Iron Head Intuition Poll (Don't calc, just guess unless you already know the answer)

[asbdsp]

PLEASE VOTE IN THE POLL BEFORE READING PAST THE OP, AND POSTING A REPLY ( Helps make the experiment a bit more valid, thank you. :) )

Situation and all caveats are described herein:

Jirachi v slower opponent without priority or any move/ability allowing them to take an action before Jirachi ( neither mon has a status condition, or additional factors effecting damage, Jirachi's opponent does NOT HAVE LEFTIES )

Jirachi is clicking iron head until the opponent stops flinching, or it runs out of it's 15 Iron Head PP.

Opponent is never switching until he gets his move off

What is the expected average damage from Iron head before the slower opponent gets a move off? (Listed in poll as both a ratio to Iron Head power, and Base Power expected value)

After voting, do feel free to calculate this out and share math insights/embarrasments. I'll post my guess, and how it compared to the actual calculation. Thanks! :)

 

[Hydrametr0nice]

Given a flinching chance of 60%, the number of expected trials until it doesn't flinch is 1 / (1 - 0.6) = 2.5

 

[cherryb0ng]

Can you format this to make it more legible? Also since this is an interesting topic I would try to explain a bit better before the poll what do you mean with "effective BP" as I had to read over and over before figuring out the implication of Jirachi going more than once to attack.


Perhaps move the explanation in your second post to the caption above the poll.
asbdsp

 

[asbdsp]

Given a flinching chance of 60%, the number of expected trials until it doesn't flinch is 1 / (1 - 0.6) = 2.5

Ding, ding!

Before even thinking to calculate it as the sum of a converging infinite sequence, I had an intuition it might be close to double damage, (hence I voted 1.96), but I was way off.

Technically our expected outcome is constrained by remaining PP, but not by too much.

As long as you have at least 6-7 PP for the move (PP is indicated by row numbers in the table), your expected value is pretty close to 2.5.

Meaning, that Iron Head when paired with Jirachi has closest to the following for a reference comparison move description.

Mean Iron Head
Type Steel

Category Physical
Power 80 BP
Accuracy 100%
Priority 0
PP -
BP increases to 200 if the Pokemon goes before the opposing Pokemon.


Obviously, it's not the same thing (has plusses and minuses, which I'll list below). But I'd wager the above move would be banned (or the mons who had it in their learnset) if it existed in any of the classic formats.

The reason our intuition fails is because the mean outcome from the probability distribution is skewed by long tail lower probability outcomes that differ greatly from the median outcome (1 single flinch).

The move "Mean Iron Head", is better than the actual Iron Head that exists, due to it's greater consistency and because Leftovers is actually a real and ubiquitous thing (however the maximum bulk wall it can get around is less than what regular Jirachi Iron Head could theoretically get around). However, a regular Jirachi Iron Head does have 2 main advantages I can think of, due to the ability to abort the sequence of Iron Head clicks in the following circumstances:

1) If you misread or miscalc the set you're attacking, and you're doing less damage than you thought, you have a 60% chance to get off scot free without meaningful consequences, which you couldn't with "Mean Iron Head".

2) If you want to speculatively scout the set that you're attacking for any reason (say, whether or not it has Lefties), you have a 60% chance to get off scot free without meaningful consequences, which you couldn't with "Mean Iron Head".


TL;DR: I think Serene Grace + Iron Head is a pretty strong guy. Eh kills all his passive checks and doesn't afraid of anything.

And Para support, or Lefties removal support (Knock off, Thief, Trick) might be pretty decent with this thing.

 

[asbdsp]

Can you format this to make it more legible? Also since this is an interesting topic I would try to explain a bit better before the poll what do you mean with "effective BP" as I had to read over and over before figuring out the implication of Jirachi going more than once to attack.


Perhaps move the explanation in your second post to the caption above the poll.
asbdsp

Sorry dude. Made this after a kind of a spur of the moment realization (don't worry my whole team didn't get flinched to death). Certainly the concept could be explained better. As far as the poll caption goes, I actually had hit the limit for poll question length.

 

[alicia76]

Interesting as an experiment! I voted before doing the calculations, but my intuition tells me that the damage expectancy will be higher than we imagine because of the serial flinchs. Jirachi with Serenity and Iron Head is formidable, and he can totally prevent a slower opponent from acting. Can't wait to see the results and compare with the real calculations!

Mini Militia App Lock​

 

[asbdsp]

Interesting as an experiment! I voted before doing the calculations, but my intuition tells me that the damage expectancy will be higher than we imagine because of the serial flinchs. Jirachi with Serenity and Iron Head is formidable, and he can totally prevent a slower opponent from acting. Can't wait to see the results and compare with the real calculations!

Mini Militia App Lock​

Below was a very succinct and accurate calculation.

Given a flinching chance of 60%, the number of expected trials until it doesn't flinch is 1 / (1 - 0.6) = 2.5

 

[asbdsp]

That said, I wonder how much para adds to the calc. Does para proc before of after the flinch, internally in the game mechanics?

 

[Hydrametr0nice]

That said, I wonder how much para adds to the calc. Does para proc before of after the flinch, internally in the game mechanics?

