DOCSLIB.ORG

Download Date | 6/19/19 12:24 AM 86 | D

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Download Date | 6/19/19 12:24 AM 86 | D J. Quant. Anal. Sports 2019; 15(2): 85–95 Daniel Daly-Grafstein* and Luke Bornn Rao-Blackwellizing field goal percentage https://doi.org/10.1515/jqas-2018-0064 percentage (eFG%). Shooting percentages play a large role in influencing both fan and coaching evaluation of play- Abstract: Shooting skill in the NBA is typically measured ers, and are often used to predict future player perfor- by field goal percentage (FG%) – the number of makes out mance when making decisions regarding free agency or of the total number of shots. Even more advanced met- draft selection. rics like true shooting percentage are calculated by count- Predicting a player’s FG% given past shooting is a dif- ing each player’s 2-point, 3-point, and free throw makes ficult task. Shooting percentages are highly variable, espe- and misses, ignoring the spatiotemporal data now avail- cially on longer shots like 3-point attempts. For example, it able (Kubatko et al. 2007). In this paper we aim to better takes roughly 750 3-point attempts before a player’s shoot- characterize player shooting skill by introducing a new ing percentage stabilizes, where over half of the variation estimator based on post-shot release shot-make probabil- in their 3-point percentage (3P%) is explained by shoot- ities. Via the Rao-Blackwell theorem, we propose a shot- ing skill, rather than noise (Blackport 2014). Additionally, make probability model that conditions probability esti- 3P% has been shown to be an unreliable metric in terms mates on shot trajectory information, thereby reducing the of its ability to discriminate between players and its stabil- variance of the new estimator relative to standard FG%. ity from one season to the next (Franks et al. 2016). As the We obtain shooting information by using optical tracking proportion of shot attempts taken as 3-pointers increases, data to estimate three factors for each shot: entry angle, with total attempts having risen nearly 50% over the last shot depth, and left-right accuracy. Next we use these fac- 8 years (Young 2016), overall FG% becomes more variable tors to model shot-make probabilities for all shots in the and less stable. 2014–2015 season, and use these probabilities to produce Part of the large variation in shooting percentages a Rao-Blackwellized FG% estimator (RB-FG%) for each is likely due to the many contextual factors that con- player. We demonstrate that RB-FG% is better than raw tribute to the probability of a shot make. Improvements FG% at predicting 3-point shooting and true-shooting per- to FG% prediction have been made by including some of centages. Overall, we find that conditioning shot-make these covariates in shot-make prediction models (Piette, probabilities on spatial trajectory information stabilizes Sathyanarayan, and Zhang 2010; Cen et al. 2015). How- inference of FG%, creating the potential to estimate shoot- ever, because of the small differences that separate the ing statistics earlier in a season than was previously true shooting skill of players in the NBA, chance varia- possible. tion may also contribute significantly to the variation and Keywords: basketball; bayesian regression; optical instability of FG%. Optical tracking data of shot trajecto- tracking; shot trajectories; variance reduction ries can potentially reduce noise in shooting metrics by allowing us to differentiate shots that rim out, air balls, and (unintentional) banks, giving us more information 1 Introduction about players’ shooting skill with fewer shots. This idea has been demonstrated recently during practice shoot- Field goal percentage is a common measure of shooting ing sessions, where FG% augmented by precise shot fac- skill and efficiency in the National Basketball Associa- tor information gathered during these sessions improved tion (NBA), and general shooting prowess is often defined the prediction of future shooting (Marty and Lucey 2017; for players by their overall FG%. It can be used in its Marty 2018). Accurate estimates of shot factors using opti- raw form, or as a component of more advanced metrics cal tracking data from live games may allow for a sim- like true-shooting percentage (TS%) or effective field goal ilar improvement in the prediction of in-game shooting metrics. In this paper, we seek to reduce the variation in pre- *Corresponding author: Daniel Daly-Grafstein, Department of dicting player FG% using NBA optical tracking data. We Statistics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada, e-mail: [email protected] begin the paper by introducing a new estimator for FG%, Luke Bornn: Department of Statistics, Simon Fraser