Docstoc

Medals Tally of Olympics Based on Weighted Points

Document Sample
Medals Tally of Olympics Based on Weighted Points Powered By Docstoc
					   International Journal of Emerging Trends & Technology in Computer Science (IJETTCS)
       Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com
Volume 1, Issue 2, July – August 2012                                          ISSN 2278-6856




      Medals Tally of Olympics Based on Weighted
                         Points
                                    Sovan Samanta and Chinmoyee Samanta
                        Department of Applied Mathematics with Oceanology and Computer Programming,
                                       Vidyasagar University, Midnapore - 721 102, India.




Abstract: Olympic games are worldwide popular events. In        Rank     country      Gold     Silver    Bronze     Total
this paper, we made a new approach to medals tally. Each          9        Italy       8          9        10        27
medal is assigned with points.                                   10       France       7         16        18        41
Keywords: weighted points, olympic, sports.                      27      Georgia       3          0        3          6
                                                                 28        Cuba        2         11        11        24
                                                                 70       Chile        0          1        0          1
                                                                 78      Armenia       0          0        6          6
1. INTRODUCTION
Olympic games is, now, called ``The greatest show on           Table 3: List of distinguishable examples in olympics
earth". The Ancient Olympic Games were a religious and                                 2012 .
athletic festival held every four years at the sanctuary of    Rank      country         Gold Silver      Bron Tota
Zeus in Olympia, Greece among representatives of several                                                    ze      l
city-states and kingdoms of Ancient Greece . Since the
                                                                 9       Hungary           8        4       5      17
modern Olympic Games began in 1896 , there have been
                                                                10       Australia         7       16       12     35
 30 Summer Olympic Games held in 22 different cities            20    Korea(Democ          4        0       2       6
and 21 Winter Olympic Games held in 18 different                             ra)
cities.                                                         21         Spain           3       10       4      17
An Olympic medal is awarded to successful players at            50        Algeria          1        0       0       1
each format of play of the Olympic Games. There are             55         India           0        2       4       6
three classes of medal: gold, awarded to the winner;
silver, awarded to the runner-up; and bronze, awarded to      In spite of little less of gold medals of a country ``A", and
the third-place competitor. The Olympic Order is              many more medals in silver and bronze i.e., many more
awarded to individuals for particularly distinguished         total medals (some times double or triple times) than a
contribution to the Olympic Movement.                         country ``B", ``B" get more credits than ``A" (see Table
Authority makes medals tally depending on only gold           1, 2, 3). This particular problem i.e., medal tally is
medals except equality of gold medals of countries. This      prepared only by gold medals except two country have
system has some problems over the years. A list of such       same number of golds, is tried to solve partially in this
distinguishable examples [1, 2, 3] is given below.            paper.


 Table 1: List of distinguishable examples in olympics
                                                              2. WEIGHTED POINT FOR MEDALS
                         2004 .
            country       Gold   Silver   Bronze     Total    A weighted point for medals is formulated as below.
 Rank                                                         Here, for gold medal 8 points are assigned. For silver
   2        China          32      17       14        63      medal 3 points are assigned at least. For bronze medal 1
   3        Russia         28      26       38        92      point is assigned at least. Now first three positions are
  17       Norway          5       0         1         6
                                                              given credits. So the third place is depended by the fourth
  18      Netherlands      4       9         9        22
                                                              positioned player. If the fourth positioned player had a
  32       Georgia         2       2         0         4
  33       Bulgeria        2       1         9        12
                                                              good chase to bronze medal winner and would have
                                                              crossed the third placed player then the result would have
                                                              changed. Thus fourth place is an important for weighted
                                                              points of medals.
 Table 2: List of distinguishable examples in olympics
                                                              Let gold medal winner earns a points, silver medal
                         2008 .
                                                              winner earns b points, bronze medal winner earns c

Volume 1, Issue 2 July-August 2012                                                                             Page 112
   International Journal of Emerging Trends & Technology in Computer Science (IJETTCS)
       Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com
Volume 1, Issue 2, July – August 2012                                          ISSN 2278-6856


points, and fourth place winner earns d points. Here the      Points earned by gold medal winner ,
points, earned by players, will be decided by the authority   MURRAY = 8
of particular formats of play
such that a  b  c  d .
                                                              Points earned by silver medal winner ,
                                                                                  52
 Points       earned   by         silver      medal            FEDERER = 3  (1       ) = 3.4
                                                                                  50
 winner        = 3  P1 ,                                     Points earned by bronze medal winner ,
                             a  b                                                        22
 where        P1 = 1              .                          DEL POTRO = 1  (1             )=2
                             a  d                                                        50


Points earned by bronze medal
winner = 1  P2 ,
                  b c
where P2 = 1          .
                  ad


 2.1 Example of weighted points in race
Here an example of race in 100 meters of olympic
2012 is given (see Table 4).
Table 4: First four stands in 100 meter race in Olympic
                          2012.
   Stands          Names          Timings
      1          Usian Bolt         9.63
      2         Youhan Blake        9.75
      3         Justin Gatlin       9.79
      4          Tyson Gay          9.80


Points earned by gold medal winner ,
Bolt = 8

  Points earned by silver medal winner ,
                     9.75  9.63                                       Figure 1: Olympic 2012 medal tally 1.
  Blake = 3  (1                ) = 3.4
                     9.80  9.63

