

So since this is supposed to be a simple thread so we'll use a simplified formula :

Calc the base damages
ROUND DOWN
Apply random factor (random factor is a number randomly chosen between 0.85 and 1, it can be 0,85 ; 0,86 ... ; 0,99 ; 1. 16 rolls, the 16 rolls you see when calcing damages : (22, 24, 24, 24, 24, 24, 24, 24, 26, 26, 26, 26, 26, 26, 26, 28) )
ROUND DOWN
Apply critical hit modifier
ROUND DOWN
Apply STAB modifier
ROUND DOWN
Apply Effectiveness
ROUND DOWN (only necessary if it was an uneffective attack)
If LO, Apply x1.3 modifier
ROUND
and not round down, yes devs were high this day

Consequences :

Rolls in LC has 1/16 of making more damages than usual. I will call this the "super roll"

Explanation :
When you calc the base damages, you obtain a number. Let's say 7,56. You round down, so you get 7.
Now you apply the random factor. The 15 first possibilites are between 0.85 and 0.99 included. So it will give something strictly under 7. And you round down again after the random factor ! So The 15 first possibilities will always do at least 1 damage less than the super roll which remains untouched, thus, remains at 7.
236+ Atk Mold Breaker Drilbur Earthquake vs. 236 HP / 0 Def Eviolite Wynaut: 13-16 (44.8 - 55.1%) -- 43.8% chance to 2HKO
(13, 13, 13, 13, 13, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16)
^ notice the 16

This is why there are SO MANY "6.3% chance to OHKO" when calcing damages. It means that only the super roll will OHKO.



Fun result : any attack can do 2 damages when not undereffective/burned/this kind of things.
Explanation :
Since the formula is 2 + something, if the something is absolutely ridiculous, you will round down at 2. but at 2, not at one. so after altering with the random factor, one of the 16 rolls will remaing at 2, even if it is a damn -6 level 1 combee attacking 252/252+ level 100 arceus :
-6 0- Atk Combee Rapid Spin vs. 252 HP / 252+ Def Arceus: 1-2 (0.2 - 0.4%) -- possibly the worst move ever
(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2)



A stabbed attack will never do "3k+2" damages.
Explanation :
Here's a calc of a Flying type Drilbur EQing wynaut :
236+ Atk Mold Breaker Drilbur Earthquake vs. 236 HP / 0 Def Eviolite Wynaut: 9-11 (31 - 37.9%) -- 71% chance to 3HKO
(9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11)

Now, with the ground type :
236+ Atk Mold Breaker Drilbur Earthquake vs. 236 HP / 0 Def Eviolite Wynaut: 13-16 (44.8 - 55.1%) -- 43.8% chance to 2HKO
(13, 13, 13, 13, 13, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16)
Where's the 14 ?

^ coming back at the formula : when you apply x1.5, you round down again.
Thus in this case :
9->13.5->13
10->15
11->16.5->16
Thus, no 14.

Because of this there are some number of hp you cannot inflict when using a stabbed attack : these are those who have no root by x l->E(1.5*x)
And these are the " 3k+2 " numbers : 2, 5, 8, 11, 14, 17, 20, 23, 26...

No point, then, trying to raise your hp one point upper in hope of tanking a specific stabbed attack when it is one of these numbers : it won't help (except if rocks, etc, etc)



A super effective / hyper effective attack will do 2k / 4k damages
Explanation/Consequences :
Effectiveness, unless you have a LO, is applied at the end of the damage calculation. Thus, it is multiplied by 2 or 4. Thus, it gives 2k / 4k numbers :

• Onix 20 HP : 0 SpA Fletchling Hidden Power Grass vs. 0 HP / 76 SpD Onix: 20-24 (100 - 120%) -- guaranteed OHKO
(20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 24)

236+ Atk Mold Breaker Drilbur Earthquake vs. 0 HP / 0 Def Onix: 18-24 (90 - 120%) -- 81.3% chance to OHKO
(18, 18, 18, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 24)

Because of this, when having mon having a x4 number of hp, it is really important to get one hp more. It completely changes the your odds of survival against x4 attacks.
Thus, cottonee changes its probability of surviving chinchou's hp poison from 0% to 94% by taking one hp more.
Onix changes it from 15% to 95% when getting hit by drilbur's eq.

