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

[SlimMan]

Not to be rude, NC, but I've argued in the Suspect thread, the C&C forum, and irl.
Quite frankly, I'm tired of it. And I don't really think it matters THAT much.
So I'm going to let this drop.
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I'm curious though, the pokemon who get Skill Link tend to have lower attacking stats than those simple attack-monsters.
But on the other hand, they get moves with a minimum of 125 base power that can also break Subs and Sashes.

I'd be curious to see a graph/chart comparing the damage dealt between something like Icicle Spear Cloyster vs. Icicle Drop Mamoswine. That's just an example, but you get my point.

 

[SP458]

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.

Your calculation is false: as you said, each hit has a 12.5% chance to crit with Scope Lens, but it means a (87.5%)^5 = 51.3% chance that all 5 hits do NOT crit, so a 48.7% chance that at least one of them crits (compared to the 27.6% chance without Scope Lens).

 

[Farewell]

Your calculation is false: as you said, each hit has a 12.5% chance to crit with Scope Lens, but it means a (87.5%)^5 = 51.3% chance that all 5 hits do NOT crit, so a 48.7% chance that at least one of them crits (compared to the 27.6% chance without Scope Lens).

Thats pretty much a Scope lense, Focus Energy, Super Luck, Absol's Night Slash's chance to critical hit (since the chance maxes at 50% per individual hit, but imagine it using BEAT UP hitting 5 times per attack). Lets do (50%)^5 = 3.125% that all 5 hits do NOT crit, so a 96.875% of Critical Hitting at least once.


If you were to use Focus Energy with Skill Link on say Cloyster (+2 levels of Critical Hit Ratio = 25% per hit then its (75%)^5 = 23.7% that all 5 do NOT crit, and 76.3% chance that at least 1 does); if you were to use both Focus Energy and Scope Lens, then the boost would be further per hit and would be (66.66%)^5 = 13.16% that all 5 do NOT crit, and a 86.84% that at least 1 does.

Factor in King's Rock for flinch on a Focus Energy Pokemon using Skill Link Rock Blast, and you would have that 76.3% to critical hit at least once, in addition to a 40% chance flinch.

 

[Axa]

Thats pretty much a Scope lense, Focus Energy, Super Luck, Absol's Night Slash's chance to critical hit (since the chance maxes at 50% per individual hit, but imagine it using BEAT UP hitting 5 times per attack). Lets do (50%)^5 = 3.125% that all 5 hits do NOT crit, so a 96.875% of Critical Hitting at least once.


If you were to use Focus Energy with Skill Link on say Cloyster (+2 levels of Critical Hit Ratio = 25% per hit then its (75%)^5 = 23.7% that all 5 do NOT crit, and 76.3% chance that at least 1 does); if you were to use both Focus Energy and Scope Lens, then the boost would be further per hit and would be (66.66%)^5 = 13.16% that all 5 do NOT crit, and a 86.84% that at least 1 does.

Factor in King's Rock for flinch on a Focus Energy Pokemon using Skill Link Rock Blast, and you would have that 76.3% to critical hit at least once, in addition to a 40% chance flinch.

Considering that Cloyster can't even LEARN Focus Energy, most of this is null and void unless you're Baton Passing.

I've always liked Skill Link Flinching, though.

 

[TM13IceBeam]

Notably, the entire point is null and void since no Skill Link Pokemon can learn Focus Energy.

 

[Destiny Warrior]

Notably, the entire point is null and void since no Skill Link Pokemon can learn Focus Energy.

Technically a Smeargle *could* Sketch the necessary moves and SKill Swap the necessary ability, but that's so fringe I don't see it mattering.

 

[Yogi Bear.]

Notably, the entire point is null and void since no Skill Link Pokemon can learn Focus Energy.

Not exactly.

If you were to use the (unrestricted) Street Pokemon Glitch (which I might add, is a pain in the @$$ to abuse IRL), Cloyster could have Focus Energy. That being said, by the nature of Smogon, you will not find it on any simulator that is not dedicated to the usage of that glitch.


That being said, I think Cloyster has better things to be doing than using Focus Energy EVER.

Edit: In other words, cool math. But how about more practical math? Someone on page 1 was calculating the probabilities of flinching and crits over multiple turns. How far should that go? I think 6 turns is fine (assuming say, a sweep).

