The final set in a tennis match: four years at Wimbledon 1

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "The final set in a tennis match: four years at Wimbledon 1"

Transcription

1 Published as: Journal of Applied Statistics, Vol. 26, No. 4, 1999, The final set in a tennis match: four years at Wimbledon 1 Jan R. Magnus, CentER, Tilburg University, the Netherlands and Franc J.G.M. Klaassen, Department of Econometrics, Tilburg University, the Netherlands SUMMARY We consider the final (deciding) set in a tennis match. We examine whether it is true that the chances for both players to win the match are equal at the beginning of the final set, even though they were not equal at the beginning of the match. We also test whether it is easier for a non-seeded man to beat a seeded player than for a non-seeded woman and whether male players are more equal in quality than female players. Does the service dominance decrease in long matches, and does winning the pre-final set provide an advantage in the final set? We use almost 90,000 points at Wimbledon to test all five hypotheses. 1 Introduction The final set - the 5th in the men's singles (at a Grand Slam event) and the 3rd in the ladies' singles - decides a tennis match. Such a deciding set occurs in about one fourth of all matches at Wimbledon. Tension is high and mistakes can be very costly. There are a number of interesting questions relating to the final set, some of which we shall investigate in this paper. For example, suppose a seed plays against a non-seed. (At Wimbledon 16 players out of 128 are seeded in order to prevent the situation that top players meet too early in the tournament.) You wish to forecast the winner. At the beginning of the match, if no further information is available, the relative frequency at Wimbledon that the non-seed wins is small, about 10-15%. What is the probability at the beginning of the final set? Is it now close to 50%? Also, is it more difficult for non-seeded women to beat a seed than for men, and are men more equal in quality than women? We also examine whether players get tired. That is, does the dominance of the service decrease in long matches (that is, in the final set)? And finally - something that commentators say - is it 1 Correspondence: Jan R. Magnus, CentER, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, the Netherlands. 1

2 true that in the final set the player who has won the previous set has the advantage? Many other hypotheses are considered in Magnus and Klaassen (1998a)-(1998d). In the statistical literature on tennis so far, people have analysed some other interesting questions. If we assume that two fixed probabilities govern the match (the probability of winning a point on service for both players), then we can calculate the probability of winning a game, set, tiebreak or match. Of the many papers in this category we mention Hsi and Burych (1971), Kemeny and Snell (1976), and Pollard (1983). The assumption that the probability of winning a point on service is constant during the match is questionable. After all, an often-heard hypothesis states that at the beginning of the final set the chances to win are equal for both players, even though at the beginning of the match one player was the favourite. The reason why the assumption of fixed probabilities has not yet been tested is that the literature on tennis is hampered by an almost complete lack of data. (In Klaassen and Magnus (1998) we analyse the assumption of fixed probabilities of winning a point on service directly. We reject it and present a model for the evolvement of the probability during the match.) Most papers are theoretical and contain no data at all. If the authors use data, they are usually either point-to-point data of one match, or based on several end-of-match results (6-4/6-3/6-3, say). Fortunately, we have a large data set. It consists of 88,883 points distributed over 481 Wimbledon matches. A second category of theoretical papers concerns the tennis scoring system and its impact on the probability of winning a match. See Maisel (1966), Miles (1984), Riddle (1988, 1989) and the comments by Jackson (1989). In this paper we analyse the effect of the difference in the scoring systems used in the men s and the ladies singles: men have to win three sets, while women have to win only two sets to win the match. This difference in itself implies that it is more difficult for non-seeded men to beat a seed than for non-seeded women. But maybe men are more equal in quality than women, which in itself would lead to more upsets in the men s singles. We use our large Wimbledon data set to show which effect actually dominates. In section 2 we briefly describe the Wimbledon data. In section 3 we examine whether there are special advantages for seeds. Do seeds often win the final set if they play against a non-seed? Is it more difficult for a woman non-seed to beat a seed than for a man non-seed, as is often argued? Are men more equal in quality than women? Section 4 is about service dominance in long matches: is it lower in the final set? The effect of the pre-final set on the final set will be investigated in section 5. Section 6 concludes. 2 The data Our data set consists of 481 matches played in the men's singles (MS) and ladies' singles (LS) 2

3 championships at Wimbledon from 1992 to For each of these matches we know the exact sequence of points. We also know at each point whether the first or the second service was in and whether the point was decided through an ace or a double fault. Table 1 provides a summary of the data. TABLE 1 We have slightly more matches for men than for women, but of course many more sets, games and points for the men s singles than for the ladies singles, since the men play for three sets won and the women for two. The men play less points per game than the women, because the dominance of their service is greater; see Magnus and Klaassen (1998a) for empirical evidence. But the women play less games per set on average (scores like 6-0 and 6-1 are more common in the ladies singles than in the men s singles), because the difference between seeded and nonseeded players is much greater, as we will show below. However, the larger gap between seeded and non-seeded women does not result in less final sets in a match compared to the men. In 30% of the matches in our data set women have to play a final set; the men in 20% of the matches. This is because the ladies play for the best of three sets, whereas the men play for the best of five sets. All matches in our data set are played on one of the five show courts : Centre Court and Courts 1, 2, 13 and 14. As a result we have in our data set almost one half of all singles matches played during these four years of our sample period. Usually matches involving top-players are scheduled on the show courts and this causes an underrepresentation in the data set of matches with non-seeded players. In order to account for this selection problem, we weigh the matches when computing statistics; see Magnus and Klaassen (1998b) for further details. To avoid too much averaging, we shall usually distinguish between the 16 seeds and the 112 non-seeds. 3 Advantage for the seeded player? Suppose a seed plays against a non-seed. At the beginning of the match, if no further information is available, the probability that the non-seed will win is small: 13.1% (2.7%) in the men s singles and 10.5% (2.5%) in the ladies singles. (Standard errors are in parentheses.) What is the probability at the beginning of the final set? Some people claim: Hypothesis 1: At the beginning of a final set both players have equal chance to win. This hypothesis is false. Naturally, the probabilities have increased, but only to 28.7% (8.7%) for the men and 17.1% (6.3%) for the ladies. Both are significantly different from 50%. (In this paper significant means that the estimate is more than 2 standard errors away from its target. At 2-2 in sets in the men's singles, it is therefore certainly not true that the chances are now even 3