And finally, pawniard's natural 21 hp protects him from low power fighting attacks such as foongus' hp fight. Which is why you need rocks to take down pawniard with this kind of tricks. Yes, rocks to take down a steel type. Welcome to LC maths.



The initial damages formula is 2 + something depending of your attack and ennemy's defense
Consequences :


-> Answer to the question every single LC player asked itself : why does 2 shadow sneak from honedge kills misdreavus when one shadow sneak at +2 doesn't
196+ Atk Honedge Shadow Sneak vs. 36 HP / 0 Def Eviolite Misdreavus: 12-14 (52.1 - 60.8%) -- guaranteed 2HKO
(12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 14)

+2 196+ Atk Honedge Shadow Sneak vs. 36 HP / 0 Def Eviolite Misdreavus: 18-24 (78.2 - 104.3%) -- 6.3% chance to OHKO
(18, 18, 18, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 24)

There are two causes : The rounding down post STAB, and the base damages. The damages before stab, effectiveness, etc, are low af (between 4 and 8 depending on +0 or +2). This is enough to consider that eh random factor removes 1 damage.

So we have the damages being 1 + something depending of attack. Actually the something depending of attack is 3.
1+3 = 4 -> 6 (STAB) -> 12 (effectiveness)
1+3*2 (bc +2) = 7 -> 10.5 (STAB) -> 10 (round down) -> 20 (effectiveness)
the 1 initial damage brings 3 damages undepending of attack at this end, and the round down on STAB makes the +2 attack lose 1 damage. So the +2 attack has 4 damages less than what we would expect : 12 * 2


-> Why is Aipom worth S+ tier (ok, A)
Now i can share my discovery with the world <3
So, what if we abuse the fact initial damages in lc count bc of the low hps by using a skill linked attack ? And what if we make it stabbed ? It creates a monstruosity :D

• Return : 102 de BP
196 Atk Aipom Return vs. 0 HP / 36 Def Eviolite Mienfoo: 10-13 (47.6 - 61.9%) -- 93.8% chance to 2HKO
(10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13)

• Double Slap : 80 BP (with skill link)
196 Atk Aipom Double Slap (5 hits) vs. 0 HP / 36 Def Eviolite Mienfoo: 15-20 (71.4 - 95.2%) -- guaranteed 2HKO
(3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4)

(showing double slap over fury swipes to increase contrast)

yep, you're actually spectating an attack with 22 BP less doing far more damages than return. And nearly the same as last resort.
Why ? Back to formula !
Take the initial formula. Consider it's 1+something with +1 for the super roll (the damages are too low for random factor making it lose more than 1)
Three cases :

"something" is in [0,1[ -> f*ck, it's rounded down at 1, Stab brings it at 1.5 .... which means rounded down at 1 ... and you end up doing 5 damages. well that's shit. This will happen for targets having 24 def or more when using jolly (adamant will also hit 16 def + eviolite targets)

"something" is in [1,2[ (nearly always) -> it's rounded down at 2. Stab brings it at 3. And thus, Aipom ends up doing AT LEAST 15 damages to any target having less than 24 def. which means 2HKO every single pokemon that doesn't resist / doesn't have tons of dam...armor. a 19 speed with better defensive stats than mienfoo with insane coverage 2HKOing every pokemon in the tier, nobody has a problem ? no ? then, to next part

"something is in [2,3[ -> 20 damages. 47.5% chance to do at least 22 damages. this happens, on jolly aipom, for targets with 11 def or less, and on adamant, 12 def or less. which means any sweeper without eviolite.
... Has anybody a probem with the fact adamant aipom has 47% chance to win the 1v1 with offensive mienfoo, without fake out ? (considering he spams dpunch and doesn't fail anticipate ofc)

Now, you can go look Planet of the Apes again. Never underestimate a monkey in the hands of scientists.




now are you able to use what you learnt to calc simple damages by head ?
If you followed everything correctly, you should be able to guess every single roll of a life orb 0 satk carvanha using hp poison against little sdef cottonee.
0 SpA Life Orb Carvanha Hidden Power Poison vs. 36 HP / 36 SpD Eviolite Cottonee: 21-26 (100 - 123.8%) -- guaranteed OHKO
(21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 26)

Damages are 1+something with +1 for super roll. Cottonee SpD isn't high and Carv Satk isn't shit so we can guess the something is 3.
(4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5)
x4 effectiveness :
(16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 20)
Life Orb :
16*1.3 = 20,8 ~ 21
20*1.3 = 26
-> (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 26)

if you found, you won't need as often to check the calculator !