  Points earned by bronze medal winner ,                      3. MEDALS' TALLY IN OLYMPIC 2012 BASED ON
                                                              WEIGHTED POINTS TO MEDALS
                    9.79  9.75
  Gatlin = 1  (1              ) = 1.8                       Here we assume the average weight of medals for each
                    9.80  9.63                               format of play as 8 to gold, 3.5 to silver, 1.5 to bronze.
                                                              We rearrange the medals tally to their current ranking.
  2.2 Example of weighted points in tennis                    We placed the country name according to gold medals.
Here an example is collected from olympic mens' tennis.       The left column indicates the ranks according to their
In bronze medal match, DEL POTRO defeated                     weighted points. In Figure 1, Russian Federation replaced
DJOKOVIC by 2  0 sets. In gold medal match,                  Great Britan in third place to official rank table.
MURRAY defeated FEDERER by 3  0 sets. Here the               Similarly, Japan, France also increased their credits in
credits to the players are set as DJOKOVIC  0 ,              rank table. Also in Figure 2, Canada made significant
 DELPOTRO  2 ,             FEDERER  2  0 = 2 ,             increase in rank table.
 MURRAY  2  3 = 5 .

Volume 1, Issue 2 July-August 2012                                                                           Page 113
   International Journal of Emerging Trends & Technology in Computer Science (IJETTCS)
       Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com
Volume 1, Issue 2, July – August 2012                                          ISSN 2278-6856




                                                        Figure 4: Olympic 2012 medal tally 4.

       Figure 2: Olympic 2012 medal tally 2.
                                               4. CONCLUSION
                                               The rank table of olympic games, asian games, etc are
                                               arranged according to their gold medals. But we have
                                               made this according to their performances. For gold
                                               medal winner, 8 points are fixed. For silver medal
                                               winner 3 to 4 points are assigned. Similarly for bronze,
                                               1 to 2 points are assigned. So good performances in
                                               third or second places i.e., tough competition to second
                                               and first placed players respectively, may give good result
                                               in rank table.
                                               This method may have some difficulties to assign credits
                                               to different sports like football, tennis, etc. We have given
                                               an example in 2.2 to clear the fact. The authority can set
                                               the rules. This technique can be applied to various
                                               sporting events.

                                               REFERENCES
                                               [1] en.wikipedia.org/wiki/2004SummerOlympics
                                               [2] en.wikipedia.org/wiki/2008SummerOlympics
                                               [3] www.london2012.com/
                                               [4] S. Samanta and M. Pal, Fuzzy tolerance graphs,
                                               International Journal of Latest Trends in Mathematics,
                                               1(2), 57-67, 2011.
                                               [5] S. Samanta and M. Pal, Fuzzy threshold graphs,
                                               CIIT International Journal of Fuzzy Systems, 3(12), 360-
                                               364, 2011.
                                               [6] S. Samanta and M. Pal, Bipolar fuzzy hypergraphs,
                                               International Journal of Fuzzy Logic Systems, 2(1), 17-
                                               28, 2012.
       Figure 3: Olympic 2012 medal tally 3.

Volume 1, Issue 2 July-August 2012                                                               Page 114
   International Journal of Emerging Trends & Technology in Computer Science (IJETTCS)
       Web Site: www.ijettcs.org Email: editor@ijettcs.org, editorijettcs@gmail.com
Volume 1, Issue 2, July – August 2012                                          ISSN 2278-6856


[7] S. Samanta and M. Pal, Irregular bipolar fuzzy
graphs, Inernational Journal of Applications of Fuzzy
Sets, 2, 91-102, 2012.
[8] S. Samanta and M. Pal, Fuzzy k -competition graphs
and p -competition fuzzy graphs, Communicated.
[9] S. Samanta and M. Pal, Fuzzy planar graphs,
Communicated.


             Sovan Samanta received his B.Sc. degree in
               2007 and M.Sc. degree in 2009 in Applied
               Mathematics from Vidyasagar University, India.
               He is now currently a research scholar in the
               Department of Applied Mathematics, Vidyasagar
University since 2010. His research interest includes fuzzy
graph theory .

             Chinmoyee Samanta received her                B.Sc.
             degree in 2007 in Applied Mathematics from
             Vidyasagar University, India.
              His research interest includes sports science.




Volume 1, Issue 2 July-August 2012                                                  Page 115

				
DOCUMENT INFO
Description: International Journal of Emerging Trends & Technology in Computer Science (IJETTCS) is an online Journal in English published bimonthly for scientists, Engineers and Research Scholars involved in computer science, Information Technology and its applications to publish high quality and refereed papers. Papers reporting original research and innovative applications from all parts of the world are welcome. Papers for publication in the IJETTCS are selected through rigid peer review to ensure originality, timeliness, relevance and readability. The aim of IJETTCS is to publish peer reviewed research and review articles in rapidly developing field of computer science engineering and technology. This journal is an online journal having full access to the research and review paper. The journal also seeks clearly written survey and review articles from experts in the field, to promote intuitive understanding of the state-of-the-art and application trends. The journal aims to cover the latest outstanding developments in the field of Computer Science and engineering Technology.