Making the Rules of Sports Fairer

The rules of many sports are not fair-they do not ensure that equally skilled competitors have the same probability of winning. As an example, the penalty shootout in soccer, wherein a coin toss determines which team kicks first on all five penalty kicks, gives a substantial advantage to the first-kicking team, both in theory and in practice. We show that a so-called Catch-Up Rule for determining the order of kicking would not only make the shootout fairer but is also essentially strategyproof. By contrast, the so-called Standard Rule now used for the tiebreaker in tennis is fair. We briefly consider several other sports, all of which involve scoring a sufficient number of points to win, and show how they could benefit from certain rule changes which would be straightforward to implement

Making the Rules of Sports Fairer

The rules of many sports are not fair—they do not ensure that equally skilled competitors have the same probability of winning. As an example, the penalty shootout in soccer, wherein a coin toss determines which team kicks first on all five penalty kicks, gives a substantial advantage to the first-kicking team, both in theory and practice. We show that a so-called Catch-Up Rule for determining the order of kicking would not only make the shootout fairer but also is essentially strategyproof. By contrast, the so-called Standard Rule now used for the tiebreaker in tennis is fair. We briefly consider several other sports, all of which involve scoring a sufficient number of points to win, and show how they could benefit from certain rule changes, which would be straightforward to implement

Making the Rules of Sports Fairer

The rules of many sports are not fair—they do not ensure that equally skilled competitors have the same probability of winning. As an example, the penalty shootout in soccer, wherein a coin toss determines which team kicks first on all five penalty kicks, gives a substantial advantage to the first-kicking team, both in theory and practice. We show that a so-called Catch-Up Rule for determining the order of kicking would not only make the shootout fairer but also is essentially strategyproof. By contrast, the so-called Standard Rule now used for the tiebreaker in tennis is fair. We briefly consider several other sports, all of which involve scoring a sufficient number of points to win, and show how they could benefit from certain rule changes, which would be straightforward to implement

Proceedings of Mathsport international 2017 conference

Proceedings of MathSport International 2017 Conference, held in the Botanical Garden of the University of Padua, June 26-28, 2017. MathSport International organizes biennial conferences dedicated to all topics where mathematics and sport meet. Topics include: performance measures, optimization of sports performance, statistics and probability models, mathematical and physical models in sports, competitive strategies, statistics and probability match outcome models, optimal tournament design and scheduling, decision support systems, analysis of rules and adjudication, econometrics in sport, analysis of sporting technologies, financial valuation in sport, e-sports (gaming), betting and sports

A Statistical Investigation into Factors Affecting Results of One Day International Cricket Matches

The effect of playing “home” or “away” and many other factors, such as batting first or second, winning or losing the toss, have been hypothesised as influencing the outcome of major cricket matches. Anecdotally, it has often been noted that Subcontinental sides (India, Pakistan, Sri Lanka and Bangladesh) tend to perform much better on the Subcontinent than away from it, whilst England do better in Australia during cooler, damper Australian Summers than during hotter, drier ones. In this paper, focusing on results of men’s One Day International (ODI) matches involving England, we investigate the extent to which a number of factors – including playing home or away (or the continent of the venue), batting or fielding first, winning or losing the toss, the weather conditions during the game, the condition of the pitch, and the strength of each team’s top batting and bowling resources – influence the outcome of matches. By employing a variety of Statistical techniques, we find that the continent of the venue does appear to be a major factor affecting the result, but winning the toss does not. We then use the factors identified as significant in an attempt to build a Binary Logistic Regression Model that will estimate the probability of England winning at various stages of a game. Finally, we use this model to predict the results of some England ODI games not used in training the model

A Political Economy of Access: Infrastructure, Networks, Cities, and Institutions