Why is Choice Band / Choice Specs inferior by far in most cases to the Life Orb ?
1) LO and Choice Band are two completely different items in damages calcs.

BaseDamage = ((((2 × Level) ÷ 5 + 2) * BasePower * [Sp]Atk) ÷ [Sp]Def) ÷ 50 + 2
= 4*BP*Atk/50Def +2
= ( BP/12.5 * Atk/Def ) +2 (simpler said like that)

Choice Band affects the damage calculation in the "BP/12.5 * Atk/def" part.
LO affects the damage at the very end of the process.


Because of this, the damages actually created by the Choice Band can be reducted by truncations (i hope this is english ?) when : Simply calcing the damages ; Applying STAB ; Applying unefficacity ; and Applying other things like burns. But this is out of the subject.

To sum it up, Choice band struggles everything the base damage struggles, and it's always a loss as only round downs are made.

Which isn't the case for the Life Orb : Life Orb takes the final damages and rounds. Not truncates, rounds.

Also, if your attack stat is a 2k+1 number, choice band will only bring k attack which means a 0.5 attack loss. Not much, but still, many little losses make a big loss.

2) Choice Band directly affects attack, and damages "can be considered as" 1+something depending of attack.
This means Choice Band doesn't affect the initial 1. This can be very important for low power moves.

Note : i don't call "low power moves" move doing low damages. STAB and efficacity aren't to be considered. Honedge shadow sneak on missy isn't 120 BP, it's 40 BP, then you do calcs on that.

An exemple : Jolly Aipom (yeah Aipom's like THE exemple for doing calcs)'s Fury swipes on 21 def target.
BaseDamage = 2+1.1 -> 3
after random factor, stab, it does 3 damages.

If you have a Choice band, the attack depending part (1.1 here) will increase to 1.65. ... and be rounded down to 3. Choice band will be like, inexistent.

While LO, coming at the end of the battle, just takes the 3 damages, and raises them to 3.9 -> 4 damages.
This is however an extreme case, Choice Band will generally do one or 2 damages more ... but it's really not worth it.

Add this to the fact LO doesn't lock you on one attack, and that in LC mon only lose 2 hp when having 20-29 hp ; 1 when having 1-19 hp ; which means it costs 8-9% (or 5% !) instead of 10%, and the LO is by far superior to the choice band.

A randomly taken roll :

236+ Atk Choice Band Mold Breaker Drilbur Earthquake vs. 0 HP / 196 Def Eviolite Mienfoo: 15-18 (71.4 - 85.7%) -- guaranteed 2HKO
(15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 18)
(I LOVE HITTING MIENFOOS)

236+ Atk Life Orb Mold Breaker Drilbur Earthquake vs. 0 HP / 196 Def Eviolite Mienfoo: 13-17 (61.9 - 80.9%) -- guaranteed 2HKO
(13, 13, 13, 13, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17)

In red : LO > CB
In blue : BC > LO


Last but... yes, least part : why do i keep mentionning "47%" or "27%"
Chance to crit is 1/16.
Chance to super roll is 1/16.
When using a multi hit move, you get 5 attempts for each.
So you have 1-(15/16)^10 = 0.47 chance to get at least one super roll / one crit. (which is necessary for aipom to do 22 damages at least instead of 20)

Out of LC result :
Around 27% chance to do at least one crit in 5 attempts (usefull on cloyster and such)


and uh
well it's over, gimme presentation tips please because it probably looks really ugly without titles, bold, colors, etc

Fowl
 
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Very well-explained. One thing I think you should note is that because Life Orb damage rounds (rather than truncates), it will always do more damage on multi-hit moves than Choice items, and will often match the power of a choice item for single-hit attacks (with few exceptions, limited to particular cases, rather than in general). This is the reason why Life Orb is so much more common than Band/Specs.
 

