BP of Multi-hit moves with Critical hits factored in.

Those who use multi-hit moves such as Bullet Seed may have noticed it already, they land critical hits more often then regular attacks. However since these critical hits are limited to one particular hit only the damage increase is disproportionally lower. As a result unlike regular moves, critical hits should be included when attempting to calculate the full potential damage of the multi-hit move. The increase in damage is easy to determine, every critical hit has the same power as 2 individual hits. For example a Breloom landing one Critical hit when hitting 4 times with Bullet Seed has the same damage output as if it would land 5 hits.

However determining the odds of landing one or more critical hits is far more difficult. That is why i've decided to do the calculations myself and post the results here as a reference for those who are interested.
Essentially what you are seeing here are the odds of having one particular ammount basepower everytime you use one of the listed moves with critical hits taken into account.

Bone Rush/Bullet Seed/Icicle Spear/Rock Blast/Sweep Slap's basepower (exact not at least!)

50 Basepower: 29.297%
2 consecutive hits 0 critical hits

75 Basepower: 31.372%
3 consecutive hits 0 critical hits + 2 consecutive hits 1 critical

100 Basepower: 18.495%
4 consecutive hits 0 critical hits + 3 consecutive hits 1 critical + 2 consecutive hits 2 critical

125 Basepower: 15.762%
5 consecutive hits 0 critical hits + 4 consecutive hits 1 critical + 3 consecutive hits 2 critical

150 Basepower: 4.374%
5 consecutive hits 1 critical hits + 4 consecutive hits 2 critical + 3 consecutive hits 3 critical

175 Basepower: 0.551%
5 consecutive hits 2 critical hits + 4 consecutive hits 3 critical

200 Basepower: 0.143%
5 consecutive hits 3 critical hits + 4 consecutive hits 4 critical

225 Basepower: 0.001%
5 consecutive hits 4 critical hits

250 Basepower: 0.0000158%
5 consecutive hits 5 critical hits



For pokemon with the ability Skill Link like Cloyster using Icicle Spear.

125 Base power: 72,458%
5 consecutive hits 0 critical hits

150 Base power: 24.14%
5 consecutive hits 1 critical hits

175 Base power: 3.18%
5 consecutive hits 2 critical hits

200 Base power: 0.215%
5 consecutive hits 3 critical hits

225 Base power: 0.007%
5 consecutive hits 4 critical hits

250 Base power: 0.000095%
5 consecutive hits 5 critical hits


For those who need to know what the odds are to do at least a certain ammount of damage, simply subtract all BP ammounts you don't need from 100%.
For example the chance of hitting with at least 100BP with Bullet seed is 100% - 29.297% - 31.372% = 39.331%
Or for Cloysters Icicle Spear hitting with at least 150 BP: 100% - 72,458 = 27.542%
 

breh

強いだね
very nice. this is always something that I'd wanted to see somewhere and this really should get its own page or something (or at least be displayed on the pages for the moves). Rather hilariously, 75 BP occurs more of the time on average than 50 bp... lol
 

BurningMan

fueled by beer
Mmh pretty cool to know that its is more likely to hit 75 BP rather than 50.
Still outside of Technician and Skill Link these moves will see little to no use.
 

chimpact

fire nation
is a Tiering Contributoris a Team Rater Alumnusis a Past SPL Champion
Maybe SD bullet seed shiftry would see some use, but I'm not so sure on that.

can Breloom ohko shandera with 3 hits from bullet seed when one is a crit?
 
This is awesome. I think it is a little bit more intuitive to the reader, however, if instead of "+" you put "or". Just a thought.
 
i used cloyster before and when i used it, i slapped on scope lens, which increases the chances of a crit.

with scope lens, each of the 5 attacks have a 12.5% chance to crit. that means a 62.5% chance that one of the attacks will crit. add in 1 shell smash, and I regularly converted 2HKOs to OHKOs. i know some people will say it's not worth it over something like life orb, but IMO it's something to think about.
 
You might also want to give the expected BP by weighting the damage with the probabilities.

It's just under 85 for non-skill link, for those interested.
 
An interesting situation that could arise from this is deciding whether to use seed bomb or bullet seed non-technician breloom and other less-used physical grass types lacking power whip. Bullet seed has an expected damage output of 84.1885, while seed bomb's is 85 (factoring in critical hits). However, there is a 39.331% chance of bullet seed have an effective power of >100 while there is only a 6.25% (chance of a critical hit) chance for seed bomb to do that. I would say both are very viable depending on how risk-averse you want to be.