Why should you read another book about transport and land use? This book differs in that we won’t focus on empirical arguments – we present political arguments. We argue the political aspects of transport policy shouldn’t be assumed away or treated as a nuisance. Political choices are the core reasons our cities look and function the way they do. There is no original sin that we can undo that will lead to utopian visions of urban life. The book begins by introducing and expanding on the idea of Accessibility. Then we proceed through several major parts: Infrastructure Preservation, Network Expansion, Cities, and Institutions. Infrastructure preservation concerns the relatively short-run issues of how to maintain and operate the existing surface transport system (roads and transit). Network expansion in contrast is a long-run problem, how to enlarge the network, or rather, why enlarging the network is now so difficult. Cities examines how we organize, regulate, and expand our cities to address the failures of transport policy, and falls into the time-frame of the very long-run, as property rights and land uses are often stickier than the concrete of the network is durable. In the part on Institutions we consider things that might at first blush appear to be short-run and malleable, are in fact very long-run. Institutions seem to outlast the infrastructure they manage. Many of the transport and land use problems we want to solve already have technical solutions. What these problems don’t have, and what we hope to contribute, are political solutions. We expect the audience for this book to be practitioners, planners, engineers, advocates, urbanists, students of transport, and fellow academics

Bowdoin Orient v.135, no.1-25 (2005-2006)

https://digitalcommons.bowdoin.edu/bowdoinorient-2000s/1006/thumbnail.jp

Bowdoin Orient v.133, no.1-24 (2003-2004)

https://digitalcommons.bowdoin.edu/bowdoinorient-2000s/1004/thumbnail.jp

Unmet goals of tracking: within-track heterogeneity of students' expectations for

Educational systems are often characterized by some form(s) of ability grouping, like tracking. Although substantial variation in the implementation of these practices exists, it is always the aim to improve teaching efficiency by creating homogeneous groups of students in terms of capabilities and performances as well as expected pathways. If students’ expected pathways (university, graduate school, or working) are in line with the goals of tracking, one might presume that these expectations are rather homogeneous within tracks and heterogeneous between tracks. In Flanders (the northern region of Belgium), the educational system consists of four tracks. Many students start out in the most prestigious, academic track. If they fail to gain the necessary credentials, they move to the less esteemed technical and vocational tracks. Therefore, the educational system has been called a 'cascade system'. We presume that this cascade system creates homogeneous expectations in the academic track, though heterogeneous expectations in the technical and vocational tracks. We use data from the International Study of City Youth (ISCY), gathered during the 2013-2014 school year from 2354 pupils of the tenth grade across 30 secondary schools in the city of Ghent, Flanders. Preliminary results suggest that the technical and vocational tracks show more heterogeneity in student’s expectations than the academic track. If tracking does not fulfill the desired goals in some tracks, tracking practices should be questioned as tracking occurs along social and ethnic lines, causing social inequality

A Corpus-driven Approach toward Teaching Vocabulary and Reading to English Language Learners in U.S.-based K-12 Context through a Mobile App

In order to decrease teachers’ decisions of which vocabulary the focus of the instruction should be upon, a recent line of research argues that pedagogically-prepared word lists may offer the most efficient order of learning vocabulary with an optimized context for instruction in each of four K-12 content areas (math, science, social studies, and language arts) through providing English Language Learners (ELLs) with the most frequent words in each area. Educators and school experts have acknowledged the need for developing new materials, including computerized enhanced texts and effective strategies aimed at improving ELLs’ mastery of academic and STEM-related lexicon. Not all words in a language are equal in their role in comprehending the language and expressing ideas or thoughts. For this study, I used a corpus-driven approach which is operationalized by applying a text analysis method. For the purpose of this research study, I made two corpora, Teacher’s U.S. Corpus (TUSC) and Science and Math Academic Corpus for Kids (SMACK) with a focus on word lemma rather than inflectional and derivational variants of word families. To create the corpora, I collected and analyzed a total of 122 textbooks used commonly in the states of Florida and California. Recruiting, scanning and converting of textbooks had been carried out over a period of more than two years from October 2014 to March 2017. In total, this school corpus contains 10,519,639 running words and 16,344 lemmas saved in 16,315 word document pages. From the corpora, I developed six word lists, namely three frequency-based word lists (high-, mid-, and low-frequency), academic and STEM-related word lists, and essential word list (EWL). I then applied the word lists as the database and developed a mobile app, Vocabulary in Reading Study – VIRS, (available on App Store, Android and Google Play) alongside a website (www.myvirs.com). Also, I developed a new K-12 dictionary which targets the vocabulary needs of ELLs in K-12 context. This is a frequency-based dictionary which categorizes words into three groups of high, medium and low frequency words as well as two separate sections for academic and STEM words. The dictionary has 16,500 lemmas with derivational and inflectional forms