Measure of centralisation in a metagame

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X-Act

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Here's a list of all centralisation numbers from July to November (the months where Doug provided stats for the Smogon and CAP servers) of all ladders:

Code:
    Ladder           Months
             Jul  Aug  Sep  Oct  Nov
-------------------------------------
  Standard    12   12   11   11   11
        UU    10    9    9   10   10
      Uber    35   31   26   27   35
   Suspect    --   13   12   22   --
       CAP    --   --   11   --   17
Little Cup    --   --   23   --   26
 
Ubers isn't supposed to be balanced so "Centralization" is wholly irrelevant.
Well, just because it's centralized doesn't mean the tier is unbalanced. There exists a balance WITHIN the small group of Pokemon that are competitively viable in Ubers.

It's just that with so many high-stat pokes, it's unsurprising that it's centralized. But the tier is hardly "Unbalanced".
 

cim

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It's unbalanced toward a specific group of Pokémon, that happen to check each other.

Also, lol Little Cup is one of the most centralized metagames out there. THough that's probably due to a lack of players.
 
nice job X- Act

just a question
we've seen that if all F = O we get 0, but does the same thing happen if all pokemon were used in an equal balance? (aka every pokemon from bulbasaur to Shymin minus UBERS) was used 5000 times each) this will never happen, but in theory if it did happen F and O just equal 0 right?
 

X-Act

np: Biffy Clyro - Shock Shock
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nice job X- Act

just a question
we've seen that if all F = O we get 0, but does the same thing happen if all pokemon were used in an equal balance? (aka every pokemon from bulbasaur to Shymin minus UBERS) was used 5000 times each) this will never happen, but in theory if it did happen F and O just equal 0 right?
Let me think of this.

Suppose a metagame having P Pokemon is such that all of them are each used U times as you say. That would mean that the total number of usages would be PU.

F is the number of Pokemon having more than PU / 37.7113 usages. This number of Pokemon can either be 0 or P. If P > 37, then F = 0, else F = P.

O is the number of Pokemon having more than PU / 176.1407 usages. This number can also be either 0 or P. If P > 176, then O = 0, else O = P.

Hence, if the number of Pokemon in the metagame is between 38 and 176, then my formula would say that it would be a very uncentralised metagame. Otherwise it would say that it would be an infinitely centralised metagame, which is the incorrect value.

Thanks for the heads-up. I'll research this further, as this formula obviously does not work in the most extreme of cases.
 

X-Act

np: Biffy Clyro - Shock Shock
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Okay, I'm locking this, since this formula is not as good as I thought it would be.
 
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