Similar decisions need to be made when deciding between icicle spear and icicle drop on mamoswine (again, very close) and rock blast vs rock slide on many rock types.
 
While we're talking about hax on multi-hit moves, has anyone considered King's Rock on Cloyster? After 5 hits, the opponent only has a .9^5 = 59% chance of attacking. Its no Jirachi Iron Head or Togekiss Air Slash, but a 40% chance of flinching is still good, no?
 
While we're talking about hax on multi-hit moves, has anyone considered King's Rock on Cloyster? After 5 hits, the opponent only has a .9^5 = 59% chance of attacking. Its no Jirachi Iron Head or Togekiss Air Slash, but a 40% chance of flinching is still good, no?
Headbutt has a 30% flinch chance. With King's Rock, I believe that it goes up to 40%.

But that doesn't make Headbutt a good choice. And Icicle Spear still doesn't make King's Rock worth it.
 

breh

強いだね
An interesting situation that could arise from this is deciding whether to use seed bomb or bullet seed non-technician breloom and other less-used physical grass types lacking power whip. Bullet seed has an expected damage output of 84.1885, while seed bomb's is 85 (factoring in critical hits). However, there is a 39.331% chance of bullet seed have an effective power of >100 while there is only a 6.25% (chance of a critical hit) chance for seed bomb to do that. I would say both are very viable depending on how risk-averse you want to be.

Similar decisions need to be made when deciding between icicle spear and icicle drop on mamoswine (again, very close) and rock blast vs rock slide on many rock types.
TBH it matters far more for Breloom than mamo. Breloom has tech, which means that Bullet Seed is almost always better. On the flipside, mamo doesn't have tech (nor is it used as a pokemon, but that's another story) so it's better off using icicle drop.
 

Mario With Lasers

Self-proclaimed NERFED king
is a Forum Moderator Alumnusis a CAP Contributor Alumnus
Wait, but you're saying Icicle Spear has ~84 BP while Icicle Drop has 85+CH... Wouldn't Icicle Spear be better then? I'd give up on that 6.25% bonus damage rate for 10 more Accuracy and the chance of breaking Substitutes any day of the week.
 
Headbutt has a 30% flinch chance. With King's Rock, I believe that it goes up to 40%.

But that doesn't make Headbutt a good choice. And Icicle Spear still doesn't make King's Rock worth it.
I have actually had decent success with King's Rock Chillachino, it will not flinch as often as jirachi or togekiss, but sweep swap is much more powerful (especially with skill link when/if released) than air slash and iron head. It is definitely a legitimate option.

TBH it matters far more for Breloom than mamo. Breloom has tech, which means that Bullet Seed is almost always better. On the flipside, mamo doesn't have tech (nor is it used as a pokemon, but that's another story) so it's better off using icicle drop.
My calculations were based on not having technician. If breloom opts for poison heal, it is pretty much a toss up which grass move to use. If it has technician, then it should always use bullet seed.

As for manmoswine:

Icicle spear average power: 84.1185

Icicle drop average power: 86.0625

Again, it is pretty much a toss up. Icicle drop will do more damage on average, has the possibility of flinching, and is less likely to do "low" damage, but icicle spear has the advantage of being "reliable" (in terms of accuracy NOT power) and possibly hitting through subs and focus sash.
 

breh

強いだね
simply put the fact that it will hit for pathetic damage 1/3 of the time is very much a turn off. even though it can outdamage icicle drop, it will only do so 40% of the time. this inconsistency is not great IMO.
 
I have actually had decent success with King's Rock Chillachino, it will not flinch as often as jirachi or togekiss, but sweep swap is much more powerful (especially with skill link when/if released) than air slash and iron head. It is definitely a legitimate option.
My point wasn't that it's a bad item. My point was that there are almost always better choices, even with Skill Link. Here is a comparison of the damage you do over two turns, assuming that a flinch will give you a third turn.


With a Life Orb, no crits, STAB, and Skill Link:
Sweep Slap will have a power of 243.75.
100% chance to have 487.5 over turns.


