International Journal of Applied Exercise Physiology 2322-3537 www.ijaep.com Vol.8 No.4 An Alternative Ranking System for Bundesliga Handball Standings by Using Google’s Pagerank Celal Gençoğlu1 and Hikmet Gümüş1 1 Faculty of Sport Sciences, Dokuz Eylül University, Izmir, Turkey. ARTICLE INFORMATION ABSTRACT Original Research Paper Application of network-based algorithms to the sports metrics is Doi: 10.26655/IJAEP.2019.12.12 addressed to several disciplines. PageRank algorithm has been used Received September. 2019 for both team sports and individual players performance assessments Accepted December. 2019 whereas there is no study to handball team rankings. Purpose of this Keywords: study is to investigate the differences between the traditional ranking PageRank system and PR algorithm in handball. Total 306 game results, scores Sport metrics Handball made, conceding goals, offense and defense-related match statistics Ranking that played in Bundesliga 2017-18 season were collected from DKB Bundesliga official web page. We estimated four different PR values by name PageRankstraight, PageRankoffence, PageRankdefense, and PageRankdifference. The official points and normalized PR scores and provide the team standings changed by using the PR algorithm. A positive correlation was found between official system ranking and PageRankstraight, PageRankoffence, PageRankdefense, and PageRankdifference respectively r=0,932, p=0,000; r=0,915, p=0,000; r=0,711, p=0,001; and r=0,926, p=0,000. In this study, the PR algorithm presented a novel approach to ranking handball teams. Further researches needed to investigate alternative ranking methods which allow objective evaluation of a team’s performance, not just game results. Finally, we do not conceive the substitute traditional system within the PR algorithm for league standings, but it could be regarded as a method of assessment team market values and distributions of income. 1. Introduction In all sports disciplines, ranking occurs from the results of the matches and has critical importance as determining champion team, attaining to the European cup participation, increasing the amount of tv income and also attracting for new fans. Depend on the sports applying a league status, tournament or knock out regulations, teams or players collect the points corresponding to the result of matches. Accordingly, International Handball Federation rules team handball ranking based on total points of the teams for winning, draw and lose respectively three, one for each side and zero points [1]. Thus, at the end of the season the number of points accumulated indicating the respective standings. However traditional point award system has limitations cause of only consider to win or lose not to opponents’ strength or weakness. Therefore, the official point awarded system may cause failure to the ranking of a team who is not as good as their standing or ranking a team who may be better placed than their ranking in handball. In fact, there are several ranking systems such as Winning Percentage, The Rating Percentage Index, Elo’s Method and Keener algorithm [2] integrating computer science to sports standings. One of the best algorithms is Google’s PageRank [3] that enables meaningful ranking web pages when someone makes a query on the engine. A key aspect of PageRank (PR) is taking into account who plays and scores against a stronger or weaker opponent during interpretation to results. International Journal of Applied Exercise Physiology www.ijaep.com VOL.8 (4) Recently, the PageRank algorithm has been used for ranking American National Football League (NFL) teams [4-6]. Additionally, Lazova and Basnarkov (2015) investigated to compare PR and conventional FIFA rankings for international soccer teams [7]. On the other hand, several attempts have been made to the implementation of PR for weighted ranking of individual performance in soccer, basketball and hockey as team sports [8-10]. Moreover, Beggs et al. (2017) and London et al. (2015) have reported that PageRank is a useful ranking system for track athletes and tennis players [11,12]. Despite the competitive structure of DKB Bundesliga, there is no alternative ranking attempt using PR in handball. This study aims to investigate the differences between the traditional ranking system and PR algorithm in handball. Part of the purpose of this study is to address the offensive and defensive performance of teams by comparing match statistics and PR algorithm. 2. Method 2.1. Data Total 306 game results, scores made and conceding goals that played in Bundesliga 2017-18 season were collected from DKB Bundesliga official web page. Also, offence and defense-related match statistics included technical error, fast break goals, goals from line player, shoot percentage of line player, goals from wing, shoot percentage of wing, goals from back players, shoot percentage of back players, total shooting percentage, block, steal, conceded fast break goals, conceded goals from wings, conceded goals from line players, conceded goals from back players, conceded 7m goals gathered for each team (https://www.dkb-handball-bundesliga.de/de/). 