development of taekwondo ranking model based on google ... · pagerank algorithm model this study...

Development of Taekwondo RankingModel Based on Google PageRank

Algorithm

Bong-Seok Kim1

1Department of Sports Coaching, Jeonju University,55069 Republic of Korea

January 26, 2018

Abstract

This study is to develop Taekwondo athlete ranking modeland verify the validity of the developed ranking model basedon Google’s PageRank algorithm. To this end, it looks into2,851 South Korean Taekwondo athletes (1,950 males, 901females) who have competed in the national competitionorganized by the Korea Taekwondo Association (KTA) in2015. In order to verify the validity of the calculated rankingusing the Google PageRank algorithm, a table of specifica-tion was used to calculate accuracy, sensitivity, specificity,and loss of information (LoI). Through the validity com-parison of the Google PageRank algorithm ranking modeland the KTA official ranking model, it was confirmed thatthe PageRank algorithm ranking model is more valid thanthe KTA official ranking model. In addition, the LoI, whichcan occur when there is no ranking or the same rankingexists, happens less in PageRank algorithm ranking modelthan in the KTA official ranking model. Therefore, it isdeemed that the Taekwondo athletes ranking model usingthe PageRank algorithm is an objective and valid rankingmodel that reflects the game results of each athlete. On thecontrary, the KTA official ranking model has disadvantagesof being unable to classify the subjective scores given by theassociation members, competition grade, rank, and others,

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International Journal of Pure and Applied MathematicsVolume 118 No. 19 2018, 1267-1278ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

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and to calculate valid ranking of all athletes participating inthe competition. Therefore, using the PageRank algorithmfor Taekwondo athletes ranking will enable a more objectiveand efficient ranking. The result of this study can be usedas basic information for the calculation of ranking in varioussports field other than Taekwondo.

Key Words : PageRank, taekwondo, ranking model,ranking validity, efficiency

1 INTRODUCTION

RANKINGS OF SPORTS GAMES have been recognized as an im-portant area of study for its economic significance. Most popularsports involve rankings of the final score, by fans and media, mak-ing necessary performance index for athletes or teams. Due to thefact that the rankings in sports are often used to assess perfor-mance levels of athletes or teams and are also used as the basisfor determining the salaries of athletes, the methods of calculatingranking have been of continual interest to researchers(Sorensen, S.,P., 2000; Lloyd, J., Conidi, F., 2015 Sunami, A et al.,2016). Start-ing in 2013, a ranking system was introduced to the sport of Taek-wondo(KTA2016; koreantaekwondo tripod2016). The calculationof ranking in Taekwondo is based on a point ranking system thattakes into consideration the wins and losses of an athlete as wellas the level of a participated competition. Since the point rankingsystem uses the results of an athlete in a competition and the levelof a competition to calculate points, it carries the advantages ofeasy calculations and a simple ranking process. However, certaindisadvantages exist in that the means by which weighted values aredetermined for each level of a competition are subjective and thenature of tournament games results in variability in the number ofpoints that can be acquired depending on opponents faced duringthe preliminary rounds(Radicchi, F., 2011). For these reasons, aPageRank algorithm-based ranking method, a method of rankingcalculation unaffected by the weighted value of the level of a com-petition and a method based on the continuity of wins and losses ofathletes, is being proposed (Lazocva & Basnarkov, 2015). PageR-ank algorithm has been used across a number of fields includingthe fields of information science, library classification, and sports

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science. The PageRank method was introduced as a means of cal-culating the ranking of tennis players at a certain period in historyand was also used to introduce the ranking of national footballteams(Chin, W., C., Wen, T., H., 2015; Lazova, V., Basnarkov, L.,2015; Beggs, C., B., Shepherd, S., J., 2017). In light of this, thisstudy aims to make use of Google’s PageRank algorithm to developa ranking model for South Korean Taekwondo athletes by weightclass and verify the validity of the developed ranking model. Theresults of the study are expected to be capable of not only rankingSouth Korean Taekwondo athletes, but also being used as basic in-formation for the calculation of ranking by the World TaekwondoFederation and in various other fields of sports.