With a King's Rock, no crits, STAB, and Skill Link:
Sweep Slap will have a power of 187.5.
40% to have a free third turn, which would give it 562.5 power.
60% chance to not get a free turn, giving it 375 power.


You have a 60% chance to lose 112.5 power over your turns.
You have a 40% chance to gain 75 power if you get that free turn.


You have a greater chance to lose power.
Not to mention that the power loss when you don't get it is greater than the power gain when you do.
 
My point wasn't that it's a bad item. My point was that there are almost always better choices, even with Skill Link. Here is a comparison of the damage you do over two turns, assuming that a flinch will give you a third turn.


With a Life Orb, no crits, STAB, and Skill Link:
Sweep Slap will have a power of 243.75.
100% chance to have 487.5 over turns.


With a King's Rock, no crits, STAB, and Skill Link:
Sweep Slap will have a power of 187.5.
40% to have a free third turn, which would give it 562.5 power.
60% chance to not get a free turn, giving it 375 power.


You have a 60% chance to lose 112.5 power over your turns.
You have a 40% chance to gain 75 power if you get that free turn.


You have a greater chance to lose power.
Not to mention that the power loss when you don't get it is greater than the power gain when you do.
then again, life orb costs health, while flinches save taking hits, there are probably a lot of cases where it might be killed by a not so strong attack solely due to the life orb recoil it took, and there are also going to be cases where a life orb sweep slap wouldnt kill, but 2 kings rock slaps will, but the opponent can kill you, meaning kings rock gives 40% chance for success over 0% chance for success

i would not call a life orb a better option at all, just a different option
 
then again, life orb costs health, while flinches save taking hits, there are probably a lot of cases where it might be killed by a not so strong attack solely due to the life orb recoil it took, and there are also going to be cases where a life orb sweep slap wouldnt kill, but 2 kings rock slaps will, but the opponent can kill you, meaning kings rock gives 40% chance for success over 0% chance for success

i would not call a life orb a better option at all, just a different option
First of all, Chillachino isn't at all bulky, and just about any offensive pokemon can 2HKO it. Which is where my "two turns" came from. So the health loss won't really matter. Because like I said, no bulk to draw from anyway.

Second of all, if you are relying on a 40% chance to kill something, shouldn't your team have another way to deal with it. For instance, Jirachi could flinch-hax a Heatran to death, but rather than relying on a bunch of flinches, you would carry something else to deal with Heatran.

Also, yes there will be those situations. But as I detailed, you lose power more of the time, which means that if you are just sending Chillachino out into battle against some completely random opponent, odds are that you'll want Life Orb.

And as I've detailed before, you lose more power by not flinching than you gain by flinching. You have a greater chance to do less damage.

Yes, King's Rock can be useful in some situations. But statistically, Life Orb will be more useful in a greater number of situations. I'm not saying that King's Rock is bad.

But I am saying that since 60% is greater than half, most of the time you will be better off with Life Orb. And that means that if you are in teambuilder trying to decide between items, you would want Life Orb. It would have a greater payoff more times, which would give you a better chance to win more times. You try to win as much as possible, so you would go with what has the greatest chance of success for you. And that is Life Orb.
 
First of all, Chillachino isn't at all bulky, and just about any offensive pokemon can 2HKO it. Which is where my "two turns" came from. So the health loss won't really matter. Because like I said, no bulk to draw from anyway.
well after life orb damage, some of those 2HKOs will turn into OHKOs, which is significant, as life orb damage is in all cases, and for that reason i feel it is just as much of an option
 
well after life orb damage, some of those 2HKOs will turn into OHKOs, which is significant, as life orb damage is in all cases, and for that reason i feel it is just as much of an option
But if it's an option because it doesn't take your health, then wouldn't that make things like Muscle Band an option? It doesn't take health.

Once again, I'm not saying that King's Rock is bad. But I am saying that it's variability and inconsistency make it somewhat situational.
 
First of all, Chillachino isn't at all bulky, and just about any offensive pokemon can 2HKO it. Which is where my "two turns" came from. So the health loss won't really matter. Because like I said, no bulk to draw from anyway.

Second of all, if you are relying on a 40% chance to kill something, shouldn't your team have another way to deal with it. For instance, Jirachi could flinch-hax a Heatran to death, but rather than relying on a bunch of flinches, you would carry something else to deal with Heatran.

