Riding a Probabilistic Support Vector Machine to the Stanley Cup
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Incorporating the Effects of Designated Hitters in the Pythagorean Expectation
Abstract The Pythagorean Expectation is widely used in the field of sabermetrics to estimate a baseball team’s overall season winning percentage based on the number of runs scored and allowed in its games thus far. Bill James devised the simplest version RS 2 p q of the formula through empirical observation as W inning P ercentage RS 2 RA 2 “ p q `p q where RS and RA are runs scored and allowed, respectively. Statisticians later found 1.83 to be a more accurate exponent, estimating overall season wins within 3-4 games per season. Steven Miller provided a theoretical justification for the Pythagorean Expectation by modeling runs scored and allowed as independent continuous random variables drawn from Weibull distributions. This paper aims to first explain Miller’s methodology using recent data and then build upon Miller’s work by incorporating the e↵ects of designated hitters, specifically on the distribution of runs scored by a team. Past studies have attempted to include other e↵ects on run production such as ballpark factor, game state, and pitching power. The results indicate that incorporating information on designated hitters does not improve the error of the Pythagorean Expectation to better than 3-4 games per season. ii Contents Abstract ii Acknowledgements vi 1 Background 1 1.1 Empirical Derivation ........................... 2 1.2 Weibull Distribution ........................... 2 1.3 Application to Other Sports ....................... 4 2 Miller’s Model 5 2.1 Model Assumptions ............................ 5 2.1.1 Continuity of the Data ...................... 6 2.1.2 Independence of Runs Scored and Allowed ........... 7 2.2 Pythagorean Won-Loss Formula .................... -
Introduction Predictive Vs. Earned Ranking Methods
An overview of some methods for ranking sports teams Soren P. Sorensen University of Tennessee Knoxville, TN 38996-1200 [email protected] Introduction The purpose of this report is to argue for an open system for ranking sports teams, to review the history of ranking systems, and to document a particular open method for ranking sports teams against each other. In order to do this extensive use of mathematics is used, which might make the text more difficult to read, but ensures the method is well documented and reproducible by others, who might want to use it or derive another ranking method from it. The report is, on the other hand, also more detailed than a ”typical” scientific paper and discusses details, which in a scientific paper intended for publication would be omitted. We will in this report focus on NCAA 1-A football, but the methods described here are very general and can be applied to most other sports with only minor modifications. Predictive vs. Earned Ranking Methods In general most ranking systems fall in one of the following two categories: predictive or earned rankings. The goal of an earned ranking is to rank the teams according to their past performance in the season in order to provide a method for selecting either a champ or a set of teams that should participate in a playoff (or bowl games). The goal of a predictive ranking method, on the other hand, is to provide the best possible prediction of the outcome of a future game between two teams. In an earned system objective and well publicized criteria should be used to rank the teams, like who won or the score difference or a combination of both. -
Quantifying the Influence of Deviations in Past NFL Standings on the Present
Can Losing Mean Winning in the NFL? Quantifying the Influence of Deviations in Past NFL Standings on the Present The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation MacPhee, William. 2020. Can Losing Mean Winning in the NFL? Quantifying the Influence of Deviations in Past NFL Standings on the Present. Bachelor's thesis, Harvard College. Citable link https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37364661 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA Can Losing Mean Winning in the NFL? Quantifying the Influence of Deviations in Past NFL Standings on the Present A thesis presented by William MacPhee to Applied Mathematics in partial fulfillment of the honors requirements for the degree of Bachelor of Arts Harvard College Cambridge, Massachusetts November 15, 2019 Abstract Although plenty of research has studied competitiveness and re-distribution in professional sports leagues from a correlational perspective, the literature fails to provide evidence arguing causal mecha- nisms. This thesis aims to isolate these causal mechanisms within the National Football League (NFL) for four treatments in past seasons: win total, playoff level reached, playoff seed attained, and endowment obtained for the upcoming player selection draft. Causal inference is made possible due to employment of instrumental variables relating to random components of wins (both in the regular season and in the postseason) and the differential impact of tiebreaking metrics on teams in certain ties and teams not in such ties. -
Machine Learning Applications in Baseball: a Systematic Literature Review
