mathematical reason why China always win by 4-1.

Discussion in 'General Forum' started by kwun, May 15, 2004.

  1. kwun

    kwun Administrator

    Joined:
    Apr 24, 2002
    Messages:
    40,503
    Likes Received:
    1,474
    Occupation:
    BC Janitor
    Location:
    Santa Clara, CA, USA
    mathematical reason why China always win Uber Cup by 4-1.

    here is a mathematical explanation why China always win by 4-1 instead of a dominating 5-0 in the Uber final events.

    as we all know that winning an individual event isn't a 100% matter. there are many factors contributing to the win and loss of a match. if we are allowed, let's peg a probability to China winning a match. say that's P(win).

    a Uber cup team tie has 5 events.

    as established above, we have a simple Binomial distribution of the probably P(n/N), ie. the probability of winning n trials in N Bernoulli trials.

    the graph of the probabilities are as plotted in the graph. this is when P(win) = 0.84. and that's where P(4/5) ~= P(5/5). in laymen terms, the probability of winning 5 out of 5 events is the same as the probability of winning 4 out of 5 events are the same.

    if we increase P(win) to > 0.84, then P(5/5) is higher, if we decrease P(win) to < 0.84, then P(4/5) is higher.

    and to me, a probability of P(0.84) is quite high in general. that's requires a very high level of consistency as well as external factors like illness and injury. and more importantly, their opponents are no push-overs either, as we can see, Korea (the previous finalists) are quite strong as well.

    thus that explains why China always lose one match out of 5 possible. and why LiYongBo always emphasize consistency.

    for the ppl who do not understand the above mathematical explanation, it is ok, it is not any mathematical breakthrough but just some small insight. basically it means that to win 5/5 is quite hard.
     

    Attached Files:

  2. Cheung

    Cheung Moderator

    Joined:
    Apr 25, 2002
    Messages:
    21,463
    Likes Received:
    3,128
    Occupation:
    wannabe badminton phototaker
    Location:
    Outside the box
    Cool :cool:

    Why didn't I think of that before? :(

    But we need the combinations of 3-0 and 3-1.

    Never get 5-0 since not all matches will be played once 3 wins are reached.

    Sheesh, the things badminton fanatics do.............. :eek:
     
  3. Joseph

    Joseph Regular Member

    Joined:
    Sep 15, 2002
    Messages:
    1,242
    Likes Received:
    0
    Location:
    San Jose, CA
    Binomial distributions...statistics...haha good stuff Kwun. Maybe I can include some of this in my presentation in my statistics class. Well...only if you give me permission to ;)
     
  4. AKFT

    AKFT Regular Member

    Joined:
    May 18, 2002
    Messages:
    216
    Likes Received:
    1
    Location:
    USA
    Kwun: Can you start by explaning what a binomial is???? :D
     
  5. wilfredlgf

    wilfredlgf Regular Member

    Joined:
    May 6, 2003
    Messages:
    2,583
    Likes Received:
    11
    Occupation:
    Security Engineer
    Location:
    Malaysia
    Binomial is what contributes to the bell curve of averages. It concerns with the calculation of probabilities of something happening within the distribution curve, given the number of samples and some other controlled elements.

    ie. The distribution of player skill levels in badminton out of 1000 samples may yield

    200 beginner levels
    350 intermediate
    300 advanced
    100 professionals
    50 world class

    thus, the bell curve. I don't quite remember how to explain the P(N/r) calculation thingy.

    Darn it, it's been eons since I did statistics and I don't regret it one bit - I never liked statistics and probabilities!

    I'm the calculus/integration type of person. ;)
     
    #5 wilfredlgf, May 15, 2004
    Last edited: May 15, 2004
  6. Zax

    Zax Regular Member

    Joined:
    Jan 12, 2003
    Messages:
    326
    Likes Received:
    0
    Occupation:
    badminton promotor :)
    Location:
    Eindhoven, the Netherlands
    Binomial Badminton

    In mathematics, the binomial distribution is a discrete probability distribution which describes the number of successes in a sequence of n independent yes/no experiments, each of which yielding success with probability p. Such a success/failure experiment is also called a Bernoulli experiment.

