Predicting Win-Loss Outcomes in MLB Regular Season Games – a Comparative Study Using Data Mining Methods
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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 .................... -
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). -
A Comparison of Rating Systems for Competitive Women's Beach Volleyball
Statistica Applicata - Italian Journal of Applied Statistics Vol. 30 (2) 233 doi.org/10.26398/IJAS.0030-010 A COMPARISON OF RATING SYSTEMS FOR COMPETITIVE WOMEN’S BEACH VOLLEYBALL Mark E. Glickman1 Department of Statistics, Harvard University, Cambridge, MA, USA Jonathan Hennessy Google, Mountain View, CA, USA Alister Bent Trillium Trading, New York, NY, USA Abstract Women’s beach volleyball became an official Olympic sport in 1996 and continues to attract the participation of amateur and professional female athletes. The most well-known ranking system for women’s beach volleyball is a non-probabilistic method used by the Fédération Internationale de Volleyball (FIVB) in which points are accumulated based on results in designated competitions. This system produces rankings which, in part, determine qualification to elite events including the Olympics. We investigated the application of several alternative probabilistic rating systems for head-to-head games as an approach to ranking women’s beach volleyball teams. These include the Elo (1978) system, the Glicko (Glickman, 1999) and Glicko-2 (Glickman, 2001) systems, and the Stephenson (Stephenson and Sonas, 2016) system, all of which have close connections to the Bradley- Terry (Bradley and Terry, 1952) model for paired comparisons. Based on the full set of FIVB volleyball competition results over the years 2007-2014, we optimized the parameters for these rating systems based on a predictive validation approach. The probabilistic rating systems produce 2014 end-of-year rankings that lack consistency with the FIVB 2014 rankings. Based on the 2014 rankings for both probabilistic and FIVB systems, we found that match results in 2015 were less predictable using the FIVB system compared to any of the probabilistic systems. -
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. -
Riding a Probabilistic Support Vector Machine to the Stanley Cup
J. Quant. Anal. Sports 2015; 11(4): 205–218 Simon Demers* Riding a probabilistic support vector machine to the Stanley Cup DOI 10.1515/jqas-2014-0093 elimination rounds. Although predicting post-season playoff outcomes and identifying factors that increase Abstract: The predictive performance of various team the likelihood of playoff success are central objectives of metrics is compared in the context of 105 best-of-seven sports analytics, few research results have been published national hockey league (NHL) playoff series that took place on team performance during NHL playoff series. This has between 2008 and 2014 inclusively. This analysis provides left an important knowledge gap, especially in the post- renewed support for traditional box score statistics such lockout, new-rules era of the NHL. This knowledge gap is as goal differential, especially in the form of Pythagorean especially deplorable because playoff success is pivotal expectations. A parsimonious relevance vector machine for fans, team members and team owners alike, often both (RVM) learning approach is compared with the more com- emotionally and economically (Vrooman 2012). A better mon support vector machine (SVM) algorithm. Despite the understanding of playoff success has the potential to potential of the RVM approach, the SVM algorithm proved deliver new insights for researchers studying sports eco- to be superior in the context of hockey playoffs. The proba- nomics, competitive balance, home ice advantage, home- bilistic SVM results are used to derive playoff performance away playoff series sequencing, clutch performances and expectations for NHL teams and identify playoff under- player talent. achievers and over-achievers. The results suggest that the In the NHL, the Stanley Cup is granted to the winner Arizona Coyotes and the Carolina Hurricanes can both of the championship after four playoff rounds, each con- be considered Round 2 over-achievers while the Nash- sisting of a best-of-seven series. -
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. -
Roster-Based Optimisation for Limited Overs Cricket
Roster-Based Optimisation for Limited Overs Cricket by Ankit K. Patel A thesis submitted to the Victoria University of Wellington in fulfilment of the requirements for the degree of Master of Science in Statistics and Operations Research. Victoria University of Wellington 2016 Abstract The objective of this research was to develop a roster-based optimisation system for limited overs cricket by deriving a meaningful, overall team rating using a combination of individual ratings from a playing eleven. The research hypothesis was that an adaptive rating system ac- counting for individual player abilities, outperforms systems that only consider macro variables such as home advantage, opposition strength and past team performances. The assessment of performance is observed through the prediction accuracy of future match outcomes. The expec- tation is that in elite sport, better teams are expected to win more often. To test the hypothesis, an adaptive rating system was developed. This framework was a combination of an optimisa- tion system and an individual rating system. The adaptive rating system was selected due to its ability to update player and team ratings based on past performances. A Binary Integer Programming model was the optimisation method of choice, while a modified product weighted measure (PWM) with an embedded exponentially weighted moving average (EWMA) functionality was the adopted individual rating system. The weights for this system were created using a combination of a Random Forest and Analytical Hierarchical Process. The model constraints were objectively obtained by identifying the player’s role and performance outcomes a limited over cricket team must obtain in order to increase their chances of winning. -
