Gen 6 How Much Hax Should You Expect?

Minority

Minority

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How Much Hax Should You Expect?

haxorus_by_xander3000-d45jias.png

(Art by Xander3000 approved by nobody)
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With Swagger finally banned I'm updating this post to include some more probabilities so that people know exactly what is "fair". Obviously knowing what to expect will have little actual influence on minimizing hax from your games but data and probabilities in general are fun stuff for some people and this data can be used as support in the future. The funny thing about hax however, is that if no outcome is ever determined then it never has to happen. This may sound extremely obvious, but in practice most people don't seem to realize that the move Sacred Fire never has to hit anything ever. Likewise, no matter how many games you play it's not impossible for that Scald you are using over Surf to never catch anything on fire. The point being made is that theoretical probability is only a rough outline of how a move should preform, but many would be surprised to learn that it is much more likely for a move to not follow its theoretical probability than it is to follow it. For example in twenty uses of Spacial Rend it should miss once, however it is more likely to not miss only once. As a result the following theoretical probabilities must be taken lightly and not as absolutes as they often prove more or less brutal, usually more since those are the ones we remember.

On the subject of understanding how much hax to expect it becomes imperative to know what "hax" actually is and this little catch-all phrase for whenever a battle doesn't go your way can be given a narrower definition. Genuine hax can be defined as when a dependent chain of highly improbable events occurs. The question now becomes just how improbable does the chain have to be to become considered "hax". Since it is quite subjective as to how improbable an event needs to be to qualify as hax, perhaps the best definition is one who's chain is so unlikely as to where you should never see it occur in all your time while playing Pokemon. I experienced such an event recently which was a quadruple miss (0/4 total uses hit in a row, a dependent set of events) with the move Sacred Fire, no accuracy modifiers were in play so the chain had a grand total of having a 0.000625% chance of occurring; so low that it would take more than 125,000 uses of Sacred Fire to ever expect such a chain to occur. This number of uses is much larger than I have, and most likely will ever use in all my time playing Pokemon and therefore should never have happened. This is what I believe to be the line where a set of events must be considered hax, however many players' definitions probably fall closer to a chain of events that should only happen to them on rare occasions, say a week or perhaps a month in which case it is possible to calculate what is hax to you based on you personal battle preferences and activity.



Evasion

Accurate Moves (Ex: Psystrike)
100% vs. +1 evasion = 75.19%
100% vs. +2 evasion = 59.88%
100% vs. +3 evasion = 50.00%
100% vs. +4 evasion = 42.91%
100% vs. +5 evasion = 37.45%
100% vs. +6 evasion = 33.33%
100% vs. +6 evasion with Brightpowder = 30.00%
100% vs. +6 evasion + Sand Veil / Snow Cloak + Brightpowder = 24.00%
Spacial Rend, Sacred Fire, Aeroblast, Pin Missile
95% vs. +1 evasion = 71.42%
95% vs. +2 evasion = 56.88%
95% vs. +3 evasion = 47.50%
95% vs. +4 evasion = 40.77%
95% vs. +5 evasion = 35.58%
95% vs. +6 evasion = 31.66%
95% vs. +6 evasion with Brightpowder = 28.5%
Rock Slide, Psycho Boost, Draco Meteor, Overheat
90% vs. +1 evasion = 67.66%
90% vs. +2 evasion = 53.89%
90% vs. +3 evasion = 45.00%
90% vs. +4 evasion = 38.62%
90% vs. +5 evasion = 33.70%
90% vs. +6 evasion = 30.00%
90% vs. +6 evasion with Brightpowder = 27.00%
Fire Blast
85% vs. +1 evasion = 63.90%
85% vs. +2 evasion = 50.89%
85% vs. +3 evasion = 42.5%
85% vs. +4 evasion = 36.48%
85% vs. +5 evasion = 31.83%
85% vs. +6 evasion = 28.33%
85% vs. +6 evasion with Brightpowder = 25.50%
Hydro Pump, Stone Edge, Dark Void
80% vs. +1 evasion = 60.15%
80% vs. +2 evasion = 47.90%
80% vs. +3 evasion = 40.00%
80% vs. +4 evasion = 34.33%
80% vs. +5 evasion = 29.96%
80% vs. +6 evasion = 26.66%
80% vs. +6 evasion with Brightpowder = 24.00%
Thunder, Focus Blast
70% vs. +1 evasion = 52.63%
70% vs. +2 evasion = 41.91%
70% vs. +3 evasion = 35.00%
70% vs. +4 evasion = 30.04%
70% vs. +5 evasion = 26.21%
70% vs. +6 evasion = 23.33%
70% vs. +6 evasion with Brightpowder = 21.00%
Stopping Sash Minimize before +4 pass with 100% accuracy move that can OHKO assuming you are faster:
40.12% x 57.09% - 100% = 77.09%

