Probabilities of Hax

[Steinhauser]

Recover spam is technically a winning battle against a move like Ice Fang if you have paralyzed their Pokémon. The chance of a full paralysis is 25%, and Ice Fang hax is only 15.6% (or a little less with defrost rate included), since flinch is not an issue. So, you have approximately a 61% chance in your favour of winning the matchup. (Similar to Hypnosis I suppose.) Of course, a freeze will probably cause a switch and is not nearly as devastating as a crit (against Celebi), so that complicates the issue.

Against a move without effects like Brick Break the odds are 25 : 6.25, or 80% in your favour.

 

[chenman333]

Yeah, Brick Break is probably a bad example. But still, but yeah, the whole Paralyze+Recover spam works much better than plain Recover spamming, which is something that Zapdos often finds itself doing.

 

[Steinhauser]

When Zapdos does it, it is taking the gamble that the attack will run out of pp before it causes an effect or crits, due to Pressure. Against attacks with 8 pp, there is only a 23% chance of a crit within the 4 turns it is used. Against attacks with 16 pp, there is a 40% chance of a crit. The odds turn in the opponent's favour when considering attacks with 24 or more PP, or 16-pp attacks with a 10% effect, like Ice Beam.

 

[Raverist]

Lovely statistics TAY, and yet we have ourselves a scenario.

Marriland bitch moans about his precious Suicune getting killed by a Porygon-Z when it paralyzed it with a thunderbolt and they suffered from parahax afterwards.

In this case, the question is: What are the odds of a parahax event where the defending pokemon is paralyzed by Thunderbolt then is unable to attack due to paralysis happening over the course of n turns?

We consider the fact that paralysis has a 25% chance of immobilisation n top of the chances of the para chance for consecutive tbolts.

 

[Amelia]

I know these is a weird question, but it does happen at times.

What is the probability of a normal move (Say, Return), doing n criticals in a row?

 

[Steinhauser]

What is the probability of a normal move (Say, Return), doing n criticals in a row?

2 turns: 0.0625^2 = 0.00390625 or 0.39%
3 turns: 0.0625^3 = 0.000244140625 or 0.02%
n turns: 0.0625^n

 

[reachzero]

I've been wondering about this one for a while: how do stages of probability for critical hits work? Most people know that under normal circumstances a critical hit has a 6.25% chance, yet I couldn't find on Smogon the answer for what the odds are of a critical hit when the attacker is Super Luck Absol using a Scope Lens attacking with Night Slash. From experience, it seems to crit at least 50% of the time, yet that seems unreasonably high. Have we researched crit up factors?

 

[Steinhauser]

In this case, the question is: What are the odds of a parahax event where the defending pokemon is paralyzed by Thunderbolt then is unable to attack due to paralysis happening over the course of n turns?

It would be something like
Turn 1: 0.025
Turn 2: 0.025 + ((0.075) * 0.25)
Turn 3: 0.025 + ((0.075) * 0.25) + (((0.075) * 0.75) * 0.25)
Turn 4: 0.025 + ((0.075) * 0.25) + (((0.075) * 0.75) * 0.25) + ((((0.075) * 0.75) * 0.75) * 0.25)

So for turn 1 we have the chance of paralysis (0.1 or 10%) times the chance of full paralysis (0.25 or 25%) to give us 0.025.

For turn 2 we have the same chance of paralysis, plus the chance that on turn 1 you were paralyzed but not fp (0.1 - 0.025 or 0.075) times the chance of fp (0.25).

For turn 3 we have the chance of paralysis + fp (0.025) plus the chance of a paralysis turn 2 and no full paralysis on turn 2, times the fp chance (1 - 0.025 * 0.25), PLUS the chance of a paralysis on turn 1 and no fp on turns 1 or 2, times the fp chance (((0.075) * 0.75) * 0.25).

For turn 4 we have the chance of paralysis + fp (0.025) plus the chance of a paralysis turn 3 and no full paralysis on turn 3, times the fp chance (1 - 0.025 * 0.25), plus the chance of a paralysis on turn 2 and no fp on turns 2 or 3, times the fp chance (((0.075) * 0.75)) * 0.25), PLUS the chance of a paralysis on turn 1 and no fp on turns 1, 2 or 3 ((((0.075) * 0.75) * 0.75) * 0.25).

Anyway, the totals are as follows:

Turn 1: 0.025 or 2.5%
Turn 2: 0.04375 or 4.4%
Turn 3: 0.0578125 or 5.8%
Turn 4: 0.068359375 or 6.8%

Feel free to do the next few numbers following that pattern but I can't be bothered.