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. -
Pythagoras at the Bat 3 to Be 2, Which Is the Source of the Name As the Formula Is Reminiscent of the Sum of Squares from the Pythagorean Theorem
Pythagoras at the Bat Steven J Miller, Taylor Corcoran, Jennifer Gossels, Victor Luo and Jaclyn Porfilio The Pythagorean formula is one of the most popular ways to measure the true abil- ity of a team. It is very easy to use, estimating a team’s winning percentage from the runs they score and allow. This data is readily available on standings pages; no computationally intensive simulations are needed. Normally accurate to within a few games per season, it allows teams to determine how much a run is worth in different situations. This determination helps solve some of the most important eco- nomic decisions a team faces: How much is a player worth, which players should be pursued, and how much should they be offered. We discuss the formula and these applications in detail, and provide a theoretical justification, both for the formula as well as simpler linear estimators of a team’s winning percentage. The calculations and modeling are discussed in detail, and when possible multiple proofs are given. We analyze the 2012 season in detail, and see that the data for that and other recent years support our modeling conjectures. We conclude with a discussion of work in progress to generalize the formula and increase its predictive power without needing expensive simulations, though at the cost of requiring play-by-play data. Steven J Miller Williams College, Williamstown, MA 01267, e-mail: [email protected],[email protected] arXiv:1406.0758v1 [math.HO] 29 May 2014 Taylor Corcoran The University of Arizona, Tucson, AZ 85721 Jennifer Gossels Princeton University, Princeton, NJ 08544 Victor Luo Williams College, Williamstown, MA 01267 Jaclyn Porfilio Williams College, Williamstown, MA 01267 1 2 Steven J Miller, Taylor Corcoran, Jennifer Gossels, Victor Luo and Jaclyn Porfilio 1 Introduction In the classic movie Other People's Money, New England Wire and Cable is a firm whose parts are worth more than the whole. -
Teen Sport in America: Why Participation Matters
TEEN SPORT IN AMERICA: WHY PARTICIPATION MATTERS January 2018 A Women’s Sports Foundation Report www.WomensSportsFoundation.org • 800.227.3988 Women’s Sports Foundation Acknowledgments This research builds on previous research and policy that view teen sports as an educational tool and public health asset. However, little to no research has scrutinized whether adolescent health and educational achievement vary from sport to sport. First, the Women’s Sports Foundation is indebted to the study authors, Nicole Zarrett, Ph.D., Philip Veliz, Ph.D., and Don Sabo, Ph.D. We’re proud to be associated with such creative and excellent researchers and writers. We are grateful to Bruce Y. Lee, M.D., M.B.A., the primary author of the policy recommendations, for his thoughtful and thorough development of recommendations that can lead to improvements in how teens experience sport. We are deeply indebted to Deborah Slaner Larkin, who originally championed the idea that each sport might make unique contributions to the health and well-being of American youth and that understanding these benefits would ultimately lead to more opportunities for youth to play sports. She was a powerful advocate and supporter for this line of research when she served as the Executive Director of the USTA Serves (now Foundation) and oversaw the development and conduct of the research that resulted in More Than A Sport: Tennis, Education, and Health, a first-of-its-kind nationwide study that compared the educational and health profiles of adolescent tennis participants with participants in other non-contact sports and contact sports, as well as high school students who did not participate in sports. -
The Shrinkage of the Pythagorean Exponents
Journal of Sports Analytics 2 (2016) 37–48 37 DOI 10.3233/JSA-160017 IOS Press The Shrinkage of the Pythagorean exponents John Chena,∗ and Tengfei Lib aKing George V School, 2 Tin Kwong Road, Homantin, Kowloon, Hong Kong bDepartment of Biostatistics, CB# 7420, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA Abstract. The Pythagorean expectation is a formula designed by Bill James in the 1980s for estimating the number of games that a baseball team is expected to win. The formula has since been applied in basketball, hockey, football, and soccer. When used to assess National Basketball Association (NBA) teams, the optimal Pythagorean exponent is generally believed to be between 14 and 17. In this study, we empirically investigated the accuracy of the formula in the NBA by using data from the 1993-1994 to 2013-2014 seasons. This study confirmed the results of previous studies, which found that the Pythagorean exponent is slightly higher than 14 in the fit scenario, in which the strengths and winning percentage of a team are calculated using data from the same period. However, to predict future winning percentages according to the current evaluations of team strengths, the optimal Pythagorean exponent in the prediction scenario decreases substantially from 14. The shrinkage factor varies from 0.5 early in the season to nearly 1 toward the end of the season. Two main reasons exist for the decrease: the current evaluated strengths correlate with the current winning percentage more strongly than they do with the future winning percentage, and the scales of strengths evaluated in the early or middle part of a season tend to exceed those evaluated at the end of the season because of the evening out of randomness or the law of averages.