1. This site uses cookies. By continuing to use this site, you are agreeing to our use of cookies. Learn More.
  2. Welcome to Pokemon Perfect, Guest!

    Our motto is Pokémon Practice makes Pokémon Perfect. We are a competitive-battling community that encourages the development of players and their ideas, and fosters positive and respectful attitudes. We love Collaboration (working together), Competition (getting stronger), and Communication (being informed).

    You are free to post everywhere, unless the thread explicitly states otherwise (usually in the case of a vote), and there are no private forums whatsoever. We just require you to not make multiple accounts. Let us greet you by posting a thread in the Introduce Yourself! forum.

  3. Tiers

    View Introduction to Tiers if you don't know what tiers are. Pokémon Perfect tiers are named differently to those on Smogon. A numeral followed by the letter U, e.g. 1U, 2U, 3U, represents a main tier on Pokémon Perfect – the '1' of '1U' representing the tier level. For a tier to be a main tier, it must be balanced (nothing is too powerful and game-breaking) and diverse enough (include a variety of Pokémon and strategies). A numeral followed by the letter P, e.g. 1P, 2P, 3P contain all Pokémon that are deemed overpowered in the respective 1U, 2U, 3U tiers. The 1st tier level allows Pokémon that are banned in the 2nd level, and this process continues down. Read the tier list, and in-depth explanations of the tiers naming system and tiering system. Also check out our analyses for all tiers.

  4. Tournaments

    RBY 1U Seasons and its master tournaments are responsible for starting up the community, and tournaments continue to play a big role in maintaining interest in the forums. Signups Open gives you a list of tournaments you can join, and Ongoing lists tournaments that you might want to follow. Additionally, you can tap to find out approximate Schedules for tournaments.

    For historical threads, check out Signups Closed, Finished tournaments and Results. We also have Nominations, Voting and Event threads for exhibitions – past and present.

All Gens The Mathematics Of Phazing

Discussion in 'Analysis and Research' started by Disaster Area, Apr 27, 2020.

  1. Disaster Area

    Disaster Area Little Ball of Furr and Power Member

    Joined:
    May 4, 2014
    Messages:
    5,594
    Likes Received:
    2,489
    Roar and other pseudo-hazing moves are not a much-discussed random element of the game and I thought that it would be a good idea to shed some light on it, trying to figure out what you should typically expect when using the move. We are interested in how long the phazing sequence will be, and maybe this could be taken further by looking at how much damage you could expect to accrue across a phazing sequence.

    Variables:
    x - Number of Pokemon on the opposing team
    y - Number of Pokemon on the opposing team which, if roared in would end the phazing sequence.

    We will restrict x and y such that x and y are integers at least equal to 1, x is at most 6, and y is between 1 and x-1.

    Assumptions:
    - If a pokemon faints, the phazing sequence ends.
    - If a pokemon won't end the phazing sequence, it will always be switched out into a Pokemon which can.
    - The sequence starts with the phazer against a Pokemon which cannot end the phazing sequence.

    Firstly, let's look at the simplest scenario, where we have y = 1. By using the assumptions, there is only one Pokemon which can end the phazing sequence, and it will always be switched in on the phazing move, and hence the phazing sequence only ends when either:
    - a pokemon faints
    - an assumption is violated
    - roar runs out of PP

    In practice, this describes the fact that if no or too little damage is dealt by the phazing move, the phazing move's PP is the first thing to go. Otherwise, either:
    - a Pokemon is forced to faint through the sequence,
    - a pokemon stays in to be phazed in to the pokemon which will end the sequence,
    - or a switch is made to a pokemon which can't end the sequence, but the pokemon which can end the sequence is brought in.

    It's not the most interesting of scenarios but nonetheless shows how if you only have one Pokemon available to end a phazing sequence, you may have to take a risk at some point to end it.

    The situation is a lot more interesting when y is at least 2. The situation can actually be described by a geometric distribution. There is an (y - 1) /(x - 1) chance of a "success" - the phazing sequence ends, so we can model a phazing sequence using a geometric distribution with probability p = (y - 1) /(x - 1). The number (y - 1) / (x - 1) comes from the following: when a pokemon switches and then is phazed, there are x - 1 possible pokemon brought in, of which y - 1 would end the sequence (as one of the y possibilities was switched in).

    Using this information, here is some basic information we can learn about phazing sequences based on various x and y values:



    Interested to see if anyone has any ideas on how to take this further! :)
     
    Last edited: Apr 27, 2020
    Typhlito likes this.
  2. magic9mushroom

    magic9mushroom BEST END. Member

    Joined:
    May 1, 2013
    Messages:
    706
    Likes Received:
    422
    This assumption is very rarely satisfied if the player getting phazed is not a moron.

    Assuming there are N 'mons (of which E can end the sequence with P utility), the 'mon in can achieve A utility by staying in, the phazer threatens T utility to the 'mon in by not phazing, and each switch (voluntary or forced) costs H then the choice matrix looks like this (for the phazee):

    Stay in/attack: A - T
    Stay in/phaze: A + EP/(N-1) - H
    Switch to non-ending/attack: -H
    Switch to non-ending/phaze: EP/(N-1) - 2H
    Switch to ending/attack: P - H
    Switch to ending/phaze: (E-1)P/(N-1) - 2H

    Obviously, if the chance the opponent will phaze is sufficiently high, then E(stay in) > E(switch to non-ending) > E(switch to ending). You have assumed a chance of phazing of 100% but also a chance of 100% that the phazee will switch to an ending 'mon; this is not in Nash equilibrium as the phazee will gain by increasing their chance of doing the other options.

    (The "switch to ending"/"switch to non-ending" flip is always at the point at which your opponent's chance of attacking is 1/N. Whether staying in is better than switching is much more complicated.)
     
    Last edited: May 14, 2020
  3. Disaster Area

    Disaster Area Little Ball of Furr and Power Member

    Joined:
    May 4, 2014
    Messages:
    5,594
    Likes Received:
    2,489
    I mean it does depend, if your skarmory keeps getting phazed in by a roar raikou, you're going to keep switching it out... but yes, it isn't always satisfied

    interesting to see how far you can take things just by loosening that assumption
     
  4. magic9mushroom

    magic9mushroom BEST END. Member

    Joined:
    May 1, 2013
    Messages:
    706
    Likes Received:
    422
    Yeah, that's why I put T in there; in that case T is xboxhueg (but on the other hand in the GSC case if you predict a Roar and you have balls of neutronium you can WW and break the chain right there, so A is, while not nearly as huge, also significant).

    But let's say you've got a Surf/IB/RestTalk Suicune in (so staying in is suicide if they STAB for little benefit if they Roar) and a Rhydon and a Blissey in the wings (and maybe some other random stuff like a Cloyster). Your best bet in that situation isn't to switch to Rhydon, it's to switch to Blissey, because then there's a chance Rhydon will get Roared in (whereas switching to Rhydon means Rhydon won't be in after Roar, and it's nearly certain that they'll Roar).

    That's why I gave the metrics for all three.
     
    Last edited: May 15, 2020
    asbdsp likes this.

Share This Page