 

[chenman333]

I've been wondering about this one for a while: how do stages of probability for critical hits work? Most people know that under normal circumstances a critical hit has a 6.25% chance, yet I couldn't find on Smogon the answer for what the odds are of a critical hit when the attacker is Super Luck Absol using a Scope Lens attacking with Night Slash. From experience, it seems to crit at least 50% of the time, yet that seems unreasonably high. Have we researched crit up factors?

http://bulbapedia.bulbagarden.net/wiki/Damage_modification

Yep, it's supposed to be 50%....

That is quite high.

 

[Misa]

It would be something like
Turn 1: 0.025
Turn 2: 0.025 + ((0.075) * 0.25)
Turn 3: 0.025 + ((0.075) * 0.25) + (((0.075) * 0.75) * 0.25)
Turn 4: 0.025 + ((0.075) * 0.25) + (((0.075) * 0.75) * 0.25) + ((((0.075) * 0.75) * 0.75) * 0.25)

So for turn 1 we have the chance of paralysis (0.1 or 10%) times the chance of full paralysis (0.25 or 25%) to give us 0.025.

For turn 2 we have the same chance of paralysis, plus the chance that on turn 1 you were paralyzed but not fp (0.1 - 0.025 or 0.075) times the chance of fp (0.25).

For turn 3 we have the chance of paralysis + fp (0.025) plus the chance of a paralysis turn 2 and no full paralysis on turn 2, times the fp chance (1 - 0.025 * 0.25), PLUS the chance of a paralysis on turn 1 and no fp on turns 1 or 2, times the fp chance (((0.075) * 0.75) * 0.25).

For turn 4 we have the chance of paralysis + fp (0.025) plus the chance of a paralysis turn 3 and no full paralysis on turn 3, times the fp chance (1 - 0.025 * 0.25), plus the chance of a paralysis on turn 2 and no fp on turns 2 or 3, times the fp chance (((0.075) * 0.75)) * 0.25), PLUS the chance of a paralysis on turn 1 and no fp on turns 1, 2 or 3 ((((0.075) * 0.75) * 0.75) * 0.25).

Anyway, the totals are as follows:

Turn 1: 0.025 or 2.5%
Turn 2: 0.04375 or 4.4%
Turn 3: 0.0578125 or 5.8%
Turn 4: 0.068359375 or 6.8%

Feel free to do the next few numbers following that pattern but I can't be bothered.

So, based on those statistics, if a pokemon is paralyzed, and manages to last for a couple of turns, the chance that a pokemon will not move in that turn would increase right?

For example, if a pokemon lasts for about 20 turns while being paralyzed, the chance that the pokemon would not move during that turn would be pretty high then. Is there a simplified equation that we could use for this, or do we have to find it manually using calculations?

either way, this is a pretty nice find. good work.

 

[Steinhauser]

So, based on those statistics, if a pokemon is paralyzed, and manages to last for a couple of turns, the chance that a pokemon will not move in that turn would increase right?

For example, if a pokemon lasts for about 20 turns while being paralyzed, the chance that the pokemon would not move during that turn would be pretty high then. Is there a simplified equation that we could use for this, or do we have to find it manually using calculations?

either way, this is a pretty nice find. good work.

No - the chance of full paralysis happening each turn to a paralyzed opponent is exactly 25%.

The list I posted was the chance that, when using TB repeatedly on a healthy opponent, it will be fully paralyzed for one turn. So after 1 turn the opponent has a 2.5% chance of being fully paralyzed. After 2 turns it has a 4.4% chance of having been fully paralyzed on either one of those two turns.

But each turn you attack the opponent only has a 2.5% chance of fully paralyzing, UNLESS you paralyzed on a previous turn, in which case he has a 25% chance of fully paralyzing.

To make things easier, consider this list:

1 attack(s)............0.25
2 attack(s)............0.4375
3 attack(s)............0.578125
4 attack(s)............0.68359375
5 attack(s)............0.7626953125
6 attack(s)............0.822021484375
7 attack(s)............0.86651611328125
8 attack(s)............0.8998870849609375
9 attack(s)............0.9249153137207031
10 attack(s)...........0.9436864852905273
11 attack(s)...........0.9577648639678955
12 attack(s)...........0.9683236479759216

This is the probability that a paralyzed opponent will be fully paralyzed at least once at some point in the given amount of turns.

 

[TAY]

I've been wondering about this one for a while: how do stages of probability for critical hits work? Most people know that under normal circumstances a critical hit has a 6.25% chance, yet I couldn't find on Smogon the answer for what the odds are of a critical hit when the attacker is Super Luck Absol using a Scope Lens attacking with Night Slash. From experience, it seems to crit at least 50% of the time, yet that seems unreasonably high. Have we researched crit up factors?