    A typical example is the following: 5% of the population are Badminton-freak. You pick 500 people randomly. How likely is it that you get 30 or more freaks? The number of freaks you pick is a random variable X which follows a binomial distribution with n = 500 and p = .05.

    There's a standard way to compute the chances but it's difficult to write down in formulas here.
     
  7. Zax

    Zax Regular Member

    Joined:
    Jan 12, 2003
    Messages:
    326
    Likes Received:
    0
    Occupation:
    badminton promotor :)
    Location:
    Eindhoven, the Netherlands
    Final Thomas Cup

    Hey Kwun,

    estimate some chances for the Thomas Cup Final match and calculate the score for us ;)

    - Mark.
     
  8. kwun

    kwun Administrator

    Joined:
    Apr 24, 2002
    Messages:
    40,503
    Likes Received:
    1,474
    Occupation:
    BC Janitor
    Location:
    Santa Clara, CA, USA
    hold on... let me bring out the crystal ball! :)
     
  9. Neil Nicholls

    Neil Nicholls Regular Member

    Joined:
    Aug 21, 2002
    Messages:
    2,908
    Likes Received:
    10
    Location:
    Cannock, UK
    The number you are looking for so that P(5-0) = P(4-1) is 5/6 or 0.833333 recurring.
    Why?
    There are 5 ways of winning 4-1 ( you can lose the 1st,2nd.3rd,4th or 5th match). So when the P(win) = 5 x P(Lose) we get what we want. And this is when P(win) = 5/6 and P(Lose) = 1/6


    (I had gone into more detail, but my PC crashed and I can't do it all again because TC final has started now)
     
  10. kwun

    kwun Administrator

    Joined:
    Apr 24, 2002
    Messages:
    40,503
    Likes Received:
    1,474
    Occupation:
    BC Janitor
    Location:
    Santa Clara, CA, USA
    does the mathematical model look different if they play to 3 wins instead of playing all 5 matches regardless of results?
     
  11. Neil Nicholls

    Neil Nicholls Regular Member

    Joined:
    Aug 21, 2002
    Messages:
    2,908
    Likes Received:
    10
    Location:
    Cannock, UK
    There are only 20 possible outcomes instead of 32 (2**5)

    assuming each pair has 84% chance of winning a match
    Win 3-0 59.3%
    Win 3-1 28.4%
    Win 3-2 9.1%
    Lose 2-3 1.7%
    Lose 1-3 1.0%
    Lose 0-3 0.4%
    96.8% chance of winning the tie (so the 84% looks too high)

    reduce the 84% to 66.666% ( 2/3 ) and you get
    Win 3-0 29.6%
    Win 3-1 29.6%
    Win 3-2 19.8%
    Lose 2-3 9.9%
    Lose 1-3 7.4%
    Lose 0-3 3.7%
    79.0% chance of winning the tie

    for a 3-1 win to be more likely than a 3-0 win, each pairs chance of winning a match has to be below 66.666%
     
  12. dlp

    dlp Regular Member

    Joined:
    Jun 19, 2002
    Messages:
    963
    Likes Received:
    1
    Occupation:
    Accountant / Coach
    Location:
    uk
    Neil what about the fact that the % chance of winning would be higher if you were leading 2-0 instead of at 1-1, i.e. the effect of the match score on the player performance, Can we have some figures on that please.

    Only kidding:)

    Perhaps Kwun and yourself can do a PHD in "Statistical Probablity of an Uber Cup tie being won by China"

    I calculate the probablity of England winning a Thomas Cup tie as follows

    England win:
    MS1 1%
    MS2 2%
    MS3 3%
    MD1 50%
    MD2 15%

    Please tell me if we can win a Thomas Cup in my lifetime :)
     
  13. Cheung

    Cheung Moderator

    Joined:
    Apr 25, 2002
    Messages:
    21,463
    Likes Received:
    3,128
    Occupation:
    wannabe badminton phototaker
    Location:
    Outside the box
    The probability is small:)
     
  14. kwun

    kwun Administrator

    Joined:
    Apr 24, 2002
    Messages:
    40,503
    Likes Received:
    1,474
    Occupation:
    BC Janitor
    Location:
    Santa Clara, CA, USA
    the USA was strong in badminton the 50's (or was it 40's). if even that is possible, and only a mere 50-60 years ago, there has got to be some small hope for England.
     

Share This Page