Jac

someday... the dream will end.
is a Battle Simulator Moderator Alumnus
Brilliant thread explaning things i have no grasp over.

Definitely using Aipom/Minccino a lot more now
 

Rowan

The professor?
is a Forum Moderator Alumnusis a Community Contributor Alumnusis a Tiering Contributor Alumnusis a Contributor Alumnus
This is actually really useful, especially for helping calculate defensive EV spreads, thanks :)

Also, multi hits are fucking weird, especially as you said on the bulkier Pokemon: check these out:

196 Atk Life Orb Aipom Double Slap (5 hits) vs. 212 HP / 196+ Def Eviolite Spritzee: 5-20 (18.5 - 74%) -- approx. 0.4% chance to 2HKO
(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4)

then after knock of...

196 Atk Life Orb Aipom Double Slap (5 hits) vs. 212 HP / 196+ Def Spritzee: 20-25 (74 - 92.5%) -- guaranteed 2HKO
(4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5)

same thing happens with Bulky Mienfoo. Bulky Mienfoo is 22 Def after Eviolite.

196 Atk Life Orb Aipom Double Slap (5 hits) vs. 156 HP / 196+ Def Eviolite Mienfoo: 5-20 (21.7 - 86.9%) -- approx. 12.1% chance to 2HKO
(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4)

then after knock off...

196 Atk Life Orb Aipom Double Slap (5 hits) vs. 156 HP / 196+ Def Mienfoo: 20-25 (86.9 - 108.6%) -- approx. 6.3% chance to OHKO
(4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5)

It seems as if for LO Aipom to do large damage with Double Slap opponents need less than 20 Def.

However, Fury Swipes, needs opponents to have Def less than 24:

196 Atk Life Orb Aipom Fury Swipes (5 hits) vs. 156 HP / 196+ Def Eviolite Mienfoo: 20-25 (86.9 - 108.6%) -- approx. 6.3% chance to OHKO
(4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5)

______________

However, Minccino doesn't need as much Knock Off support due to its higher base power move

196 Atk Life Orb Minccino Tail Slap (5 hits) vs. 212 HP / 196+ Def Eviolite Spritzee: 20-25 (74 - 92.5%) -- guaranteed 2HKO
(4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5)

then after knock off... nothing happens.

196 Atk Life Orb Minccino Tail Slap (5 hits) vs. 212 HP / 196+ Def Spritzee: 20-25 (74 - 92.5%) -- guaranteed 2HKO
(4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5)

Minccino needs the opponent to have a defense of less than 30 to do good damage with Life Orb (excluding resists ofc) and nothing that doesn't already resist runs that so Minccino might be the better initial wallbreaker. However, due to Aipom's 1 more speed point and access to Knock Off regardless I'm not sure which is better overall.


tl;dr
Aipom's Double Slap needs the opponent to have a Defense less than 20 to be useful (with LO)
Aipom's Fury Swipes needs the opponent to have a Defense less than 24 to be useful (with LO)
Minccino's Tail Slap needs the opponent to have a Defense less than 30 to be useful (with LO)
(all excluding resists)

Aipom should get Tail Slap. :'(
 
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the calculator doesn't have fury swipes implemented, so when you see a calc with Aipom + Tail Slap, it's a Fury Swipes (a Tail Slap handmade 18 power)
--

Wanted to answer the posts, then a thunder started and i had to cut off internet :( I should get an Electivire.

Kappaten said:
Very well-explained. One thing I think you should note is that because Life Orb damage rounds (rather than truncates), it will always do more damage on multi-hit moves than Choice items, and will often match the power of a choice item for single-hit attacks (with few exceptions, limited to particular cases, rather than in general). This is the reason why Life Orb is so much more common than Band/Specs.
This is mainly true, i'll soon add a part about why is LO nearly as strong as choice band, however "it will always do more damage on multi-hit moves than Choice items" -> your always is wrong

I didn't write an entire part about LO so i'll summarize here : LO and Choice Band are two completely different items in damages calcs.