Stopping Sash Minimize before +4 pass with 100% accuracy move that can OHKO assuming you are slower:
59.88% x 42.91% = 25.69%

Double Team Leftovers Blaziken / Scolipede starting at +2 evasion vs. 100% accuracy move that can OHKO:
Approx 2.76% to prevent any evasion gains before next pass




Example: Moving 0/1
The first number represents the number of successes, while the second is the number of attempts. In this case the probability represents the likelihood of NOT moving with a single attempt under these parameters.

30% Flinch + Paralysis
Moving 0/1
[(0.3) + (0.7)(0.25)](100) = 47.5%

Moving 1/1
(0.7)(0.75)(100) = 52.5%

Moving 0/2
(.475^2)(100) = 22.5625%

Moving 1/2
[(.475)(.525) + (.475)(.525)](100) = 49.875%

Moving 2/2
(.525^2)(100) = 27.5625%

60% Flinch + Paralysis
Moving 0/1
[(0.6) + (0.4)(0.25)](100) = 70%

Moving 1/1
(0.4)(0.75)(100) = 30%

Moving 0/2
[(0.6) + (0.4)(0.25)][(0.6) + (0.4)(0.25)](100) = 49%

Moving 1/2
[(0.7)(0.3) + (0.3)(0.7)](100) = 42%

Moving 2/2
(0.4)(0.75)(0.4)(0.75)(100) = 9%

Moving 0/3
(0.7^3)(100) = 34.3%

Moving 1/3
(0.3)(0.7)(0.7)(3)(100) = 44.1%

Moving 2/3
(0.3)(0.3)(0.7)(3)(100) = 18.9%

Moving 3/3
(0.3^3)(100) = 2.7%

Moving 0/4
(0.7^4)(100) = 24.01%

Moving 1/4
(0.3)(0.7)(0.7)(0.7)(4)(100) = 41.16%

Moving 2/4
(0.3)(0.3)(0.7)(0.7)(6)(100) = 26.46%

Moving 3/4
(0.3)(0.3)(0.3)(0.7)(4)(100) = 7.56%

Moving 4/4
(0.3^4)(100) = 0.81%

70% Accuracy Moves
Hit 0/2
(0.3^2)(100) = 9%

Hit 1/2
(0.3)(0.7)(2)(100) = 42%

Hit 2/2
(0.7^2)(100) = 49%

Hit 0/3
(0.3^3)(100) = 2.7%

Hit 1/3
(0.3)(0.3)(0.7)(3)(100) = 18.9%

Hit 2/3
(0.3)(0.7)(0.7)(3)(100) = 44.1%

Hit 3/3
(0.7^3)(100) = 34.3%

Hit 0/4
(0.3^4)(100) = 0.81%

Hit 1/4
(0.3^3)(0.7)(4)(100) = 7.56%

Hit 2/4
(0.7)(0.7)(0.3)(0.3)(6)(100) = 26.46%

Hit 3/4
(0.3)(0.7^3)(4)(100) = 41.16%

Hit 4/4
(0.7^4)(100) = 24.01%

Critical Hits
Double Crit
(.0625^2)(100) = 0.390625%

Triple Crit
(.0625^3)(100) = 0.0244140625%

At Least One Crit in Five Turns
(.9375^5)(100) – 100 = 27.5803566%

At Least One Crit in Ten Turns
(.9375^10)(100) – 100 = 47.5539525%

At Least One Crit in Twenty Turns
(.9375^20)(100) – 100 = 72.49412101%

At Least One Crit in Thirty Turns
(.9375^30)(100) – 100 = 85.57425364%
 
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Just a minor nitpick but when you have the probability of something happening twice in 4 turns, you should multiply by 6, not 4. There are 6 possible pairs of turns that the probability could happen on.

Moving twice out of 4 moves with 60% paraflinch should be 26.45% and 2 out of 4 parafusion turns should be 32.95898...(we don't really need that many digits lol)
 
Zebstrika said:
Just a minor nitpick but when you have the probability of something happening twice in 4 turns, you should multiply by 6, not 4. There are 6 possible pairs of turns that the probability could happen on.
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Thanks for catching this. I don't know how I made that mistake since the probs need to add up to 100% and they didn't before.
 