2.2. Procedure The algorithm relies on to determine the importance of a webpage, the interconnection of the web. Mathematically, the algorithm can calculate by a system of coupled equations described below. 휔 푞 1 − 푞 푃 = (1 − 푞) ∑ 푃 푖푗 + + ∑ 훿 (푆표푢푡) 푖 푗 푆표푢푡 푁 푁 푗 푗 푗 푗 ω out In the formula ij is the weight of a link and s j = Σiωij is the out-strength of a link. pi is the PR score assigned to team i and represents the fraction of the overall ‘‘influence’’ sitting in the steady state of the diffusion process on vertex i. As it is an iterative algorithm within 500 iterations, calculation summation of all PageRank values was equaled to 1. 6-digit scaled fixed-point data format used to make calculations to compare PageRank values accurately. Damping factor is considered as 0.85. The algorithm relies on a basic that losing team send a part of the value which given before to the winning team. In other words, the more losing team has low-value therefore transfer value will be low too. In other words, the weighted ranking algorithm process the winning teams received a link from loser team. Throughout this, it is a stronger team with more incoming links from losing teams. For instance, there are A, B and C teams played against each other. If A defeats B, a directed link is accomplished from B to A. This link represents an amount of given value of the team. So, the value is proportional to the fraction of wins between A and B. Hence, if PR algorithm takes into account all the competing teams, a weighted and directed network is established (Figure 1). 70 International Journal of Applied Exercise Physiology www.ijaep.com VOL.8 (4) Figure1. Beaten team transfers the part of their own value to the defeated side in PR algorithm Table 1 presents an example matched-ups for A, B, and C teams and ranking according to who beats who. Provided that team ‘C’ has the best PR value with three winning and 1 lose, but both ‘B’ and ‘A’ teams got the same number of winning and loses. With this in mind, Team ‘A’ ranked 2nd with higher PR value owing to ‘A’ won against a stronger opponent such as ‘C’. Table1. An example of Team (‘A’, ‘B’ and ‘C’) standings according to PageRank algorithm Ranking Win Lose Team 0.39738 3 1 'C' 0.38777 1 2 'A' 0.21485 1 2 'B' We estimated four different PR values by name PageRankstraight, PageRankoffence, PageRankdefense, and PageRankdifference. PageRankstraight, consider only win-lose while excluding draws because of no any valuation change. In PageRankoffence and PageRankdefense estimations, goals used as the link between teams and the team who conceded a goal exchange the part of the value. Therefore the team with minimum PageRankdefense score is the worst performance, on the contrary, all other PR scores. PageRankdefense score was computed as 1-PRvalue in order to backward ranking. The margin of victory in a game was used to compute PageRankdifference. All PR scores were normalized between the maximum and minimum official league points (56-13) to provide a more meaningful comparison. 2.3. Statistical Analysis Collected data were calculated in MATLAB [MATLAB and Statistics Toolbox Release 2018, The MathWorks, Inc., Natick, Massachusetts, United States]. The rankings gathered from the official system and PR scores were compared using Spearman’s Rank Correlation. In addition, nonparametric Spearman correlation was executed to verify the relation between PR scores and match analysis variables (IBM Corp. Released 2013. IBM SPSS Statistics for Windows, Version 22.0. Armonk, NY: IBM Corp.). The correlations were distributed according to R-values and significance of correlation was considered according to Hopkins scale (r˂0.1; 0.1-0.3; 0.3-0.5; 0.5-0.7; 0.7-0.9; ˃0.9; 1) 71 International Journal of Applied Exercise Physiology www.ijaep.com VOL.8 (4) [13]. Statistical significance was assumed at p < 0.05. 3. Results The official standings included results, awarded points, scores made, goals conceded and difference as average was presented in Table 2. It also shows the PageRankstraight, PageRankoffence, PageRankdefense, and PageRankdifference scores of teams. Table2. Bundesliga Handball Teams standings according to the official system and PR values in the 2017-18 season SFG: SG Flensburg-Handewitt; RNL:Rhein-Neckar Löwen; BER: Füchse Berlin; SCM: SC Magdeburg; THW: THW Kiel; HAN: TSV Hannover-Burgdorf; MTM: MT Melsungen; LEI: SC DHfK Leipzig; TBV: TBV Lemgo Lippe; FAG: FRISCH AUF Göppingen; WET: HSG Wetzlar; GWD: TSV GWD Minden; HCE: HC Erlangen; TVB: TVB 1898 Stuttgart; GUM: VfL Gummersbach; LUD: The owls Ludwigshafen; NLB: TuS N-Lübbecke; TVH: TV 05/07 Hüttenberg. The correlations between official points and PR scores demonstrated at Table 3.