BaseDamage = ((((2 × Level) ÷ 5 + 2) * BasePower * [Sp]Atk) ÷ [Sp]Def) ÷ 50 + 2
= 4*BP*Atk/50Def +2
= ( BP/12.5 * Atk/Def ) +2 (simpler said like that)

Choice Band affects the damage calculation in the "BP/12.5 * Atk/def" part.
LO affects the damage at the very end of the process.

For exemple i'll take the part of Aipom hitting 16 def Spritzee.
Base Damage = (18/12.5 * 16/24) + 2 = 0.96 +2 = 2.96
Truncate -> 2
Random factor -> 1 (super roll stays at 2)
At this point, the damage calculation is a complete fail for Aipom, you can apply the STAB, 1 -> 1.5 -> 1 , you can apply the life orb, 1 -> 1.3 -> 1, it will stay at 1. (except for the super roll which goes from 3 to 4)

196 Atk Life Orb Aipom Fury Swipes (5 hits) vs. 212 HP / 196+ Def Eviolite Spritzee: 5-20 (18.5 - 74%) -- approx. 0.4% chance to 2HKO
(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4)

when the damages go down to 1, you "can't escape" the 1.

However, with Choice band, the 0.96 depending of attack will be multiplied by 1.5, making it 1.44, rounded down at 1.
Then 3 becomes 2 with random factor, and 3 with STAB.

196 Atk Choice Band Aipom Fury Swipes (5 hits) vs. 212 HP / 196+ Def Eviolite Spritzee: 15-20 (55.5 - 74%) -- guaranteed 2HKO
(3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4)

--

everything (life orb put apart) depends of the "BP/12.5 * Atk/Def" part.
As Cork stated, Jolly Aipom needs opponent to have less than 24 def.
This is because : 18/12.5 * 16/24 = 0.96 ; and 18/12.5 * 16/23 = 1.001
it's all about what you lose by rounding down.

Notice than to get 5 damages more at the end, you need the attack/def depending part to double !
Aipom needs opponent to have 22 def or less to deal 15 damages ? He needs them to have 11 def or less to deal 20. Or to be +2.... which explain why you should NOT use Choice Band !
Which is why Aipom looked to me at first as not needing attack, but numbers are mean, he exactly needs full atk to hit the meta :( If he got Tail Slap, you could play Aipom with 0 atk and 2HKO the world.

Your results about knock off make sense cork as knocking off the eviolite result in multiplying the BS/12.5*Atk/Def part by 1.5 (by dividing def by 1.5)
Everything about gaining damages with low power move is about making the Atk/Def get higher than a entire number.


I actually used this to seek for the changes when you use Adamant Aipom over Jolly one, when you obtain something slightly over an entire number it means you win one (or two if stab) damage
BS/12.5 * Atk/Def
18/12.5 * 17/24 = 1.02 > 1 => Adamant will do 15 damages to full def porygon/spritzee
40/12.5 * 17/18 = 3.02 > 3 => Adamant will do 2 (in this case) damages more to 12 def + eviolite targets (such as offensive foo)
18/12.5 * 17/12 = 2.04 > 2 => Adamant will do 20 damages to 12 def knocked off targets (such as offensive foo, once again)


Btw imo Aipom is still far better than Minccino. Adamant Aipom is an upgraded Minccino, with insane movepool (knock off ; brick break ; fake out ; u-turn ; element punches ; gunk shot ; taunt ; twave). It also has 2 defs point more (so 3 after evio) which makes it more bulky than Mienfoo (kills me when i see analysis crying about Aipom's frailness, 55/55/55 ?..)
there's like 0 reason to use minccino over aipom unless you want to win 5% accuracy.



EDIT : (i doubt double post is allowed so ..)
Hugely edited first post : two parts added, one about LO and one about probas when using skill link attacks. Presentation enhanced with color/bold/underline. Clear Formula for LC added at the top of the thread.
 
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For someone familiar with other metas' but new to little cup, this is very helpful. I didn't realize little cup calcs were this different from standard lvl 100 metas. It makes a lot of sense and is written so that those of us without math degrees can read it (though, as you said, there isn't too much hard math.) Props to you.
 

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