This was rather silly but there was some person using this
(this is what I was told what Froslass was after fighting her)
froslass.gif

Froslass (F) @ Brightpowder
Ability: Snow Cloak
EVs: 4 HP / 252 SpA / 252 Spe
Timid Nature
- Hail
- Blizzard
- Shadow Ball
- Double Team
it got up to +6 evasion with Brightpowder and Snow Cloak active. Thankfully there were no hazards on the field so switch stalling her out with Heatran and Ho-Oh was easy (she was last mon). I was just curious what the probability was with all of these modifiers.
 
Rotosect said:
Considering crap like this is allowed in ubers:
http://replay.pokemonshowdown.com/ubers-134332739
http://replay.pokemonshowdown.com/ubers-134370349
you should expect a lot of hax until action is taken.
(Is that Denisss, by the way?)
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In the first replay 4/6 attacks against +1 and then +2 evasion were successful. This is about normal, the first match wasn't won by hax, rather it was won by a skilled and exploitative use of Baton Pass, evasion just made it so that two attacks missed which wasn't actually that big of a deal and should have been expected.

In the second replay hax was also not really an issue, that battle was basically won on turn three. At +1 evasion 4/5 of Xerneas' attacks hit Scolipede which is also a "normal" amount of hax. I actually refer to this exact same scenario in the OP, if Scolipede had started at +2 instead of +1 Xerneas had about a 3% of stopping any further evasion which is basically nothing, at +1 the odds are a bit better but Scolipede also had Ingrain making the odds probably close to 0% of stopping any evasion gains. Not hax, in fact it would have been hax if Scolipede had lost.

I've been using quite a bit of evasion pass and those replays are quite excellent uses of it manipulating the odds completely in your favor.
 
This is helpful, surely also the possibility of hitting consecutively is important to mention too. And it doesn't really answer the thread title of how much hax you should expect.. it doesn't even define hax. And this isn't relevant purely to ubers, but to all tiers, albeit there is no general discussion in which you have posting rights in which would make a better place to put it. I think the way I'd define hax personally is an event which you'd only expect to see typically once per week, due to its low probability. The way you would work it out when I did it was days per week [7] x number of battles per day [example estimation of 20] x number of opportunities per match of improbable events [again needs estimation but say 5] and then the inverse of the resulting number, and then you say if an event in that match happened with a probability lower than that, then the event is haxy. Obviously it's not a perfect barometer and could do with tuning and varies player-to-player, as well as by playstyle-matchup, but a general idea of that kind was what I had hoped for when I clicked upon this thread.
 
Piexplode said:
it doesn't really answer the thread title of how much hax you should expect.. it doesn't even define hax. The way you would work it out when I did it was days per week [7] x number of battles per day [example estimation of 20] x number of opportunities per match of improbable events [again needs estimation but say 5] and then the inverse of the resulting number, and then you say if an event in that match happened with a probability lower than that, then the event is haxy. Obviously it's not a perfect barometer and could do with tuning and varies player-to-player, as well as by playstyle-matchup, but a general idea of that kind was what I had hoped for when I clicked upon this thread.
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You only need to define something when that something is unclear or misunderstood; such as the differences between checks / counters which many newer players use almost interchangeably. It is obvious even to new players what hax is, which is whenever a set of events occurs that are unlikely (that's the broad definition that most players agree upon or understand it as, i.e. missing three of your Focus Blasts in a row, an event that is statistically less likely to happen than what should happen). I agree that what I consider to actually be hax is a string of events much more rare than how payers typically throw the word around, but there is no right or wrong is this area so I didn't bother trying to define it and it really doesn't matter. In fact it could easily be interpreted that hitting two Focus Blasts in a row is hax considering that it is less likely to occur than missing a combination of one or both.

Since hax doesn't really have a solid definition since players may agree or disagree to what extent of bad luck is worth bitching about, it's even harder to find a single exact answer to how much hax you should expect per game, especially when, as you mentioned, such things are based on play style and matchup. In fact I was going to answer the question "how many critical hits should you see per match?" in this thread when I updated it, however I was immediately smacked with variables that made an accurate answer to the question impossible without narrowing the question. The most basic example is a comparison of stall vs. stall to HO vs. HO. Naturally the more turns there are in a match the more attacking moves were probably used, and therefore the more crits you should expect. Things get worse when you try to factor in moves with odd critical hit ratios along with abilities, etc. If I had access to a mess of data such as the amount of stall builds vs. HO builds used, the amount of times Shadow Claw was used on Showdown, etc. from someone like Dr. Antar I could probably find some really deep stuff relating to hax, however such data might not even exist or would be ridiculously painful to accurately obtain.