This is something that bugged me for a while, but I now know how the critical hit stages work: there are five "stages" of critical hits. The first (Stage 0) is what normal moves achieve (a 6.25% or 1/16 chance). Stage 1 is 12.5% (or 1/8); Stage 2 is 25% (or 1/4); Stage 3 is 33% (or 1/3); and stage 4 is the maximum, with a 50% critical hit ratio. Here is a chart which lists those probabilities:

Chances to score a critical hit given stage N

Stage          chance
0..................6.25%
1..................12.5%
2..................25%
3..................33%
4..................50%

As far as the actual manipulations go, Scope Lens / Razor Claw increase the stage by one; Lansat Berry increases the stage by one; high critical hit ratio moves increase it by one; Focus Energy increases it by two; Lucky Punch and Stick increase the stage by two when attached to Chansey* and Farfetch'd, respectively; Super Luck increases the stage by one**.

So overall I would say that the crit increasing items are a waste of time. Night Slash is really only good on Absol and Honchkrow, since the jump by 18.75% is actually pretty significant (as opposed to only a 6.25% jump on any other pokemon). Absol with Focus Energy could be entertaining in UU I suppose (50% chance to crit with each attack), especially if some of the more potent attackers end up banned, but overall it shouldn't be something you rely on.

*I am not sure if Lucky Punch works for only Chansey or the entire Chansey line.

**Some sources (Serebii and Bulbapedia) suggest that Super Luck will "double" the current attack stage (they start at stage 1); however, I confirmed a few weeks ago through in-game testing that Smogon's description of Super Luck is probably correct.

 

[Flashstorm1]

This was a very interesting read, considering I never imagined just how high the probability of getting a critical hit becomes after a few turns. Personally, I only complain about hax when it is game changing, and in that case, anyone has a right to become frustrated, don't you agree? The probability of getting a critical hit on a CRUCIAL turn should be much much lower than the statistics derived in this thread, in which case, the argument is useless. Generally, one should be able to force the opponent to switch or just faint it before the probabilities of hax even get that high anyways.

 

[Broth3r]

Focus Energy increases it by two

Wrong: It increases it by one. In that case, we would have a Stage 5 situation, that is, 100% critical chance, with Super Luck (1) + Focus Energy (2) + Scope Lens (1) + Stage 2 Move (1) = 5.

 

[Mekkah]

*I am not sure if Lucky Punch works for only Chansey or the entire Chansey line.

Chansey only.

 

[Erazor]

In that case, we would have a Stage 5 situation, that is, 100% critical chance

Wrong, Stage 5 is a 50% chance, not 100%.

 

[Broth3r]

I'm considering normal crit as stage 0

 

[Erazor]

I'm considering normal crit as stage 0

The maximum chance of a crit happening in a turn is 50%, how does it go to 100%?

 

[Broth3r]

Exactly.
What I'm saying is TAY is wrong when he says that Focus Energy gives +2, it gives +1 and i'm just saying what would happen if it was +2.

 

[Erazor]

Ok, sorry. My bad.

 

[lati0s]

Exactly.
What I'm saying is TAY is wrong when he says that Focus Energy gives +2, it gives +1 and i'm just saying what would happen if it was +2.

no actually focus energy does raise yout crit stage 2 stages http://www.smogon.com/dp/moves/focus_energy

but its stilll impossible to go past stage 4

 

[Broth3r]

no actually focus energy does raise yout crit stage 2 stages http://www.smogon.com/dp/moves/focus_energy

but its stilll impossible to go past stage 4

So technically it could go up to 100%, but the limit is 50%
Thanks for clearing this up.

 

[TAY]

Wrong: It increases it by one. In that case, we would have a Stage 5 situation, that is, 100% critical chance, with Super Luck (1) + Focus Energy (2) + Scope Lens (1) + Stage 2 Move (1) = 5.

Focus Energy definitely increases by two. Stage 4 isn't the maximum because what would be stage 5 cannot be achieved, Stage 4 is the maximum because the game caps it there. It can't "technically" or in any other sense go above 50%. that is the maximum possible critical hit ratio.

 

[Aldaron]

To be honest, this probably would just increase my whining (if I wasn't already aware of it)

I rarely bemoan an opponent "getting lucky" so much as detest the mechanics of Pokemon lol.

This is why we should work to create a "reduced probability" modded metagame!

 

[Tangerine]

The only reason this thread doesn't explain much yet is because in most cases "hax" only happens to you and none to your opponent in a given match. That's the only time I will ever whine about it anyway!

Someone find me the probability of that please =)