This is an Accepted Manuscript of an article published by Taylor & Francis in Applied Artificial Intelligence on February 26 2018, available online: https://doi.org/10.1080/08839514.2018.1442991 Machine Learning Applications in Baseball: A Systematic Literature Review Kaan Koseler ([email protected]) and Matthew Stephan* ([email protected]) Miami University Department of Computer Science and Software Engineering 205 Benton Hall 510 E. High St. Oxford, OH 45056 Abstract Statistical analysis of baseball has long been popular, albeit only in limited capacity until relatively recently. In particular, analysts can now apply machine learning algorithms to large baseball data sets to derive meaningful insights into player and team performance. In the interest of stimulating new research and serving as a go-to resource for academic and industrial analysts, we perform a systematic literature review of machine learning applications in baseball analytics. The approaches employed in literature fall mainly under three problem class umbrellas: Regression, Binary Classification, and Multiclass Classification. We categorize these approaches, provide our insights on possible future ap- plications, and conclude with a summary our findings. We find two algorithms dominate the literature: 1) Support Vector Machines for classification problems and 2) k-Nearest Neighbors for both classification and Regression problems. We postulate that recent pro- liferation of neural networks in general machine learning research will soon carry over into baseball analytics. keywords: baseball, machine learning, systematic literature review, classification, regres- sion 1 Introduction Baseball analytics has experienced tremendous growth in the past two decades. Often referred to as \sabermetrics", a term popularized by Bill James, it has become a critical part of professional baseball leagues worldwide (Costa, Huber, and Saccoman 2007; James 1987). -
Loss Aversion and the Contract Year Effect in The
Gaming the System: Loss Aversion and the Contract Year Effect in the NBA By Ezekiel Shields Wald, UCSB 2/20/2016 Advisor: Professor Peter Kuhn, Ph.D. Abstract The contract year effect, which involves professional athletes strategically adjusting their effort levels to perform more effectively during the final year of a guaranteed contract, has been well documented in professional sports. I examine two types of heterogeneity in the National Basketball Association, a player’s value on the court relative to their salary, and the presence of several contract options that can be included in an NBA contract. Loss aversion suggests that players who are being paid more than they are worth may use their current salaries as a reference point, and be motivated to improve their performance in order to avoid a “loss” of wealth. The presence of contract options impacts the return to effort that the players are facing in their contract season, and can eliminate the contract year effect. I use a linear regression with player, year and team fixed effects to evaluate the impact of a contract year on relevant performance metrics, and find compelling evidence for a general contract year effect. I also develop a general empirical model of the contract year effect given loss aversion, which is absent from previous literature. The results of this study support loss-aversion as a primary motivator of the contract year effect, as only players who are marginally overvalued show a significant contract year effect. The presence of a team option in a player’s contract entirely eliminates any contract year effects they may otherwise show. -
Exploring Chance in NCAA Basketball
Exploring chance in NCAA basketball Albrecht Zimmermann [email protected] INSA Lyon Abstract. There seems to be an upper limit to predicting the outcome of matches in (semi-)professional sports. Recent work has proposed that this is due to chance and attempts have been made to simulate the distribution of win percentages to identify the most likely proportion of matches decided by chance. We argue that the approach that has been chosen so far makes some simplifying assumptions that cause its result to be of limited practical value. Instead, we propose to use clustering of statistical team profiles and observed scheduling information to derive limits on the predictive accuracy for particular seasons, which can be used to assess the performance of predictive models on those seasons. We show that the resulting simulated distributions are much closer to the observed distributions and give higher assessments of chance and tighter limits on predictive accuracy. 1 Introduction In our last work on the topic of NCAA basketball [7], we speculated about the existence of a “glass ceiling” in (semi-)professional sports match outcome prediction, noting that season-long accuracies in the mid-seventies seemed to be the best that could be achieved for college basketball, with similar results for other sports. One possible explanation for this phenomenon is that we are lacking the attributes to properly describe sports teams, having difficulties to capture player experience or synergies, for instance. While we still intend to explore this direction in future work,1 we consider a different question in this paper: the influence of chance on match outcomes. -