2 MATERIALS AND METHODS

A. Research Subjects Of Taekwondo competitions organized by theKorea Taekwondo Association in South Korea during the year 2015,the match records of 2,851 athletes (1,950 males, 901 females), whohave participated in G2 level competitions (Association President’sCup, President’s Cup, Defense Minister Flag), G4 level competi-tions (Superior Athlete Selection, International Open), or G5 levelcompetitions (Domestic Ranking), were used to develop the rankingmodel and verify its validity. The number of matches considered inthe study was 5,438 in total (3,489 for male, 1,949 for female).

B. Analysis This study uses NetMiner 4 for the purpose of de-veloping a Taekwondo athlete ranking model using the PageRankAlgorithm. In order to apply the PageRank algorithm, the damp-ing factor was set at .15. Secondly, it was assumed that if thePageRank-based Taekwondo athlete ranking model is consideredmore valid than the conventional ranking model used by the Ko-rea Taekwondo Association, the ranking calculated by PageRankis likely to have a greater rate of accurately sorting the actual out-come of competitions. For instance, should an athlete have thehigher ranking of two athletes, whose rankings were both calculatedbased on the model, and have a higher rate of winning in actualgames against the athlete who does not, the model can be consid-ered relatively more valid. A table of specification was prepared to

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calculate accuracy, sensitivity, specificity, and loss of information(LoI). SPSS 21.0 and Microsoft Excel 2013 were used and the levelof statistical significance was set at 0.05.

3 RESULTS AND DISCUSSION

A. Calculation of ranking in Taekwondo athletes using Google’sPageRank algorithm model

This study aims to make use of Google’s PageRank algorithmto calculate the ranking of the national Taekwondo athletes basedon weight classes. It is to give explanations of how to calculatea ranking of Taekwondo athletes by applying Googles PageRankalgorithm. To this end, data for match results of -57kg female ath-letes were used to calculate the ranking of Taekwondo athletes withthe use of Googles PageRank algorithm. In order to introduce thecalculation of the ranking based on Googles PageRank algorithm,Table I below made use of data of the top 5 female athletes of -57kg.

TABLE IMATCH DATA OF TAEKWONDO ATHLETES

Above shows the match results of 5 female athletes of -57kg infive types of competition (Association Presidents Cup, President’sCup, Defense Minister Flag, Superior Athlete Selection, DomesticRanking). It indicates that Lim So-ra (Suseong-gu office) won 7and lost 4 out of 11 matches while Park Ji-seung (Seoul PhysicalEducation High School) won 11 and lost 4 out of 15 matches, andKim Da-yeong (Korea National Sport University won 17 and lost1 out of 18 matches. Figure 2 reveals the details of Figure 1 for

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the calculation of the ranking of Taekwondo athletes using Google’sPageRank algorithm. However, details of match results were pre-sented for those of Lim ◦◦ and Park ◦◦ only as an example.

TABLE IIDETAILS OF MATCH RESULTS

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Based on the results of Table II above, the initial matrix offive athletes is calculated as shown in the left column of Figure 1,and the match results are structured as shown on the right side ofFigure 1 below. The row indicates the number of games won, andthe column indicates the number of games lost. Thus, all diagonalmatrices are marked with 0, and

A12indicates that Lim ©© (A) has one win over Park©©(B),A13indicates that Lim©© has one win over Kim©©(C),A14 indicates that Lim©© has no wins over In©©(D), andA15indicates that Lim©© has no wins over Lee©©(E),resulting in a total of 2 wins.

Fig. 1. Initial matrix and structured matrix

Qi,j can be calculated by substituting the initial matrix of Figure1 into Equation (1), and the results are presented in Figure 2 below.

Qi,j = (1 − d)Ai,j∑N

k=1 Ai,k+ d

N(1)

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Fig. 2. Transformed value of matrix Q

The values of the transformed matrix of Figure 2 are calculatedby the following Equation (2), and the initial vector is calculatedas shown in Figure 3.

∏T =

∏TQ (2)

Fig. 3. Calculation of the eigenvector

When Figure 3. is calculated by the Markov Chain involution,the eigenvector matrix

∏T can be calculated at a certain stage.

The eigenvector matrix∏

T is shown in Figure 4 below.

Fig. 4. Matrix of the eigenvector

The ranking is calculated in descending order of eigenvectormatrices calculated, and thus Lim©© is ranked 1st, followed by

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Park©©, Kim©©, In©© and Lee©©. Table III summarizes therankings that are calculated using the match results and GooglesPageRank algorithm.