This guy.

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)

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.

Amount of Attacks Faced on Turn 1:
0: .4
1: .6

Turn 2:
0: .16
1: .48
2: .36

Turn 3:
0: .064
1: .288
2: .432
3: .216

Turn 4:
0: .0256
1: .1536
2: .3456
3: .3456
4: .1296

Turn 5:
0: .01024
1: .0768
2: .2304
3: .3456
4: .2592
5: .07776

Turn 6:
0: .004096
1: .036864
2: .13824
3: .27648
4: .31104
5: .186624
6: .046656

That's the binomial distribution of the amount of attacks you'll take over the course of 6 turns given a 40% chance to flinch your target. If you're using Iron Head Jirachi, you'd literally just flip the numbers (0 becomes X, X becomes 0, etc.)
As always, Paraylsis, Confusion, Attraction and other effects will decrease the average amount of attacks you take.
Question: is .4 really the probability the chance of icicle spear + King's Rock causing a flinch? Or did I miss something?

Keep in mind that this doesn't factor in support moves. So moves like Torment, Protect, Substitute all screw with this. So does Priority. Mach Punch being what Cloyster and Chin. fear the most. Also, killing your target will get you ANOTHER turn regardless.

 

[Farewell]

instead of focus energy, it could use that critical hit berry as well.

 

[VaporeonIce]

I personally don't think getting a crit on a single hit of a 5-hit, 125 BP move, boosting it to a 5-hit, 150 BP move, is all that exciting. Use a Life Orb if you want more power, or use King's Rock if you're feeling lucky.

 

[Thorhammer]

Question: is .4 really the probability the chance of icicle spear + King's Rock causing a flinch? Or did I miss something?

King's Rick adds a 10% flinch chance to each hit. With five hits, the chance of getting at least one flinch is approximately 41%.

I wonder how these critical hit percentages might be different with a Scope Lens in the equation... Here's how it looks for Skill Link, at least:

125 BP (0 crits): 51.3%
150 BP (1 crit): 28.6%
175 BP (2 crits): 13.5%
200 BP (3 crits): 5.1%
225 BP (4 crits): 1.4%
250 BP (5 crits): 0.2%

Average: 144.5 BP

Hm... Well, assuming this is all accurate, Scope Lens is still completely worthless. I guess I'm glad I answered my own question.

 

[Yogi Bear.]

King's Rick adds a 10% flinch chance to each hit. With five hits, the chance of getting at least one flinch is approximately 41%.
I wonder how these critical hit percentages might be different with a Scope Lens in the equation... Here's how it looks for Skill Link, at least:

125 BP (0 crits): 51.3%
150 BP (1 crit): 28.6%
175 BP (2 crits): 13.5%
200 BP (3 crits): 5.1%
225 BP (4 crits): 1.4%
250 BP (5 crits): 0.2%

Average: 144.5 BP

Hm... Well, assuming this is all accurate, Scope Lens is still completely worthless. I guess I'm glad I answered my own question.

Confirming that first calculation. The chance of getting ANY flinch in the sequence of five is equal to 1- P(no flinches).

P(no flinches) = P(no flinch for one check)^number of checks.
P(no flinches) = .9^5 = .59049

1-.59049 = .40951

The Probability of getting a flinch with a Skill Link'd attack is 40.951% with King's Rock. The distribution I provided before will off somewhat, but it is a relatively good estimate of your chances. I will edit it to the actual distribution if desired.

Chances an opponent will be unable to attack after a K'sR SL attack given that the opponent is paralyzed: .704755 (Realistic)
Given that the opponent is Confused AND paralyzed: .8523775 (wishes keeping a Pokemon on Parafusion was easy)
Given that the opponent is Parafusioned and Attracted: .92618875 (wishes keeping a Pokemon on Parafustraction was easy)

Conclusion: Thorhammer is educated in Statistics. I ran through the calcs and got the same 144.5.

 

[petrie911]

I wonder how these critical hit percentages might be different with a Scope Lens in the equation... Here's how it looks for Skill Link, at least:

125 BP (0 crits): 51.3%
150 BP (1 crit): 28.6%
175 BP (2 crits): 13.5%
200 BP (3 crits): 5.1%
225 BP (4 crits): 1.4%
250 BP (5 crits): 0.2%

Average: 144.5 BP

I'm not sure how you got those numbers, but they're not right. The actual distribution would be

51.3% 36.6% 10.5% 1.5% .1% .03%

with an average BP of 140.6. This is the same as if it were a 125 BP single attack and you were using scope lens.

