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Undestanding Baseball Team Standings and Streaks  [PDF]
C. Sire,S. Redner
Physics , 2008, DOI: 10.1140/epjb/e2008-00405-5
Abstract: Can one understand the statistics of wins and losses of baseball teams? Are their consecutive-game winning and losing streaks self-reinforcing or can they be described statistically? We apply the Bradley-Terry model, which incorporates the heterogeneity of team strengths in a minimalist way, to answer these questions. Excellent agreement is found between the predictions of the Bradley-Terry model and the rank dependence of the average number team wins and losses in major-league baseball over the past century when the distribution of team strengths is taken to be uniformly distributed over a finite range. Using this uniform strength distribution, we also find very good agreement between model predictions and the observed distribution of consecutive-game team winning and losing streaks over the last half-century; however, the agreement is less good for the previous half-century. The behavior of the last half-century supports the hypothesis that long streaks are primarily statistical in origin with little self-reinforcing component. The data further show that the past half-century of baseball has been more competitive than the preceding half-century.
Human Wagering Behavior Depends on Opponents' Faces  [PDF]
Erik J. Schlicht,Shinsuke Shimojo,Colin F. Camerer,Peter Battaglia,Ken Nakayama
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0011663
Abstract: Research in competitive games has exclusively focused on how opponent models are developed through previous outcomes and how peoples' decisions relate to normative predictions. Little is known about how rapid impressions of opponents operate and influence behavior in competitive economic situations, although such subjective impressions have been shown to influence cooperative decision-making. This study investigates whether an opponent's face influences players' wagering decisions in a zero-sum game with hidden information. Participants made risky choices in a simplified poker task while being presented opponents whose faces differentially correlated with subjective impressions of trust. Surprisingly, we find that threatening face information has little influence on wagering behavior, but faces relaying positive emotional characteristics impact peoples' decisions. Thus, people took significantly longer and made more mistakes against emotionally positive opponents. Differences in reaction times and percent correct were greatest around the optimal decision boundary, indicating that face information is predominantly used when making decisions during medium-value gambles. Mistakes against emotionally positive opponents resulted from increased folding rates, suggesting that participants may have believed that these opponents were betting with hands of greater value than other opponents. According to these results, the best “poker face” for bluffing may not be a neutral face, but rather a face that contains emotional correlates of trustworthiness. Moreover, it suggests that rapid impressions of an opponent play an important role in competitive games, especially when people have little or no experience with an opponent.
Hitting Is Contagious in Baseball: Evidence from Long Hitting Streaks  [PDF]
Joel R. Bock, Akhilesh Maewal, David A. Gough
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0051367
Abstract: Data analysis is used to test the hypothesis that “hitting is contagious”. A statistical model is described to study the effect of a hot hitter upon his teammates’ batting during a consecutive game hitting streak. Box score data for entire seasons comprising streaks of length games, including a total observations were compiled. Treatment and control sample groups () were constructed from core lineups of players on the streaking batter’s team. The percentile method bootstrap was used to calculate confidence intervals for statistics representing differences in the mean distributions of two batting statistics between groups. Batters in the treatment group (hot streak active) showed statistically significant improvements in hitting performance, as compared against the control. Mean for the treatment group was found to be to percentage points higher during hot streaks (mean difference increased points), while the batting heat index introduced here was observed to increase by points. For each performance statistic, the null hypothesis was rejected at the significance level. We conclude that the evidence suggests the potential existence of a “statistical contagion effect”. Psychological mechanisms essential to the empirical results are suggested, as several studies from the scientific literature lend credence to contagious phenomena in sports. Causal inference from these results is difficult, but we suggest and discuss several latent variables that may contribute to the observed results, and offer possible directions for future research.
Winning strategies in congested traffic  [PDF]
Ferenc Jarai-Szabo,Zoltan Neda
Physics , 2012, DOI: 10.1142/S0129183112500635
Abstract: One-directional traffic on two-lanes is modeled in the framework of a spring-block type model. A fraction $q$ of the cars are allowed to change lanes, following simple dynamical rules, while the other cars keep their initial lane. The advance of cars, starting from equivalent positions and following the two driving strategies is studied and compared. As a function of the parameter $q$ the winning probability and the average gain in the advancement for the lane-changing strategy is computed. An interesting phase-transition like behavior is revealed and conclusions are drawn regarding the conditions when the lane changing strategy is the better option for the drivers.
Cantor-winning sets and their applications  [PDF]
Dzmitry Badziahin,Stephen Harrap
Mathematics , 2015,
Abstract: We introduce and develop a class of \textit{Cantor-winning} sets that share the same amenable properties as the classical winning sets associated to Schmidt's $(\alpha,\beta)$-game: these include maximal Hausdorff dimension, invariance under countable intersections with other Cantor-winning sets and invariance under bi-Lipschitz homeomorphisms. It is then demonstrated that a wide variety of badly approximable sets appearing naturally in the theory of Diophantine approximation fit nicely into our framework. As applications of this phenomenon we answer several previously open questions, including some related to the Mixed Littlewood conjecture and the $\times2, \times3$ problem.