Open Evan Bittner Thesis.Pdf
THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF STATISTICS PREDICTING MAJOR LEAGUE BASEBALL PLAYOFF PROBABILITIES USING LOGISTIC REGRESSION EVAN J. BITTNER FALL 2015 A thesis submitted in partial fulfillment of the requirements for a baccalaureate degree in Statistics with honors in Statistics Reviewed and approved* by the following: Andrew Wiesner Lecturer of Statistics Thesis Supervisor Murali Haran Associate Professor of Statistics Honors Adviser * Signatures are on file in the Schreyer Honors College. i ABSTRACT Major League Baseball teams are constantly assessing whether or not they think their teams will make the playoffs. Many sources publish playoff probabilities or odds throughout the season using advanced statistical methods. These methods are somewhat secretive and typically advanced and difficult to understand. The goal of this work is to determine a way to calculate playoff probabilities midseason that can easily be understood and applied. The goal is to develop a method and compare its predictive accuracy to the current methods published by statistical baseball sources such as Baseball Prospectus and Fangraphs. ii TABLE OF CONTENTS List of Figures .............................................................................................................. iii List of Tables ............................................................................................................... iv Acknowledgements ..................................................................................................... -
Why the 2020 LA Dodgers Are the Greatest Team of All Time
Floersch UWL Journal of Undergraduate Research XXIV (2021) Why the 2020 Dodgers Are the Greatest Team of All Time, at least statistically Sean Floersch Faculty Mentor: Chad Vidden, Mathematics and Statistics ABSTRACT This paper explores the use of sports analytics in an attempt to quantify the strength of Major League Baseball teams from 1920-2020 and then find which team was the greatest team of all time. Through the use of basic baseball statistics, ratios were personally created that demonstrate the strength of a baseball team on offense and defense. To account for slight year to year differences in the ratios, standard deviations to the yearly mean are used and the personally created Flo Strength metric is used with the standard deviations. This allows the ratios to be compared across all seasons, with varying rules, number of teams, and number of games. These ratios and Flo Strength metric go through statistical testing to confirm that the ratios are indeed standardized across seasons. This is especially important when comparing the strange Covid-19 2020 baseball season. After quantifying all the team strengths, it is argued that the 2020 Los Angeles Dodgers are the greatest team of all time. INTRODUCTION The 2020 Covid MLB Season In a year like no other, with a pandemic locking down society, racial inequalities becoming the forefront of the news, and division across the country mounting, sports were turned to for a sense of normalcy. Slowly, sports returned, but in a way never seen before. The NBA returned, isolated in a bubble. Strict protocol was put in place in the NHL and MLS in order to ensure player and personnel safety. -
Team Payroll Versus Performance in Professional Sports: Is Increased Spending Associated with Greater Success?
Team Payroll Versus Performance in Professional Sports: Is Increased Spending Associated with Greater Success? Grant Shorin Professor Peter S. Arcidiacono, Faculty Advisor Professor Kent P. Kimbrough, Seminar Advisor Duke University Durham, North Carolina 2017 Grant graduated with High Distinction in Economics and a minor in Statistical Science in May 2017. Following graduation, he will be working in San Francisco as an Analyst at Altman Vilandrie & Company, a strategy consulting group that focuses on the telecom, media, and technology sectors. He can be contacted at [email protected]. Acknowledgements I would like to thank my thesis advisor, Peter Arcidiacono, for his valuable guidance. I would also like to acknowledge my honors seminar instructor, Kent Kimbrough, for his continued support and feedback. Lastly, I would like to recognize my honors seminar classmates for their helpful comments throughout the year. 2 Abstract Professional sports are a billion-dollar industry, with player salaries accounting for the largest expenditure. Comparing results between the four major North American leagues (MLB, NBA, NHL, and NFL) and examining data from 1995 through 2015, this paper seeks to answer the following question: do teams that have higher payrolls achieve greater success, as measured by their regular season, postseason, and financial performance? Multiple data visualizations highlight unique relationships across the three dimensions and between each sport, while subsequent empirical analysis supports these findings. After standardizing payroll values and using a fixed effects model to control for team-specific factors, this paper finds that higher payroll spending is associated with an increase in regular season winning percentage in all sports (but is less meaningful in the NFL), a substantial rise in the likelihood of winning the championship in the NBA and NHL, and a lower operating income in all sports. -