I might add my own personal definition of hax to the thread which follows along similar lines to yours, however such a calculation is extremely difficult because, believe it or not, the sheer amount of individually highly implausible events when combined is actually much higher than most people expect. In other words, there are thousands of different ways in which a player can experience what they call hax. As for the title of the thread I believe that it is answered well enough but I agree some more general elaboration and estimations (because Pokemon is some complicated that's the best anyone could do) on how much hax can you expect per given match would be interesting and I'll continue to update with new stuff.
 
Minority Suspect said:
You only need to define something when that something is unclear or misunderstood; such as the differences between checks / counters which many newer players use almost interchangeably. I think personally I disagree with it, just because it is clear in someone's head what something is, does not make is actually clear what it is. The foundations of mathematics got in a mess duing the 1900s for similar reasons >.> (not that you'd really know much about mathematical history, but what I'm saying is true.) It is obvious even to new players what hax is, which is whenever a set of events occurs that are unlikely (that's the broad definition that most players agree upon or understand it as, i.e. missing three of your Focus Blasts in a row, an event that is statistically less likely to happen than what should happen). I agree that what I consider to actually be hax is a string of events much more rare than how payers typically throw the word around, but there is no right or wrong is this area so I didn't bother trying to define it and it really doesn't matter. In fact it could easily be interpreted that hitting two Focus Blasts in a row is hax considering that it is less likely to occur than missing a combination of one or both.

Since hax doesn't really have a solid definition since players may agree or disagree to what extent of bad luck is worth bitching about, it's even harder to find a single exact answer to how much hax you should expect per game, especially when, as you mentioned, such things are based on play style and matchup. In fact I was going to answer the question "how many critical hits should you see per match?" in this thread when I updated it, however I was immediately smacked with variables that made an accurate answer to the question impossible without narrowing the question. The most basic example is a comparison of stall vs. stall to HO vs. HO. At this point I think a mention of the importance of critical hits.. I guess looking at the number of places within a game where a critical hit might have an impact upon the outcome, and I would estimate that this value varies less between stall and HO, although it might vary more with balance say, and crit-fishing in HO vs Stall matchups is a bit of a different, but still relevant matter. Still, I appreciate what you're saying. Naturally the more turns there are in a match the more attacking moves were probably used, and therefore the more crits you should expect. Things get worse when you try to factor in moves with odd critical hit ratios along with abilities, etc. If I had access to a mess of data such as the amount of stall builds vs. HO builds used, the amount of times Shadow Claw was used on Showdown, etc. from someone like Dr. Antar I could probably find some really deep stuff relating to hax, however such data might not even exist or would be ridiculously painful to accurately obtain. Agreed, but in ubers at least, high critical hit moves are virtually non-existant, so you could try and create a metric without that consideration, albeit clearly other issues remain.

I might add my own personal definition of hax to the thread which follows along similar lines to yours, however such a calculation is extremely difficult because, believe it or not, the sheer amount of individually highly implausible events when combined is actually much higher than most people expect. That sounds about right. In other words, there are thousands of different ways in which a player can experience what they call hax. As for the title of the thread I believe that it is answered well enough but I agree some more general elaboration and estimations (because Pokemon is so complicated that's the best anyone could do) on how much hax can you expect per given match would be interesting and I'll continue to update with new stuff. It might interest you that some people have taken using mathematics to a new level within pokemon, particularly in Generation 1; might I redirect you here? [Equivalent threads are also posted on PO and RBY2K10 forums.]
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Here is an interesting case study, I saw MoxieInfinite had posteded this video on his youtube channel:
and then I promptly show using high school statistics that his results aren't sufficient to reject the idea that focus blast has a mean accuracy of 70%. And all after being up 36 hours straight; it goes to show how misleading our intuition about probability can be.

My comment went:

If we assume a null hypothesis of mean=70, at a (very standard) significance level of 5% (we'll do one-tailed), then then p(x is less than or equal to 63) for x ~ b (binomial) (100, 0.7), with x representing the number of times focus blast hits, is approximated by y ~ N [normal] (70, 21), thus the probability of hitting equal to or less than 63 is P(x<64)= (with continuity correction) P(y<63.5) = P(z<(63.5-70)/[sqrt21])=P(z<-1.42..)=1-P(z<1.42..) which is approximately 7.78%.Thus the null hypothesis is not rejected, and your 63/100 is not sufficient evidence to suggest that there is a mean accuracy of focus blast less than that of 70%, as stated. Nice myth you bust.