Distances between the winning numbers in Lottery  [PDF]
Konstantinos Drakakis
Mathematics , 2005,
Abstract: We prove an interesting fact about Lottery: the winning 6 numbers (out of 49) in the game of the Lottery contain two consecutive numbers with a surprisingly high probability (almost 50%).
Complementary cooperation, minimal winning coalitions, and power indices  [PDF]
Zhigang Cao,Xiaoguang Yang
Computer Science , 2009, DOI: 10.1016/j.tcs.2012.11.033
Abstract: We introduce a new simple game, which is referred to as the complementary weighted multiple majority game (C-WMMG for short). C-WMMG models a basic cooperation rule, the complementary cooperation rule, and can be taken as a sister model of the famous weighted majority game (WMG for short). In this paper, we concentrate on the two dimensional C-WMMG. An interesting property of this case is that there are at most $n+1$ minimal winning coalitions (MWC for short), and they can be enumerated in time $O(n\log n)$, where $n$ is the number of players. This property guarantees that the two dimensional C-WMMG is more handleable than WMG. In particular, we prove that the main power indices, i.e. the Shapley-Shubik index, the Penrose-Banzhaf index, the Holler-Packel index, and the Deegan-Packel index, are all polynomially computable. To make a comparison with WMG, we know that it may have exponentially many MWCs, and none of the four power indices is polynomially computable (unless P=NP). Still for the two dimensional case, we show that local monotonicity holds for all of the four power indices. In WMG, this property is possessed by the Shapley-Shubik index and the Penrose-Banzhaf index, but not by the Holler-Packel index or the Deegan-Packel index. Since our model fits very well the cooperation and competition in team sports, we hope that it can be potentially applied in measuring the values of players in team sports, say help people give more objective ranking of NBA players and select MVPs, and consequently bring new insights into contest theory and the more general field of sports economics. It may also provide some interesting enlightenments into the design of non-additive voting mechanisms. Last but not least, the threshold version of C-WMMG is a generalization of WMG, and natural variants of it are closely related with the famous airport game and the stable marriage/roommates problem.
Hitting Streaks Don't Obey Your Rules: Evidence That Hitting Streaks Aren't Just By-Products of Random Variations  [PDF]
Trent McCotter
Statistics , 2009,
Abstract: There have been more hitting streaks in Major League Baseball than we would expect. All batting lines of MLB hitters from 1957-2006 were randomly permuted 10,000 times and the number of hitting streaks of each length from 2 to 100 was measured. The average count of each length streak was then compared to the corresponding total from real-life, when the games were in chronological order. The number of streaks in real-life was significantly higher than over the random permutations. Non-starts (such as pinch-hitting appearances) were removed since these may be unduly reducing the number of streaks in the permutations; the number of streaks in the permutations increased but was still significantly lower than real-life totals. Possible explanations are given for why more streaks have appeared in real-life than we would expect, including possibly the hot hand idea. Contact at trentm@email.unc.edu
Power Indices and minimal winning Coalitions  [PDF]
Werner Kirsch,Jessica Langner
Computer Science , 2008,
Abstract: The Penrose-Banzhaf index and the Shapley-Shubik index are the best-known and the most used tools to measure political power of voters in simple voting games. Most methods to calculate these power indices are based on counting winning coalitions, in particular those coalitions a voter is decisive for. We present a new combinatorial formula how to calculate both indices solely using the set of minimal winning coalitions.
Triathlon: swimming for winning  [cached]
Journal of Human Sport and Exercise , 2011,
Abstract: Swimming performance in triathlon gradually gets of overriding importance in view of the final positioning in a race. It is important to end up swimming in the leading group(s) and to consider the impact of the swim stage on the 2 remaining sports disciplines in order to outbalance the athlete’s effort and to be able to keepracing for a good position until the end of the race. Unlike cycling and running where the performance mainly depends on conditioning, the performance in swimming is a subtle combination of conditioning and technical abilities. Even elite swimmers may lose a lot of performance if their outstanding conditioning is not coupled with an excellent swimming technique. Triathletes very often suffer from a lack of technique and despite the wetsuit, which partially outbalances this shortcoming, they spend a lot of energy in the swimstage without reaping any success, energy which is then not on hand anymore for the rest of the race. Therefore, swimming technique should be the groundwork in the multi-year planning AND should befocussed on in each training session during the whole carrier of the triathlete. Monitoring the combination of time/stroke rate/stroke length is thus a must. Periodisation in triathlon is much more complex than in “single” sports. Not only the sports specific weaknesses/strengths of the athlete but also the intrinsicinteraction between cycling, running and swimming on training effects and his swim-technical qualities will rule the periodisation. Additionally the level of technique will also set volume, intensity and form of training exercises. Simple to complex tests can help to make the right choice. This makes from triathlon an exciting sport, not only for the athlete but also for the coach and supporting teams. This article will summarise some practical implications on periodisation and on swimming training in triathlon.
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