How Often Does the Best Team Win- A Unified Approach to Understan
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How Often Does the Best Team Win- A Unified Approach to Understan
SMITH COLLEGESmith ScholarworksMathematics and Statistics: Faculty PublicationsMathematics and Statistics2018How Often Does the Best Team Win? A Unifi How Often Does the Best Team Win- A Unified Approach to Understanied Approach to Understanding Randomness in North American SportMichael J. LopezSkidmore CollegeGregory J. MatthewsLoyola University ChicagoBenjamin BaumerSmith College, bbaumer@smith.eduFollow this and additional works at: https://scholarworks.smith.edu/mth_facpubs Ờ“ Part of the Mathematics Common How Often Does the Best Team Win- A Unified Approach to UnderstansRecommended CitationLopez. Michael J.; Matthews, Gregory J.; and Baumer, Benjamin, "How Often Does the Best Team Win? A Unified Approach to UnderstanHow Often Does the Best Team Win- A Unified Approach to Understan
ding Randomness in North American sport' (2018) Mathematics and Statistics Faculty Publications, Smith College, Northampton, MA https://scholarworks.sSMITH COLLEGESmith ScholarworksMathematics and Statistics: Faculty PublicationsMathematics and Statistics2018How Often Does the Best Team Win? A Unifi How Often Does the Best Team Win- A Unified Approach to Understan of Smith Scholarworks For more information, please contact schoiarworks@smith eduSubiut/Ud tn CĂr /lunnói oỊSlatMtir-.aarXiv:1701.05976v3 [stat.AP] 22 Nov 2017HOW OFTEN DOES THE BEST TEAM WIN?A UNIFIED APPROACH TO UNDERSTANDING RANDOMNESS IN NORTH AMERICAN SPORTBy Michael J. LopezSkidmore CollegeAN How Often Does the Best Team Win- A Unified Approach to UnderstanDBy Gregory J. Matthews Loyola University ChicagoANDBy Benjamin s. BaumerSmith College.Statistical applications in sports haw long centered on how toHow Often Does the Best Team Win- A Unified Approach to Understan
best separate signal (e.g. team talent) from random noise. However, most of this work has concent .rated on a single sport , and t he development of mSMITH COLLEGESmith ScholarworksMathematics and Statistics: Faculty PublicationsMathematics and Statistics2018How Often Does the Best Team Win? A Unifi How Often Does the Best Team Win- A Unified Approach to Understanesian state-space models using bett ing market data that can bo uniformly applied across sport ing organizations to better understand the role of randomness in game outcomes. These models can be used to extract estimates of team strength, the between-season, within-season, and game-to-game variabili How Often Does the Best Team Win- A Unified Approach to Understanty of team strengths, as well each team’s home advantage. We implement our approach across a decade of play in each of the National Football League (NHow Often Does the Best Team Win- A Unified Approach to Understan
EL). National Hockey League (NHL), National Basketball Association (.NBA), and Major League Baseball (MLB), finding that the NBA demonstrates both theSMITH COLLEGESmith ScholarworksMathematics and Statistics: Faculty PublicationsMathematics and Statistics2018How Often Does the Best Team Win? A Unifi How Often Does the Best Team Win- A Unified Approach to Understande by proposing new metrics for judging competitiveness across sports leagues, both within the tegular season and using traditional postseason tournament formats. Alt hough we focus on sports, we discuss a number of other situations in which our generalizable models might be usefully applied.1. Intr How Often Does the Best Team Win- A Unified Approach to Understanoduction. Most observers of sport, can agree that game outcomes are to some extent subject, to chance. The line drive that miraculously finds the fielHow Often Does the Best Team Win- A Unified Approach to Understan
der’s glove, the fumble that, bounciw harmlessly out-of-bouncLs, the puck that ricochets into the net off of an opponent’s skate, or the referee’s whiSMITH COLLEGESmith ScholarworksMathematics and Statistics: Faculty PublicationsMathematics and Statistics2018How Often Does the Best Team Win? A Unifi How Often Does the Best Team Win- A Unified Approach to Understanently play bettor or worse than theKcijuHow Often Does the Best Team Win- A Unified Approach to Understan
ue’s teams. For example, is team i better than team j? And ư so. how confident arc we in making this claim? Central to such an imderstanding of sportiSMITH COLLEGESmith ScholarworksMathematics and Statistics: Faculty PublicationsMathematics and Statistics2018How Often Does the Best Team Win? A Unifi How Often Does the Best Team Win- A Unified Approach to Understanzations of random variables. As a simple example, ư the probability that team i beats team j at time k is 0.75, this implies that in a hypothetical infinite number of games between the two teams at time k, i wins throe times as often as j. Unfortunately, in practice, team i will typically only play How Often Does the Best Team Win- A Unified Approach to Understanteam j once at time k. Thus, game outcomes alone are unlikely to provide enough information to precisely estimate true probabilities, and. in turn, teHow Often Does the Best Team Win- A Unified Approach to Understan
am strengths.Given both national public interest and an academic cmiosity that has extended across disciplines, many innovative techniques have been dSMITH COLLEGESmith ScholarworksMathematics and Statistics: Faculty PublicationsMathematics and Statistics2018How Often Does the Best Team Win? A Unifi How Often Does the Best Team Win- A Unified Approach to Understanel. Corresponding estimates of talent arc often cheeked or calibrated by comparing out-of-sample estimated probabilities of wins and losses to observed outcomes. Such exercises do more than drive water-cooler conversation as to which team may be better. Indeed* estimating team rankings has driven th How Often Does the Best Team Win- A Unified Approach to Understane development of advanced Statistical models (Bradley and Terry, 1952; Gliekman and Stern, 1998) and occasionally played a role in the decision of whiHow Often Does the Best Team Win- A Unified Approach to Understan
ch teams arc eligible for continued postseason play (OFF. 2014).SMITH COLLEGESmith ScholarworksMathematics and Statistics: Faculty PublicationsMathematics and Statistics2018How Often Does the Best Team Win? A UnifiSMITH COLLEGESmith ScholarworksMathematics and Statistics: Faculty PublicationsMathematics and Statistics2018How Often Does the Best Team Win? A UnifiGọi ngay
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