Also, yes there will be those situations. But as I detailed, you lose power more of the time, which means that if you are just sending Chillachino out into battle against some completely random opponent, odds are that you'll want Life Orb.

And as I've detailed before, you lose more power by not flinching than you gain by flinching. You have a greater chance to do less damage.

Yes, King's Rock can be useful in some situations. But statistically, Life Orb will be more useful in a greater number of situations. I'm not saying that King's Rock is bad.

But I am saying that since 60% is greater than half, most of the time you will be better off with Life Orb. And that means that if you are in teambuilder trying to decide between items, you would want Life Orb. It would have a greater payoff more times, which would give you a better chance to win more times. You try to win as much as possible, so you would go with what has the greatest chance of success for you. And that is Life Orb.
I disagree with this. Here is a "per two turns" calc assuming you are using an unaquirable 20 BP move that hits 5 times with skill link (for simplicity) an infinite amount of times. I will also make the assumption that the opponent is slower and can OHKO your pokemon with one of its moves (situational yes, but not outrageous given Chillachino's speed and bulk):<br />
<br />
Life Orb: Turn 1: 100*1.3 = 130 power, then you are fainted next turn.

King's Rock: Turn 1: 100 power + 40% chance of flinching
Turn 2: 40%*100 = 40 power on average
Total: 140 total power on average.

I do realize that life orb is much more reliable, but pokemon is more about managing probability in the long run than simply reliability. King's rock will actually do more damage over two turns on average, than life orb (think fire blast vs flamethrower).

There are many other factors that are near-impossible to calculate (like what if you OHKO the opponent and don't need two turns?) but my main point is that king's rock should not be considered "good but inferior" like you are saying.



edit: See post below for correct calculation (although mine is technically "correct" for a two turn span)
 
King's Rock: Turn 1: 100 power + 40% chance of flinching
Turn 2: 40%*100 = 40 power on average
Total: 140 total power on average.
I'd just like to add that this King's Rock calculation is actually incorrect (although the correct one looks slightly better for King's Rock, actually).

You need to factor in the chance of getting more than one flinch.

Turn 1: 100 power
Turn 2: 40 power
Turn 3: 16 power
etc.

We can find the actual expected power here with an infinite geometric series with initial term of 100 and common ratio of .4. This converges to 100/(1-.4), or roughly 166.6 base power. Someone check my math on that, but I believe that should be correct.
 
Yes, you are absolutely correct. I was just trying to make the point that the power is higher from king's rock than life orb, assuming that the opponent can kill you in one hit.
 
Note that King's Rock is much better with stuff like sandstorm, hail, or toxic spikes around on their side. King's Rock is probably better with sandstorm or hail in general, as no LO recoil and they take the same amount of extra damage, but LO might edge ahead if you are poisoned.

We also need to note that King's Rock does nothing if the opponent outspeeds, uses priority, has inner focus, or switches. It also boosts the opponent if they have steadfast (potentially multiple times).

Here are some calculations, assuming that you can survive N hits.

Starting a solution for N hits.
Turn 1: 100 power.
Turn 2: 100 power. (.6 of having taken damage)
Turn 3: 100 power. (.36 of having taken damage twice, .48 of having taken damage once)

In general, on turn X, you have a chance of never having taken damage equal to (.4^(X-1)). Even more generally, the probabilities for the number of times you've taken damage on turn X follow a basic trend.

Chance of zero times damaged: (.4^(X-1))
Chance of every time being damaged: .6^(X-1)

Start of turn 1:
Zero times: 1

So, let's take the start of turn 2, for example.
Zero times: .4
One time: .6

And the start of turn 3.
Zero times: .16
One time: .48 = 1-(.16 + .36)
Two times: .36

The start of turn 4 is where it gets slightly trickier.
We need to use a binomial distribution for that.
Probability of being hit exactly n times on turn X =
n!/(X-1) * .6 ^ (X-1) * .4 ^ (X-1-n)

I'll work on making an expected damage calculation assuming you can survive a certain number of hits based on that. This is also potentially useful for things like Jirachi and non-skill link flinchers like breloom, although .6 and .4 would have to be replaced.

Edit: For an effective base power in terms of number of times you can be hit, the base power of the move, and the flinch chance, we need to get into cumulative distribution functions to start. This'll be a bit more difficult.
 

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