University, RB-FG%, based on aggregating shot-make probabilities. Burnaby, British Columbia V5A 1S6, Canada, e-mail: [email protected] Estimation of shot-make probabilities is then split into Unauthenticated Download Date | 6/19/19 12:24 AM 86 | D. Daly-Grafstein and L. Bornn: Rao-Blackwellizing field goal percentage two main parts. First, using spatio-temporal information Therefore, inference for θ is the same under the provided by the tracking data, we model shot trajectories Bernoulli and expected Beta-Binomial distributions. in order to estimate the depth, left-right distance, and Furthermore, suppose we obtain Xi (make or miss) and entry angle of balls entering the basket. Next, we use a pi (the probability that shot i will go in). Let Π(Xi , pijθ, v) regression model to estimate the probability of each shot be the joint distribution of Xi and pi. It follows that: going in. We define the average of these estimated prob- abilties, RB-FG%, as our new estimator of FG% for each Π(Xi , pijθ, v) = Π(Xijpi)Π(pijθ, v) player. Finally, we compare the predictive ability of the RB- where Π(Xijpi) and Π(pijθ, v) are the Bernoulli and Beta FG% estimator to its raw counterpart that does not utilize distributions, respectively. Consequently we have that trajectory information. given pi, Xi is independent of θ. Thus pi is sufficient for θ. Now let θ^ be the raw FG% estimate and θ^RB be the RB-FG% estimate. We have: 2 The Rao-Blackwellized N 1 X θ^ = Xi (FG%) estimator N i=1 In this section we introduce our new estimator for FG% N (︀ )︀ 1 X based on shot-make probabilities. When trying to predict θ^ = E θ^jp , ... , pN = pi (RB-FG%) RB 1 N a player’s future FG% using their past FG%, each shot i=1 Xi is treated as Bernoulli random variable with proba- Thus the RB-FG% is simply the conditional expecta- bility of success θ, where θ is a measure of the player’s tion of raw FG% given these shot-make probabilities pi. true FG%. However, shot trajectories provided by optical Because under the Beta-Binomial model pi is sufficient for tracking data give us more information for each shot than θ, by the Rao-Blackwell Theorem we have: simply whether it is a make or a miss. Incorporating this information into a shot model may allow us to reduce the (︀ )︀ (︀ )︀ MSE θ^RB ≤ MSE θ^ variance involved in estimating and predicting shooting skill. Therefore, we can define an alternative model where Unfortunately, we are unable to know the true prob- the probability of a shot-make varies depending on its ability that a shot will go in. Therefore, as decribed trajectory, and shots are modeled as Beta-Bernoulli ran- below, we will use estimates of shot-make probabilities dom variables Xi ∼ Bern(pi) with pi ∼ Beta(θv, (1−θ)v), based on shot trajectory information to obtain an esti- θ where again is the true FG% of a player, defining their mate of RB-FG%. Using an estimate of θ^RB means that corresponding Beta distribution of shot-make probabil- the inequality above does not necessarily hold. How- ties. Each player’s shooting ability is now modeled by a ever, as we will see in Section 4, our estimates of shot- Beta distribution, and the probability of a shot going in fol- make probabilites are accurate and precise enough that p p lows a Bernoulli distribution indexed by i, where i is a this estimate of θ^RB still leads to a decrease in vari- draw from that player’s Beta distribution. ance and prediction error relative to raw FG%. For sim- As shown below, inference under the model in which plicity, moving forward we will refer to the RB-FG% shots are treated as Bernoulli random variables and infer- estimator based on estimated shot-make probabilities ence under the expected Beta-Binomial of our new model as θ^RB. is the same (Skellam 1948). Let Π(Xijθ, v) be the likelihood of the expected Beta-Binomial distribution, i.e. the likeli- hood of the Beta-Binomial distribution if you mariginalize 3 Estimating shot-make out the pi’s, and let B(·) be the beta function. probabilities 1 Z Xi+θv−1 (1−θ)v−Xi pi (1 − pi) Π(Xijθ, v) / dpi B(θv, (1 − θ)v) 3.1 Measuring shot factors 0 B X + θv − X + − θ v In order to estimate shot-make probabilities, we first mea- / ( i , 1 i (1 ) ) B(θv, (1 − θ)v) sure three shot factors based on how each shot entered the basket – left-right accuracy, depth, and entry angle – fol- X −X / θ i (1 − θ)(1 i) lowing the procedure of Marty and Lucey (2017). We define Unauthenticated Download Date | 6/19/19 12:24 AM D. Daly-Grafstein and L. Bornn: Rao-Blackwellizing field goal percentage | 87 left-right accuracy as the deviation of the ball from the the shot in the tracking data, we use a quadratic polyno- centre of the hoop as the ball crosses the plane of the bas- mial to model the height, and estimate the coefficients by ket (Figure 1A).
