Journal of Sports Analytics 4 (2018) 31–63 31 DOI 10.3233/JSA-160165 IOS Press Ranking regular seasons in the NBA’s Modern Era using grey relational analysis Sean Pradhana,b,∗ aDepartment of Sport Management, University of Michigan, Ann Arbor, MI, USA bCenter for Sport Marketing Research (C-SMAR), University of Michigan, Ann Arbor, MI, USA Abstract. In the last few decades, the sports world has seen the precipitous rise of data-driven player analysis methods across many professional sports. In light of these advents to the field, the current paper offers a novel application of a multi-criteria classification scheme developed within the scholarly literature, that being: grey relational analysis (GRA), to the milieu of professional sports. Specifically, this technique is utilized in the context of the National Basketball Association (NBA) to rank regular seasons during the Modern Era (i.e., since the 1979-80 season, after the merger between the NBA and ABA) through the use of a constellation of statistics. A sample of 100 seasons initially classified by player efficiency rating (PER) were examined using GRA. Findings from the present study illustrate that Stephen Curry’s recent MVP campaign during the 2015-16 season for the Golden State Warriors was the top ranked overall regular season out of those sampled in the Modern Era. The use of GRA is compared to current popular indicators for player evaluation and efficiency. Future directions and implications for professional sports are discussed. Keywords: Player analytics, grey relational analysis (GRA), National Basketball Association (NBA), ranking, Modern Era 1. Introduction analytics has emerged as a pioneering field that has sought to resolve such issues for teams. With tac- The primary aspiration for virtually all clubs in tics, such as moneyball and sabermetrics, used in the many team sports is victory. As succinctly stated various domains, (Mason and Foster, 2007), the quan- by former New York Jets head coach and current titative analysis of sports has allowed teams to not football analyst for ESPN, Herman Edwards: “you only maximize player performance while keeping in play to win the game” (Yoder, 2012). While this mind any hindrances attributable to a salary cap, but goal may be simple in and of itself, there are many has also led to many teams succeeding in their respec- barriers that each team faces, such as privations in tive sports. Some prominent cases of such flourishing financial resources, deficiencies in talented players, applications of analytics include many from Major or an inability to attract rising stars from the free League Baseball (MLB), such as the Oakland Ath- agency market to a team’s locality. Accordingly, the letics, Boston Red Sox, and Houston Astros among sports world has seen a surplus of teams plagued others. by these factors. However, with the recent and quite Although sports analytics has been embraced by rapid economic expansion as witnessed through the many within the sports industry (i.e., teams and cor- escalation in television deals throughout the profes- porations), the body of scholarly research on this sional sports leagues and ensuing upsurges in salary matter has been limited. In addition, not all teams in caps as well as discrepancies in athlete talent, sports the various professional sports leagues have accepted such analysis as the standard as a means to contribute ∗ Corresponding author: Sean Pradhan, Department of Sport or enhance the direction of player operations. For Management, University of Michigan, Ann Arbor, MI 48109 USA. Tel.: +1 734 647 0945; Fax: +1 734 647 2808; E-mail: instance, a plethora of skeptics within the industry [email protected]. remain apprehensive on the viability of data-driven 2215-020X/18/$35.00 © 2018 – IOS Press and the authors. All rights reserved This article is published online with Open Access and distributed under the terms of the Creative Commons Attribution Non-Commercial License (CC BY-NC 4.0). 32 S. Pradhan / Ranking regular seasons in the NBA’s Modern Era using grey relational analysis player analysis, such as within the National Bas- 3. Grey relational analysis ketball Association (NBA). While some teams like the Dallas Mavericks, Houston Rockets, Philadel- Grey systems theory was first developed by Deng phia 76ers, and San Antonio Spurs have vigorously (1982) to describe the process of studying problems invested in these analytic resources (Pelton, 2015), when only partially known information is accessible there still lie many who have not fully adopted statis- within a limited sample, conditions often common tical applications in player evaluations. Bearing these to practical, real-world issues (Liu and Lin, 2010). notions in mind, the current study aims to harness Grey systems theory