TABLE IIIMATCH RESULTS AND RANKING OF PAGERANK

Park©© with a record of 11-4 has a higher winning rate thanLim©© with 7-4. However, while Lim©© won over relatively bet-ter performing athletes including Park©© and Kim©©, Park©©won over a relatively poor performer Lee©©, resulting in a lowerranking In addition, Kim©© showed a low value in the PageR-ank algorithm despite a high-winning rate because she mostly wonover underperforming athletes. This is a characteristic of GooglePageRank algorithm that puts weighted value according to relativeimportance. Thus, it is fair to say that there is a meaningful differ-ence between 4 losses of Lim©© and those of Park ©©. In thisregard, this method is distinguished from Bradley-Terry’ s modelwhich calculates a ranking according to the winning rate used inthe field of most professional sports, and put weighted value onrecords against the opponent.

B. Validity of the ranking model of Taekwondo athletes usingthe PageRank Algorithm

Based on the win-loss records of 5,438 matches, the PageRankAlgorithm was applied to calculate ranking. To verify the validity ofthe ranking model, the accuracy, sensitivity, specificity, and LoI ofboth ranking methods (Korea Taekwondo Association, PageRank)were calculated and compared with the actual outcome of matches.Figure 5 below shows the calculated results of the four validity

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indexes using the table of specification that compares the rankingsto the actual outcome of matches.

Fig. 5. Validity Results Based on Binary Classification (Females-57kg)

The results indicated that the accuracy, sensitivity, specificity,and LoI of the Korea Taekwondo Association Ranking Model were.797, .771, .829, and .412, respectively, and those of the GooglePageRank algorithm-based ranking model were .863, .844, .883,and .000, respectively.

TABLE IVCOMPARISON OF VALIDITY INDEXES BY WEIGHT

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4 CONCLUSION

As a result of the validity comparison of the PageRank algorithmranking model and the KTA official ranking model, the PageRankalgorithm ranking model is more valid than the KTA official rankingmodel. In addition, the LoI that can occur with no ranking orthe same ranking, PageRank algorithm ranking model is less thanthe KTA official ranking model. Therefore, PageRank algorithmranking model is more valid than the KTA official ranking model.In conclusion, The Taekwondo athletes ranking model using thePageRank algorithm is an objective and valid ranking model basedon the game results of the each athlete. On the contrary, the KTAofficial ranking model has many disadvantages in calculating validranking of the athletes because it is subjectively to select the scoreallocation and the competition grade. Therefore, when we use thePageRank algorithm, it will complement the shortcomings of theKTA official ranking model, and it will be possible to calculatemore objective and efficient ranking. The result of this study willbe used as basic information in various sports field for developinga valid ranking model.

References

[1] Beggs, C., B., Shepherd, S., J., 2017. Emmonds, S., Jones,B., A novel application of PageRank and user preference algo-rithms for assessing the relative performance of track athletesin competition: PLoS One, 12(6):e0178458. doi: 10.1371/jour-nal.pone.0178458. eCollection.

[2] Chin, W., C., Wen, T., H., 2015. Geographically ModifiedPageRank Algorithms: Identifying the Spatial Concentra-tion of Human Movement in a Geospatial Network: PLoSOne. 10(10): e0139509. doi: 10.1371/journal.pone.0139509.eCollection. http://koreantaekwondo.tripod.com/rank.htmhttp://www.koreataekwondo.org

[3] Lazova, V., Basnarkov, L., 2015. PageRank Approach toRanking National Football Teams: arXiv preprint arXiv,1503.01331.

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[4] Radicchi, F., 2011. Who is the best player ever? A complexnetwork analysis of the history of professional tennis: PloSone, 6(2): e17249.

[5] Sorensen, S., P., 2000. An overview of some methods for rank-ing sports teams, USA: University of Tennessee.

[6] Sunami, A., Sasaki, K., Suzuki, Y., Oguma, N., Ishihara, J.,Nakai, A., Yasuda, J., Yokoyama, Y., Yoshizaki, T., Tada, Y.,Hida, A., Kawano, Y., J., 2016.Validity of a Semi-QuantitativeFood Frequency Questionnaire for Collegiate Athletes: J Epi-demiol, 26(6): 284-91. doi: 10.2188/jea.JE20150104.

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development of taekwondo ranking model based on google ... · pagerank algorithm model this study...

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