Load more

Recommended publications
  • Difference-Based Analysis of the Impact of Observed Game Parameters on the Final Score at the FIBA Eurobasket Women 2019
    Original Article Difference-based analysis of the impact of observed game parameters on the final score at the FIBA Eurobasket Women 2019 SLOBODAN SIMOVIĆ1 , JASMIN KOMIĆ2, BOJAN GUZINA1, ZORAN PAJIĆ3, TAMARA KARALIĆ1, GORAN PAŠIĆ1 1Faculty of Physical Education and Sport, University of Banja Luka, Bosnia and Herzegovina 2Faculty of Economy, University of Banja Luka, Bosnia and Herzegovina 3Faculty of Physical Education and Sport, University of Belgrade, Serbia ABSTRACT Evaluation in women's basketball is keeping up with developments in evaluation in men’s basketball, and although the number of studies in women's basketball has seen a positive trend in the past decade, it is still at a low level. This paper observed 38 games and sixteen variables of standard efficiency during the FIBA EuroBasket Women 2019. Two regression models were obtained, a set of relative percentage and relative rating variables, which are used in the NBA league, where the dependent variable was the number of points scored. The obtained results show that in the first model, the difference between winning and losing teams was made by three variables: true shooting percentage, turnover percentage of inefficiency and efficiency percentage of defensive rebounds, which explain 97.3%, while for the second model, the distinguishing variables was offensive efficiency, explaining for 96.1% of the observed phenomenon. There is a continuity of the obtained results with the previous championship, played in 2017. Of all the technical elements of basketball, it is still the shots made, assists and defensive rebounds that have the most significant impact on the final score in European women’s basketball.
    [Show full text]
  • An Analysis of the Contract Year Phenomenon in the NBA: Do Players Perform Better Or Worse Tyler Gaffaney Claremont Mckenna College
    Claremont Colleges Scholarship @ Claremont CMC Senior Theses CMC Student Scholarship 2013 An Analysis of the Contract Year Phenomenon in the NBA: Do Players Perform Better or Worse Tyler Gaffaney Claremont McKenna College Recommended Citation Gaffaney, Tyler, "An Analysis of the Contract Year Phenomenon in the NBA: Do Players Perform Better or Worse" (2013). CMC Senior Theses. Paper 768. http://scholarship.claremont.edu/cmc_theses/768 This Open Access Senior Thesis is brought to you by Scholarship@Claremont. It has been accepted for inclusion in this collection by an authorized administrator. For more information, please contact [email protected]. CLAREMONT McKENNA COLLEGE An Analysis of the Contract Year Phenomenon in the NBA: Do Players Perform Better or Worse? SUBMITTED TO Professor Ricardo Fernholz AND Dean Nicholas Warner BY Tyler Gaffaney for SENIOR THESIS Fall 2013 December 2, 2013 Acknowledgements First, I would like to thank anyone who contributed to this thesis in any way. I would also like to thank my family, especially my parents for their support over the years. Specifically, I would like to thank my reader Professor Ricardo Fernholz for his keen insight and continued advice. Without his help, this thesis would not have been possible. i Abstract The present study uses a novel measure of over performance (percent deviation from career average) to analyze the contract year phenomenon in the NBA. Historically, the literature has pointed toward over performance across almost all statistical measures of performance. However, previous research has assumed that all players are universally affected by the presence of a contract year in the same manner.
    [Show full text]
  • Forecasting Most Valuable Players of the National Basketball Association
    FORECASTING MOST VALUABLE PLAYERS OF THE NATIONAL BASKETBALL ASSOCIATION by Jordan Malik McCorey A thesis submitted to the faculty of The University of North Carolina at Charlotte in partial fulfillment of the requirements for the degree of Master of Science in Engineering Management Charlotte 2021 Approved by: _______________________________ Dr. Tao Hong _______________________________ Dr. Linquan Bai _______________________________ Dr. Pu Wang ii ©2021 Jordan Malik McCorey ALL RIGHTS RESERVED iii ABSTRACT JORDAN MALIK MCCOREY. Forecasting Most Valuable Players of the National Basketball Association. (Under the direction of DR. TAO HONG) This thesis aims at developing models that would accurately forecast the Most Valuable Player (MVP) of the National Basketball Association (NBA). R programming language was used in this study to implement different techniques, such as Artificial Neural Networks (ANN), K- Nearest Neighbors (KNN), and Linear Regression Models (LRM). NBA statistics were extracted from all of the past MVP recipients and the top five runner-up MVP candidates from the last ten seasons (2009-2019). The objective is to forecast the Point Total Ratio (PTR) for MVP during the regular season. Seven different underlying models were created and applied to the three techniques in order to produce potential outputs for the 2018-19 season. The best models were then selected and optimized to form the MVP forecasting algorithm, which was validated by predicting the MVP of the 2019-20 season. Ultimately, two underlying models were most robust under the LRM framework, which is considered the champion approach. As a result, two combination models were constructed based on the champion approach and proved to be most efficient.