In fact, I'm reasonably certain the analysis in the OP is wrong. Every hit has a 1/16 chance to crit, independent of how many hits there are. This means that each hit has an expected power of 26.5625. The expected number of hits, given that you have a 3/8 chance of 2 or 3 and a 1/8 chance of 4 or 5, is 3. Thus, the expected power of the attack is 79.6875. This is just 1.0625 * 75, where 75 is the expected power ignoring critical hits.

In other words, you don't have to adjust the BP for critical hits, and this topic is pointless.

 

[XienZo]

I'm not sure how you got those numbers, but they're not right. The actual distribution would be

51.3% 36.6% 10.5% 1.5% .1% .03%

with an average BP of 140.6. This is the same as if it were a 125 BP single attack and you were using scope lens.

In fact, I'm reasonably certain the analysis in the OP is wrong. Every hit has a 1/16 chance to crit, independent of how many hits there are. This means that each hit has an expected power of 26.5625. The expected number of hits, given that you have a 3/8 chance of 2 or 3 and a 1/8 chance of 4 or 5, is 3. Thus, the expected power of the attack is 79.6875. This is just 1.0625 * 75, where 75 is the expected power ignoring critical hits.

In other words, you don't have to adjust the BP for critical hits, and this topic is pointless.

In B/W, the probability of 2-3-4-5 hits are 1/3-1/3-1/6-1/6 respectively, which is why your calculations are off.

Also, the reason why we're calculating the Critical hits for multi-hit moves is because they're relatively more common, and thus, they influence the damage more often than normal moves. (Only 1 out of 16 normal moves are affected by crits, while more than 1 out of 4 Skill-link'd multi hits attacks will be affected by crits, enough to justify calculations for.)

 

[petrie911]

Hmm, they changed the ratios. How interesting. Not that it affects anything that I said. To demonstrate...

The expected power without crits is 79.17, multiplying this by 1.0625 gives 84.11, which is exactly the expected power the OP's analysis gives.

In other words, my point still stands.

 

[TM13IceBeam]

Not exactly.

If you were to use the (unrestricted) Street Pokemon Glitch (which I might add, is a pain in the @$$ to abuse IRL), Cloyster could have Focus Energy. That being said, by the nature of Smogon, you will not find it on any simulator that is not dedicated to the usage of that glitch.

I've been involved in the discussion in the thread of Street Pokemon, and IMO Cloyster is so badly outclassed by shit like Sheer Cold Machamp and Spore Deo-S it's not even funny.

Shell Smash will always be better anyway.

 

[HavenKing]

Man, Cinccino is going to be so much fun to use.

 

[XienZo]

Hmm, they changed the ratios. How interesting. Not that it affects anything that I said. To demonstrate...

The expected power without crits is 79.17, multiplying this by 1.0625 gives 84.11, which is exactly the expected power the OP's analysis gives.

In other words, my point still stands.

Expected power isn't as useful though:

Let's say that some pokemon requires a Base 125 power move in order to KO a poke (assuming damage roll stays constant). However, they only have access to a Base 120 move that always fails to KO. The expected Base Power accounting for crits is going to be

120 x 1.0625 = 127.5

which suggests that they have enough power for a KO. However, this is completely misleading; the pokemon will only KO when they get a crit: 6.25% of the time.

Instead, the OP approaches it differently.

Let's go back to the same example, but they're now using a multi-hit move. The OP reveals that the probability you get 125+ base power is

100-29.297-31.372-18.495 = 20.836%

of the time. This percentage is actually useful; you WILL indeed get a KO 20.836% of the time. Furthermore, if we hadn't accounted for crits, we'd get that it would KO only

1/6 = 16.7%

which is fairly off from the actual number, thus justifying the need for these calculations.


Basically, an expected value is far less useful than the actual distribution of values, which is what the OP gives us.

 

[Lork]

for technician should we just times the bps given in the first post by 1.5? just trying to work out the average bp for technican multihit moves on my cinccino