It doesn't matter which effect procs first. The expected number of trials with paralysis would be 1 / (1 - 0.7) = 3.33..., since there's a 70% chance the target can't act, calculated as 1 - (1 - 0.6)(1 - 0.25)

 

[Kingrock4334]

I know with all my heart JiracJirachi's Iron Head basepower is whatever it needs to be https://replay.pokemonshowdown.com/gen5draft-2316119117?p2

 

[asbdsp]

It's not "whatever it needs to be", but we generally underestimate it. When you're outsped, it's accurate to consider it like a 200 BP move, with variance.

 

[igiveuponaname]

math aside why is the poll set to end in 2030

 

[bdt2002]

I think I might be misunderstanding the question at hand and what you're actually asking, because there's a lot of big numbers being thrown around here that don't necessarily relate to the question in the OP. I just read up again on the thing about flinches but I still don't think I understand completely. Iron Head has a base power value of 80, and after STAB that should go up to 120, right? The random damage roll multiplier can range from 0.85x to 1x, so if we assume each value X from 0.85 and 1.0 has a 1 in 16 chance of being rolled, the average damage roll should be somewhere around 0.925x, which because Pokémon's RNG mechanics are quite frankly stupid rounds down to a 16-bit binary estimate of 0.92x if binary value 0 = 0.85x, 1 = 0.86x, 2 = 0.87x, and so on. The closest answer choice to 120 BP x 0.925 damage roll I could find on the poll was 114, so that's what I clicked before realizing I had to reread that part about flinches like I said. Statistically speaking, Serene Grace Iron Head should have a 60% flinch rate, but the odds of rolling multiple 60% flinches in a row is less than 50% (60% squared should be 36%), so shouldn't the correct answer be 228 BP per two turns or 348 BO per three turns if we assume two flinches per three turns on average?

 

[Hydrametr0nice]

I think I might be misunderstanding the question at hand and what you're actually asking, because there's a lot of big numbers being thrown around here that don't necessarily relate to the question in the OP. I just read up again on the thing about flinches but I still don't think I understand completely. Iron Head has a base power value of 80, and after STAB that should go up to 120, right? The random damage roll multiplier can range from 0.85x to 1x, so if we assume each value X from 0.85 and 1.0 has a 1 in 16 chance of being rolled, the average damage roll should be somewhere around 0.925x, which because Pokémon's RNG mechanics are quite frankly stupid rounds down to a 16-bit binary estimate of 0.92x if binary value 0 = 0.85x, 1 = 0.86x, 2 = 0.87x, and so on. The closest answer choice to 120 BP x 0.925 damage roll I could find on the poll was 114, so that's what I clicked before realizing I had to reread that part about flinches like I said. Statistically speaking, Serene Grace Iron Head should have a 60% flinch rate, but the odds of rolling multiple 60% flinches in a row is less than 50% (60% squared should be 36%), so shouldn't the correct answer be 228 BP per two turns or 348 BO per three turns if we assume two flinches per three turns on average?

Yeah, you're misunderstanding the question. The OP is simply asking what the average BP (battle power) of Iron Head would be, given its 60% flinch chance and accounting for the cumulative probability of the opponent being unable to move. The answer is 2.5 × 80 = 200 BP, or, if factoring in paralysis (as mentioned in a later post), the answer is 3.(3) × 80 = 266.66... BP. That's all.

 

[gephicka]

way late but wtvr

i was being a little silly here and tried to pull AP calc on this one, doing this at 5am as a disclaimer

40% being the chance of no flinch, so then .4^x being the function for the chance to not flinch as you continue to click iron head
i thought if you find the average value of the function you may be able to use that value to determine at which pp it would be most likely to stop
but i think i fried my brain a little & made this more complicated than it needs to be

if there is a way to do this similar to what i did lmk im curious (also exhuasted)

 

[Vertigo]

way late but wtvr

i was being a little silly here and tried to pull AP calc on this one, doing this at 5am as a disclaimer
View attachment 741762
40% being the chance of no flinch, so then .4^x being the function for the chance to not flinch as you continue to click iron head
i thought if you find the average value of the function you may be able to use that value to determine at which pp it would be most likely to stop
but i think i fried my brain a little & made this more complicated than it needs to be

if there is a way to do this similar to what i did lmk im curious (also exhuasted)

You have almost the correct idea, but instead of acting on real numbers you should act on integers (since turn count is an integer).
For the sake of argument, let's assume infinite PPs and turns (since the value with PPs factored in is extremely close).
T1: You click IH and you are guaranteed at the very least a damage multiplier of x1 (since it always hits).
T2: The probability you get to click IH and the opponent has flinched the turn prior is 0.6, so the expected contribution to the total multiplier is base multiplier (in this case, x1) * 0.6.
T3: The probability you get to click IH and the opponent has flinched the turn prior is now 0.6 * 0.6. The expected contribution to the total multiplier is 1 * 0.6^2.
Turn n: You only get there if the opponent flinched the prior n-1 turns. The probability of this happening is 0.6^n-1, so the expected contribution to the total multiplier is 1 * 0.6^n-1.

The total expected damage multiplier is the sum of all multipliers from each potential attack, which assuming an infinite number of turns and PPs is a geometric series of common ratio 0.6. Since the common ratio is less than 1 (and greater than -1), this series is convergent and we can calculate its sum.

Other people in this thread mentioned the geometric series already, but I think expanding on it a little bit to demonstrate why it's the sum of a geometric series is a good exercise, but yeah that was a good way to approach it gephicka