    [Show full text]
  • Mathematics Improves Basketball
    Mathematics Improves Basketball Angelica Klivan, Iris Latorre, Carmen Rosa, Cristian Yepes Early Start Program Math 105, Professor Gary Welz, Peer Mentor Kenny Gonzalez Introduction Terms to Know Methodology &RQFOXVLRQ In the game of basketball, mathematics is used ƒ True Shooting Percentage (TS%)- A statistic in ● Three players will shoot from three different Mathema constantly to improve one’s performance. basketball used to gauge shooting efficiency that positions: tics is key - Chest Height Achieving the objective of shooting a takes into consideration points scored from three in pointers, field goals, and free-throws to get a basketball includes using percentages and - Chin Height basketbal measure of points scored each shooting attempt. l. Most angles. By finding the most consistent - Over Head Height players percentage of shots made while using a certain ƒ Trajectory- A curve or surface cutting a family of curves or surfaces at a constant angle All players will shoot from the free throw line. do not angle, you can find out which player will score Each player will start from a different position, In I actively the most baskets. While shooting a ball into ƒ Backspin- A backward spin given to a moving ball, focus on causing it to stop more quickly or rebound at a resulting in a different trajectory, and continue to the basket, there has to be a mental projection mathema steeper angle upon hitting a surface rotate with each shot. on how a certain angle will affect the outcome tics while Each player will take 10 shots per position. they are of the shot.
    [Show full text]
  • Actual Vs. Perceived Value of Players of the National Basketball Association
    Actual vs. Perceived Value of Players of the National Basketball Association BY Stephen Righini ADVISOR • Alan Olinsky _________________________________________________________________________________________ Submitted in partial fulfillment of the requirements for graduation with honors in the Bryant University Honors Program APRIL 2013 Table of Contents Abstract .................................................................................................................................1 Introduction ...........................................................................................................................2 How NBA MVPs Are Determined .....................................................................................2 Reason for Selecting This Topic ........................................................................................2 Significance of This Study .................................................................................................3 Thesis and Minor Hypotheses ............................................................................................4 Player Raters and Perception Factors .....................................................................................5 Data Collected ...................................................................................................................5 Perception Factors .............................................................................................................7 Player Raters .........................................................................................................................9
    [Show full text]
  • NBA Statistics Feeds
    Updated 10.01.18 NBA Statistics Feeds 2017-18 Season 1 SPORTRADAR NBA STATISTICS FEEDS Updated 10.01.18 Table of Contents NBA Statistics Feeds .................................................................................................................................... 3 Coverage Levels ............................................................................................................................................. 4 League Information ....................................................................................................................................... 5 Game & Series Information ........................................................................................................................ 7 Venue Information .......................................................................................................................................10 Team Information ........................................................................................................................................11 Player Information .......................................................................................................................................13 Boxscore Information .................................................................................................................................16 Play-by-Play Information ...........................................................................................................................18 Period Statistics – Team ............................................................................................................................22
    [Show full text]
  • Scoring and Shooting Abilities of NBA Players
    Journal of Quantitative Analysis in Sports Volume 6, Issue 1 2010 Article 1 Scoring and Shooting Abilities of NBA Players James Piette, University of Pennsylvania Sathyanarayan Anand, University of Pennsylvania Kai Zhang, University of Pennsylvania Recommended Citation: Piette, James; Anand, Sathyanarayan; and Zhang, Kai (2010) "Scoring and Shooting Abilities of NBA Players," Journal of Quantitative Analysis in Sports: Vol. 6: Iss. 1, Article 1. Available at: http://www.bepress.com/jqas/vol6/iss1/1 DOI: 10.2202/1559-0410.1194 ©2010 American Statistical Association. All rights reserved. Scoring and Shooting Abilities of NBA Players James Piette, Sathyanarayan Anand, and Kai Zhang Abstract We propose two new measures for evaluating offensive ability of NBA players, using one- dimensional shooting data from three seasons beginning with the 2004-05 season. These measures improve upon currently employed shooting statistics by accounting for the varying shooting patterns of players over different distances from the basket. This variance also provides us with an intuitive metric for clustering players, wherein performance of players is calculated and compared to his cluster center as a baseline. To further improve the accuracy of our measures, we develop our own variation of smoothing and shrinkage, reducing any small sample biases and abnormalities. The first measure, SCAB or, Scoring Ability Above Baseline, measures a player's ability to score as a function of time on court. The second metric, SHTAB or Shooting Ability, calculates a player's propensity to score on a per-shot basis. Our results show that a combination of SCAB and SHTAB can be used to separate out players based on their offensive game.