And one could easily argue about the sample size but I think it was probably good enough.
 
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Well there is obviously a difference between theoretical probability and empirical probability, and as I mention in the OP the theoretical probability of anything is typically more likely to not follow in application which is counter-intuitive. In regards to Focus Blast it can have 70% theoretical accuracy and still never hit anything ever, having an empirical probability of 0% since every time acc is cal(ed) the event is independent. It's similar to how the empirical results of Blackjack make it so that the Martingale is an unreliable betting strat. It's insane that people use moves that never have to hit anything ever but it's better than having to hope for a crit. We all know that the theoretical probability of Focus Blast is 70%, but I wonder if there is enough data collected to where its empirical probability could be calculated; like if all Focus Blast uses were recorded and we knew how many of them were successful. I'm willing to bet that this value is lower than 70%, but not far enough off to even come close to proving that 70% theoretical accuracy is a lie.
 
Although interestingly there is a way to consistently beat the house in Blackjack, I think it's called the Kelly strategy (I don't know the full details though).
 
Minority Suspect said:
Well there is obviously a difference between theoretical probability and empirical probability, and as I mention in the OP the theoretical probability of anything is typically more likely to not follow in application which is counter-intuitive. In regards to Focus Blast it can have 70% theoretical accuracy and still never hit anything ever, having an empirical probability of 0% since every time acc is cal(ed) the event is independent. It's similar to how the empirical results of Blackjack make it so that the Martingale is an unreliable betting strat. It's insane that people use moves that never have to hit anything ever but it's better than having to hope for a crit. We all know that the theoretical probability of Focus Blast is 70%, but I wonder if there is enough data collected to where its empirical probability could be calculated; like if all Focus Blast uses were recorded and we knew how many of them were successful. I'm willing to bet that this value is lower than 70%, but not far enough off to even come close to proving that 70% theoretical accuracy is a lie.
Click to expand...

You must still be highly intoxicated.
 
Minority Suspect said:
Well there is obviously a difference between theoretical probability and empirical probability, and as I mention in the OP the theoretical probability of anything is typically more likely to not follow in application which is counter-intuitive. In regards to Focus Blast it can have 70% theoretical accuracy and still never hit anything ever, having an empirical probability of 0% since every time acc is cal(ed) the event is independent. It's similar to how the empirical results of Blackjack make it so that the Martingale is an unreliable betting strat. It's insane that people use moves that never have to hit anything ever but it's better than having to hope for a crit. We all know that the theoretical probability of Focus Blast is 70%, but I wonder if there is enough data collected to where its empirical probability could be calculated; like if all Focus Blast uses were recorded and we knew how many of them were successful. I'm willing to bet that this value is lower than 70%, but not far enough off to even come close to proving that 70% theoretical accuracy is a lie.
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sure the impirical probability will not be 70%...ever. That doesnt mean anything - the probability of it hitting is still 70%, no more and no less. You can never bet with or against probability because there is a 50/50 shot you are wrong. You are trying to say that despite the probability of something happening being 70% that we can bank on the actual probability going a certain direction - which is completely illogical and by general logic makes your argument completely irrelevant.
This is something the internet loves to do in my experience, i call it the 2+2=5 syndrome. the people love to overcomplicate simple logic by using a differentiated, biased logic and claiming simple stuff to be an illogical fallacy. The result is people doing unecessary work to not be right because they want to attempt to prove common logic wrong. IDK if its a i want to be cool thing or what but it is pointless and i find it pathetically half-minded. Rather than trying to overcomplicate something and assuming that the simple answer is incorrect, people need to try to justify the simple solution, there is no logic that suggests its wrong and in fact most logic says its right in this case.

really internet, stop assuming everything is wrong with little to no justification of such. It results in so much misinforment and people believing wrong things, sometimes on a much larger scale than this (i am looking at you, storm chase video from being safe from a tornado under a bridge (look it up)).

as stated above it doesnt take more than high school statistics to prove your hypothesis wrong, as physical calculations always trump theoretical logic (especially when its misled -.-)
 
It's good pokemon collects so many people who understand maths above high/secondary school level. I'm going to do maths at uni in a few months and people on here have taught me stuff I've not met yet to an extent (and I'm going to arguably the 2nd-best maths course in the country (if I get the grades))
 
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