Using Bayesian Statistics to Rank Sports Teams (Or, My Replacement for the BCS)
Ranking Systems The Bradley-Terry Model The Bayesian Approach Using Bayesian statistics to rank sports teams (or, my replacement for the BCS) John T. Whelan [email protected] Center for Computational Relativity & Gravitation & School of Mathematical Sciences Rochester Institute of Technology π-RIT Presentation 2010 October 8 1/38 John T. Whelan [email protected] Using Bayesian statistics to rank sports teams Ranking Systems The Bradley-Terry Model The Bayesian Approach Outline 1 Ranking Systems 2 The Bradley-Terry Model 3 The Bayesian Approach 2/38 John T. Whelan [email protected] Using Bayesian statistics to rank sports teams Ranking Systems The Bradley-Terry Model The Bayesian Approach Outline 1 Ranking Systems 2 The Bradley-Terry Model 3 The Bayesian Approach 2/38 John T. Whelan [email protected] Using Bayesian statistics to rank sports teams Ranking Systems The Bradley-Terry Model The Bayesian Approach The Problem: Who Are The Champions? The games have been played; crown the champion (or seed the playoffs) If the schedule was balanced, it’s easy: pick the team with the best record If schedule strengths differ, record doesn’t tell all e.g., college sports (seeding NCAA tourneys) 3/38 John T. Whelan [email protected] Using Bayesian statistics to rank sports teams Ranking Systems The Bradley-Terry Model The Bayesian Approach Evaluating an Unbalanced Schedule Most NCAA sports (basketball, hockey, lacrosse, . ) have a selection committee That committee uses or follows selection criteria (Ratings Percentage Index, strength of schedule, common opponents, quality wins, . ) Football (Bowl Subdivision) has no NCAA tournament; Bowl Championship Series “seeded” by BCS rankings All involve some subjective judgement (committee or polls) 4/38 John T. -
Keshav Puranmalka
Modelling the NBA to Make Better Predictions ARCHpES by MASSACHU Keshav Puranmalka OCT 2 9 2 3 B.S., Massachusetts Institute of Technology(2012) Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Master of Engineering in Computer Science and Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 2013 © Massachusetts Institute of Technology 2013. All rights reserved. A uthor,....................... .............. Department of Electrical Engineering and Computer Science August 23, 2013 Certified by. ........... ..... .... cJ Prof. Leslie P. Kaelbling Panasonic Professor of Computer Science and Engineering Thesis Supervisor A ccepted by ......... ................... Prof. Albert R. Meyer Chairman, Masters of Engineering Thesis Committee 2 Modelling the NBA to Make Better Predictions by Keshav Puranmalka Submitted to the Department of Electrical Engineering and Computer Science on August 23, 2013, in partial fulfillment of the requirements for the degree of Master of Engineering in Computer Science and Engineering Abstract Unexpected events often occur in the world of sports. In my thesis, I present work that models the NBA. My goal was to build a model of the NBA Machine Learning and other statistical tools in order to better make predictions and quantify unexpected events. In my thesis, I first review other quantitative models of the NBA. Second, I present novel features extracted from NBA play-by-play data that I use in building my predictive models. Third, I propose predictive models that use team-level statistics. In the team models, I show that team strength relations might not be transitive in these models. Fourth, I propose predictive models that use player-level statistics. -
Sport Analytics
SPORT ANALYTICS Dr. Jirka Poropudas, Director of Analytics, SportIQ [email protected] Outline 1. Overview of sport analytics • Brief introduction through examples 2. Team performance evaluation • Ranking and rating teams • Estimation of winning probabilities 3. Assignment: ”Optimal betting portfolio for Liiga playoffs” • Poisson regression for team ratings • Estimation of winning probabilities • Simulation of the playoff bracket • Optimal betting portfolio 11.3.2019 1. Overview of sport analytics 11.3.2019 What is sport analytics? B. Alamar and V. Mehrotra (Analytics Magazine, Sep./Oct. 2011): “The management of structured historical data, the application of predictive analytic models that utilize that data, and the use of information systems to inform decision makers and enable them to help their organizations in gaining a competitive advantage on the field of play.” 11.3.2019 Applications of sport analytics • Coaches • Tactics, training, scouting, and planning • General managers and front offices • Player evaluation and team building • Television, other broadcasters, and news media • Entertainment, better content, storytelling, and visualizations • Bookmakers and bettors • Betting odds and point spreads 11.3.2019 Data sources • Official summary statistics • Aggregated totals from game events • Official play-by-play statistics • Record of game events as they take place • Manual tracking and video analytics • More detailed team-specific events • Labor intensive approach • Data consistency? • Automated tracking systems • Expensive