    [Show full text]
  • Essays in Basketball Analytics
    Essays in Basketball Analytics Suraj Keshri Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2019 c 2019 Suraj Keshri All Rights Reserved ABSTRACT Essays in Basketball Analytics Suraj Keshri With the increasing popularity and competition in professional basketball in the past decade, data driven decision has emerged as a big competitive edge. The advent of high frequency player tracking data from SportVU has enabled a rigorous analysis of player abilities and interactions that was not possible before. The tracking data records two-dimensional x-y coordinates of 10 players on the court as well as the x-y-z coordinates of the ball at a resolu- tion of 25 frames per second, yielding over 1 billion space-time observations over the course of a full season. This dissertation offers a collection of spatio-temporal models and player evaluation metrics that provide insight into the player interactions and their performance, hence allowing the teams to make better decisions. Conventional approaches to simulate matches have ignored that in basketball the dy- namics of ball movement is very sensitive to the lineups on the court and unique identities of players on both offense and defense sides. In chapter 2, we propose the simulation in- frastructure that can bridge the gap between player identity and team level network. We model the progression of a basketball match using a probabilistic graphical model. We model every touch event in a game as a sequence of transitions between discrete states. We treat the progression of a match as a graph, where each node represents the network structure of players on the court, their actions, events, etc., and edges denote possible moves in the game flow.
    [Show full text]
  • A Starting Point for Analyzing Basketball Statistics
    Journal of Quantitative Analysis in Sports Volume 3, Issue 3 2007 Article 1 A Starting Point for Analyzing Basketball Statistics Justin Kubatko, The Ohio State University and basketball- reference.com Dean Oliver, Basketball on Paper and Denver Nuggets Kevin Pelton, Seattle Sonics & Storm Dan T. Rosenbaum, University of North Carolina at Greensboro and Cleveland Cavaliers Recommended Citation: Kubatko, Justin; Oliver, Dean; Pelton, Kevin; and Rosenbaum, Dan T. (2007) "A Starting Point for Analyzing Basketball Statistics," Journal of Quantitative Analysis in Sports: Vol. 3: Iss. 3, Article 1. DOI: 10.2202/1559-0410.1070 ©2007 American Statistical Association. All rights reserved. Brought to you by | University of Toronto-Ocul Authenticated Download Date | 3/2/16 11:03 PM A Starting Point for Analyzing Basketball Statistics Justin Kubatko, Dean Oliver, Kevin Pelton, and Dan T. Rosenbaum Abstract The quantitative analysis of sports is a growing branch of science and, in many ways one that has developed through non-academic and non-traditionally peer-reviewed work. The aim of this paper is to bring to a peer-reviewed journal the generally accepted basics of the analysis of basketball, thereby providing a common starting point for future research in basketball. The possession concept, in particular the concept of equal possessions for opponents in a game, is central to basketball analysis. Estimates of possessions have existed for approximately two decades, but the various formulas have sometimes created confusion. We hope that by showing how most previous formulas are special cases of our more general formulation, we shed light on the relationship between possessions and various statistics.
    [Show full text]
  • Basketball Reference Nba Pace by Year
    Basketball Reference Nba Pace By Year brontosauruses.tawdrily.Holotypic Single-entry Hal kids Aubrey shaggily and neoterizing eutrophic and monthly, Albrechther sasines she alwaysunderspending demonstrably, smear petrologically her she robe-de-chambre attack and it soli. jaunts agglomerate his Fep_object be efficient, and tarik black told silver screen and nail against regression techniques, by reference nba pace factor is an emotional return in what exactly constitutes a professional service synergy sports How will players perform this season? Steal rate estimates the percentage of opponent possessions that end with a steal by a player. TODO: we should review the class names and whatnot in use here. Despite this, player salaries have struggled to keep pace. Made some crucial adds using the smart tool and daily player projection tool. What does the community think of players? Offensive rebound percentage is an estimate of the percentage of available offensive rebounds a player grabbed while he was on the floor. Data: Share of population by weight category. Time leading scorers list. Rebound rate is a common stat found on any advanced stats site. NBA pace factor is an advanced basketball stat to help you bet smarter and make more money betting totals, spreads, and more. How do you become a referee for a math journal? The formula adds positive stats and subtracts negative ones through a statistical point value system. Of course, the downside is the loss of Anderson, to a division rival no less. Fique por dentro do calendário de NBA, por data e com toda a informação do início das partidas, cobertura na TV e mais.
