Blonk numbers and Center of the Cubieverse

Discussion in 'General Speedcubing Discussion' started by Stefan, Apr 12, 2010.

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  1. keemy

    keemy Member

    151
    0
    Dec 29, 2007
    WCA:
    2006CORR01
    darn I'm 375th I should go to some comps on other continents.
     
  2. Stefan

    Stefan Member

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    May 7, 2006
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    Interesting question I don't have an answer for yet: Can your rank get *worse* by going to a competition?

    More precisely, compare these two scenarios:
    1) You participated in competition X.
    2) You didn't participate in competition X.
    That's the only difference, everything else is the same.

    In scenario 1, your average distance is probably lower and definitely not higher (unless you're connecting to an otherwise unconnected part of the graph). But what about your rank? By being there you not only lower your own average distance, you're also lowering other people's average distance. Is it possible that your rank is better in scenario 2?

    Btw, I'm putting this on hold until Friday, need to work on something else now.
     
    Last edited: Apr 13, 2010
  3. Mike Hughey

    Mike Hughey Super Moderator Staff Member

    8,738
    300
    Jun 7, 2007
    Indianapolis
    WCA:
    2007HUGH01
    YouTube:
    MikeHughey1
    My daughters Marie and Rebecca have exactly the same stats too. (They've been to all the same competitions together.) They are both 410 in the cubieverse.

    Is there any other pair of competitors with identical stats who can beat their rank? :D
     
  4. Stefan

    Stefan Member

    7,287
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    May 7, 2006
    WCA:
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    Joel and Maria are the first who have the same average and thus share the same rank, 51:
    http://stefan-pochmann.info/cubieve...YM01&showDists=Show+distances+for+this+WCA-ID
    http://stefan-pochmann.info/cubieve...OR01&showDists=Show+distances+for+this+WCA-ID

    Robin and Monika are the first with identical stats, at rank 134.
    http://stefan-pochmann.info/cubieve...OH02&showDists=Show+distances+for+this+WCA-ID
    http://stefan-pochmann.info/cubieve...MM01&showDists=Show+distances+for+this+WCA-ID
    They're joined by Adam at rank 134 (the first triple) with the same average but different stats:
    http://stefan-pochmann.info/cubieve...LL03&showDists=Show+distances+for+this+WCA-ID
     
  5. Edam

    Edam Premium Member

    433
    0
    Sep 23, 2008
    Devon, UK
    WCA:
    2008WILL03
    YouTube:
    blackoutcurtain
    first triple, excellent. :)
     
  6. Stefan

    Stefan Member

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  7. keemy

    keemy Member

    151
    0
    Dec 29, 2007
    WCA:
    2006CORR01
    yo I made a counter example on a graph but it was comparing having a comp with 2 people versus if 1 didn't show up so technically not allowed by wca rules but I don't want to make a more complicated graph.

    [​IMG]

    so I'm trying to make it so with the comp top left comp goer will pass the bottom right comp goer (will worry about the rest of the people later, also I am going to use the sum of distances rather than average because the ranks will be the same)

    so I want to find some solutions to the system of inequalities.

    4m+3+2+k > 3+2k+(m+1) and 2(m+1) + (k+1) < 2k + (m+2)

    simplifying we get 3m+1 > k and m+1 < k which works for k=3, m=1

    then to verify i draw the graph with k=3 and m=1 (you can imagine it XP) and check to make sure what i wanted happened. As it turns out the bottom right comp goer was originally ranked 2nd and goes down the 3rd by attending the comp.

    If someone wants to construct a case were at least 12 people must go to a competition that would be nice (or prove it's impossible)

    oh and qq wrote a graph theory sounding definition for the question if anyone is interested:

    start with a graph of people, with "distance" defined as avg minimal distance to other vertices, and "rank" defined as a point's rank in the list of possible distances. If you add a K_n to the graph (you can add vertices if you want), can you make the rank of any vertex in that K_n strictly worse compared to leaving that vertex out of the K_n and adding a K_(n-1) without them.

    and I guess we want a case with n>= 13
     
    Last edited: Apr 18, 2010
  8. qqwref

    qqwref Member

    7,828
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    Dec 18, 2007
    a <script> tag near you
    WCA:
    2006GOTT01
    YouTube:
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    Hey, Stefan, how many people are at most distance 3 from everyone else in the large group of connected people? It seems that some of the top 10 people have this property, but they don't all.
     
  9. Stefan

    Stefan Member

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    No problem with the non-WCA-compliant competition size, that's arbitrary anyway. I disagree with your example, though.

    If I understand and analyzed your example correctly, he actually went from rank 5 to shared rank 3.
    dontgo.png

    Michael: Will check that tomorrow.
     