posits that through the procure- and apply previously established methods of analysis, ment, organization, and analysis of such available founded within scholarly research, to the quantita- data, research can better solve problems utilizing var- tive assessments of players in order to draw practical ious criteria (Deng, 1982). The process of GRA was implications for the sports industry. conceived by Deng (1982, 1989) as a means to aid in the MCDM based on a series of apparent char- acteristics within a grey system, in reference to the 2. Intentions concept of a black box wherein information is known (white) or unknown (black). In other words, grey In light of the dearth of player analysis in the information takes into consideration both knowns and NBA, the current study intends to offer a unique unknowns within a system and through the use of contribution to the field of sports analytics by provid- GRA seeks to quantify performance using a matrix- ing a classification scheme of performance through derived grade based on available data (Deng, 1982). the sampling of current and former athletes from The GRA technique has been successfully applied the NBA. Using a theoretically validated technique in scores of research within engineering, such as in prominently used in engineering (i.e., grey relational laser cutting and optics (Chen et al., 2011), neural analysis [GRA]), we present an innovative appli- networking models (Lai et al., 2005), and electrical cation of this method as well as a bridge between discharge machining processes (EDM; Lin and Lin, theory itself (i.e., in this case grey systems the- 2002). ory, the conceptual underpinning behind GRA) and Deng (1982, 1989) stipulated a series of steps practice within the sports industry. In the present con- within GRA in order to calculate grey relational text, we aim to make use of player statistics as the grades (i.e., numerical scores signaling the influence criteria in determining the most successful regular that specific factors have on a system; Yu et al., 2011) season achieved by an NBA player in the Mod- based on sampled data. To be specific, Deng outlined ern Era. The proposed utilization of the GRA as a five main steps in order to normalize an assembly player evaluation system has vast contributions to the of data and convert such figures into grey relational field of not only sports analytics, but also hierarchal grades to generate a ranking system in determining multi-criteria decision making (MCDM) applied in the most influential, or highest performing, factor. engineering. To begin with, data (x) are first arranged in a com- The main contributions of the current study are parison matrix based upon a particular number of two-fold. This study intends to (a) provide an exten- performance indicators (n) that are to be contrasted sion of GRA within a unique context in the analysis of against one another (m). players and (b) propound a novel technique for prac- ⎡ ⎤ xm (n) xm (n) ... xm (n) titioners to employ in determining the efficiency of ⎢ x n x n ... x n ⎥ both current and prospective players. These contribu- ⎣ m ( ) m ( ) m ( ) ⎦ tions can potentially fuel advancements in scouting xm (n) xm (n) ... xm (n) methods, both on an amateur and professional level, wherein teams can make better judgments concerning Subsequently, a referential series point (x0)is player acquisitions. Moreover, these outcomes may selected based upon the aim for the specific perfor- even aid in player salary negotiations for teams, in mance indicator. On one hand, if the ideal target which clubs can utilize MCDM techniques, such as outcome for such an indicator aims for those of GRA, to make comparisons between similar play- higher values, then the highest value in the compari- ers and offer fair and more well-informed contracts son matrix group is selected as the referential series based on not only the market-level of compensation, point. On the other hand, if lower values are indicative but also performance. of better performance, then the lowest series value is S. Pradhan / Ranking regular seasons in the NBA’s Modern Era using grey relational analysis 33 chosen as the reference point. Following this, the data 3.1. Grey relational analysis in sports from the comparison matrix are normalized by uti- lizing appropriate factor type calculations that obtain While research directly employing GRA in sports difference scores between observed values (xi ) and is relatively scant, several scholars have attempted to referential series points. Benefit type factor calcu- do so. For example, Huang et al. (2006) investigated lations are conducted on observed data for a given the competitive abilities of NBA teams from both indicator (k) that aim for higher values to produce the Eastern and Western