    [Show full text]
  • Sport & Entertainment
    Volume 1, Issue 1, February 2015 EDITOR Joris Drayer D.H. Kwak Stacy Warner Bob Heere Temple University University of Michigan East Carolina University University of South Carolina Brendan Dwyer Daniel Lock Jules Woolf [email protected] Virginia Commonwealth Griffith University Ohio University ASSOCIATE EDITOR University Eric MacIntosh Xiaoyan Xing Chad Seifried Andrea Eagleman Ottawa University Capital University of Physi- Louisiana State University Griffith University Kimberly Mahoney cal Education and Sport [email protected] Sheranne Fairley University of New Haven Masayuki Yoshida EDITORIAL BOARD University of Queensland Haylee Mercado Biwako Seikei Sport College Artemisia Apostolopoulou Kevin Filo University of South Carolina EDITORIAL ASSISTANT Robert Morris University Griffith University Brianna Newland Henry Wear Khalid Ballouli Damian Gallagher University of Delaware University of South Carolina University of South Carolina University of Ulster Nico Schulenkorf MANAGING EDITOR Tim Breitbarth Marion Hambrick University of Technology Matt Brann Bournemouth University University of Louisville Sydney FiT Publishing Beth Cianfrone Yuhei Inoue Stephen Shapiro Georgia State University University of Minnesota Old Dominion University DESIGNER Jamie Pein Geoff Dickson Jeremy Jordan Brian Soebbing Auckland University of Temple University Louisiana State University Technology Shannon Kerwin Scott Tainsky Brock University University of Illinois Sport & Entertainment Review is an electronic journal owned Subscription rates: US: $50 (individual), $200 (institution). by the University of South Carolina’s Department of Sport Back issue articles are searchable and can be downloaded at and Entertainment Management and published three times www.fitpublishing.com. a year (February, June, and October) by FiT Publishing, A Division of the International Center for Performance Ex- Advertising: A current rate card is available upon request.
    [Show full text]
  • Ranking Methods for Data Analytics on Players' Performance in Basketball Games
    Università degli studi di Padova Dipartimento di Scienze Statistiche Corso di Laurea Magistrale in Scienze statistiche Relazione Finale Ranking methods for data analytics on players’ performance in basketball games Relatore Ch.ma Prof.ssa Laura Ventura Dipartimento di Scienze Statistiche Correlatore Ch.mo Prof. Luigi Salmaso Correlatore Ch.mo Prof. Livio Corain Dipartimento di Tecnica e Gestione dei sistemi industriali Laureando Silvio Vadruccio Matricola N 1106878 Anno Accademico 2017/2018 Contents Introduction 11 1 The mathematics of hoops 13 1.1 Basketball meets data . 14 1.2 The rise of basketball data analysis . 17 1.3 Basketball data analysis worldwide . 21 1.4 A game of spaces . 22 1.4.1 Talking with numbers . 23 1.5 Data, data, data . 24 1.6 Roles in basketball . 25 2 Performance measures 27 2.1 The player or the team? . 27 2.1.1 Bottom-up measures . 28 2.1.2 Top-down measures . 29 2.2 Player value metrics . 30 2.2.1 Possessions . 31 2.2.2 Player Efficiency Rating . 33 2.2.3 Wins produced . 37 2.2.4 Approximate Value . 41 3 Basketball Data 47 3.1 The box score . 48 3.2 Play-by-play . 54 3.3 Combining the data . 57 3.3.1 Extracting player’s performance from opponent’s pro- duction . 58 3.3.2 Extracting player’s performance from team’s production 63 3.3.3 Levelling players performances . 63 4 Ranking method for sport data analysis 65 4.1 Round robin design . 66 4.2 Testing hypothesis and ranking . 68 4.2.1 Properties of the ranking estimator .
    [Show full text]