    Last edited: Apr 18, 2010
  10. keemy

    keemy Member

    151
    0
    Dec 29, 2007
    WCA:
    2006CORR01
    Stefan: B, C, D shouldn't be connected to each other. (so just add 2 to what you have b,c,d as in both your graphs)
     
    Last edited: Apr 18, 2010
  11. megaminxwin

    megaminxwin Current Clock NR Holder

    574
    0
    Feb 17, 2010
    WCA:
    2010MACA01
    Distances to me:
    0:1 (me)
    1:32
    2:563
    3:4659
    4:3757
    5:76
    none:19
    Average: 3.3608
    So I'm number 8676 in the list.

    My Blonk Number:
    3: Me
    Melbourne Summer Open 2010
    2: Dene Beardsley
    San Francisco Open 2009
    1: Bob Burton
    WC 2005
    0: Michiel Van Der Blonk
    So my Blonk Number is 3.

    w00t random statistics
     
  12. Tim Reynolds

    Tim Reynolds Premium Member

    995
    34
    Jun 28, 2006
    Boston, MA
    WCA:
    2005REYN01
    YouTube:
    timbreynolds
    Last night I was curious who else was near the top of the list of average distances, so Dave and I found the top 33. Not surprisingly, everyone on that list went to WC2009. Stefan, do you know who's highest on the list that didn't go to WC2009?
     
  13. anders

    anders Member

    159
    1
    Mar 6, 2008
    Sweden
    WCA:
    2003LARS01
    I didn't go to WC2009.
     
  14. Tim Reynolds

    Tim Reynolds Premium Member

    995
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    Jun 28, 2006
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    2005REYN01
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    ...Ah, right. D'oh. I guess I assumed that since the other 32 of the top 33 did, you did too.
     
  15. anders

    anders Member

    159
    1
    Mar 6, 2008
    Sweden
    WCA:
    2003LARS01
    That was a fair assumption, but I moved to Singapore right before the WC. I did my planning when it still was said that the WC will take place in Hong Kong...
     
  16. Yes We Can!

    Yes We Can! Member

    2,310
    69
    Jan 27, 2009
    Berlin, Germany
    WCA:
    2009DIEC01
    YouTube:
    FCCZJ1903
    2: Cornelius Dieckmann
    WC2009
    1: Lars Vandenbergh
    WC2005
    0: Michiel van der Blonk

    Yay :D

    My average number is 2.1333 :)
    (279th)
     
  17. JBCM627

    JBCM627 Member

    799
    0
    Apr 27, 2008
    Ohio, USA
    WCA:
    2006MERT01
    Would it be possible to see some sort of geographic representation of Blonk numbers? As in, a world map with an average number for each country. I wonder if there would be an obvious geographic correlation between average Blonk number and location of the 2 Blonk competitions (WC03 & WC05).

    Should be straightforward enough to implement with one of these:
    http://en.wikipedia.org/wiki/Wikipedia:Blank_maps#World
     
  18. Stefan

    Stefan Member

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    May 7, 2006
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    New page showing everybody's stats (except the guys from the lone Dubai competition). Still rough and not using the newest data, but nice enough to show:
    http://stefan-pochmann.info/cubieverse/cubieverse.html

    26, you can see it now on that new page by sorting by distance 4 and seeing there are 26 with nobody at distance 4.

    Yes, only four do.

    And Piti truly is the master of connections. He's at most 3 away from everyone and has the smallest number of distance-3 persons. All that with only 9 competitions.
     
    Last edited: Apr 20, 2010
  19. Stefan

    Stefan Member

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    Added showing number of competitions.

    After Piti (rank 10 with only 9 competitions), the best ranks with fewest competitions are:

    Rank 39 with only 5 competitions: Baramee Pookcharoen
    Rank 96 with only 4 competitions: Arnold Soeparjanto
    Rank 124 with only 3 competitions: Denis Goepfert
    Rank 129 with only 2 competitions: Michael Layher (WC2007 and WC2009)
    Rank 321 with only 1 competition: Eileen Henfling and 17 other people who only competed at WC2009

    And in the other direction, bad rank despite many competitions:

    Rank 1000 despite 20 competitions: Shenjia Zhang (only competed in east China)
    Rank 5586 despite 10 competitions: Syoji Takamatsu (only competed in Japan)
    Rank 7074 despite 8 competitions: Krzysztof Zygowski (only competed in Poland)
    Rank 8325 despite 4 competitions: Ming-Yi Lin (only competed in Taiwan)

    (this list is incomplete, done by hand)
     
    Last edited: Apr 20, 2010
  20. qqwref

    qqwref Member

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    Seems like rank is quite highly dependent on how many/which world competitions you've been to.

    Interesting result: Bob Burton has been to competitions with the most unique people.
     

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