4 between the seed and the non-seed. The seed is still very much the favourite. This is even clearer in the ladies singles. At 1-1 in sets, the seeded player still has a probability of 82.9% (6.3%) to win the match! (Of course, strictly speaking we can only test hypotheses for the Wimbledon tournament. However, we believe that most of our conclusions, at least qualitatively, also apply to other professional tournaments, in particular non-clay tournaments.) At first sight, the estimated probabilities of winning the final set, 28.7% for the men and 17.1% for the women, also seem to indicate that it is more difficult for a female non-seed to beat a seed than for a male, as is often claimed. However, one should keep in mind that the male non-seed has to win two sets to arrive at the final set, whereas the woman has to win only one set. So, when arriving at the final set, the quality difference between the non-seed and the seed is generally smaller for the men than for the women. This in itself will already result in a higher probability of winning the final set for non-seeded men than for non-seeded women. Hypothesis 2: Upsets are more common in the men s singles than in the ladies singles. An upset occurs when a non-seeded player beats a seeded player. In the ladies singles the probability of an upset is 10.5% (2.5%), which is not significantly different from the 13.1% (2.7%) of the men. Therefore, we have no evidence for a difference between men and women regarding the difficulty of achieving an upset. However, as we will explain below, this does not mean that there is no difference between men and women regarding the strength of seeds compared to non-seeds. It is often argued that Hypothesis 3: Anyone in the top one-hundred for the men can beat the number one, but this is not true for the women. Of course, formally speaking this is nonsense, since any woman can beat the number one with non-zero probability. What is meant is that the men are more equal in quality than the women. Our results show that this is indeed the case. The probability of winning a set for a non-seed against a seed is 24.9% (1.8%) for the men and 18.0% (2.1%) for the women, which is significantly lower. The results concerning hypotheses 2 and 3 seem to be contradictory. On the one hand, upsets are equally likely in the men s singles as in the ladies singles. On the other hand, non-seeded men have a much higher probability of winning a set against a seed than non-seeded women. These results can be reconciled by remembering that men have to win three sets, whereas women have to win only two sets. Therefore, even though non-seeded men win one set more easily than nonseeded women, they have about equal difficulty in beating a seed. 4

5 4 Does the dominance of the service decrease? Tennis matches can last for two or three hours or longer. The players get tired and therefore, possibly, their service becomes less powerful. But is this true? Hypothesis 4: In long matches the dominance of the service decreases. We will examine this hypothesis by comparing the service dominance in the final set with that in earlier sets. There are, at least, two effects that may result in less service dominance in the final set. First, the server can indeed get tired in the final set. Secondly, the receiver gets increasingly better acquainted with his/her opponent s service during the match. To distinguish between both effects, we will estimate a simple logit model; see e.g. McFadden (1984). The first effect is represented by a dummy variable which is one in the final set and zero otherwise. The second effect, the learning effect, can be captured by the number of the set the players are in. For example, in the first set the receiver has received less services to learn his/her opponent s service than in the second set. This leads to the following specification of the probability of winning a point on service: Pr(point won on service) = ( # dummy final set + 2 # set number ), (1) where is the logistic distribution function, (x)=exp(x)/(1+exp(x)). Hypothesis 4 implies a negative value for 1, whereas the learning effect makes 2 negative, as well. Estimating this model using all matches, however, results in a downward bias of the learning effect. Set numbers higher than three for the men and two for the women not only indicate more learning, but also imply that players are more equal. After all, matches between very unequal players have already stopped after three (MS) and two (LS) sets. If players are more equal, this results in lower probabilities of winning a point on service. So, in total, high set numbers imply a negative value for 2 in (1), even if there is no learning effect at all. To solve this bias problem one could estimate the parameters in (1) separately for 3,4 and 5 sets matches (MS) and for 2 and 3 sets matches (LS). The set number then no longer contains information about the relative strength of players. To increase estimation efficiency, however, we impose that the learning effect, 2, is the same for all types of matches and pool all matches together. We thus have the following specification: Pr(point won on service) ( 3 0 #d #d #d 5 1 #dummy final set 2 #set number ) (2) for the men, where d 3 is a dummy which is one in case of a three-set match and zero otherwise. The dummies d 4 and d 5 represent the four- and five-set matches. Formula (2) shows that each 5

6 4 type of match has its own intercept 03, 0 or 05, which is the correction for the bias problem 2 discussed above. For the ladies singles we have only dummies d 2 and d 3 and intercepts 0 and 3. Table 2 presents the maximum likelihood estimation results for all parameters in (2). Standard 0 errors are in brackets and a * denotes significance. TABLE 2 We see that the probability of winning a point on service is not lower in the final set, once we have corrected for the learning effect. For the women the probability is even higher, although not significantly. The learning effect is negative for both men and women, but again insignificant. So, there is no decrease in service dominance during the match. Hypothesis 4 is false. 5 The final and pre-final set We complete our discussion with an analysis about the relation between the final and pre-final set. More specifically, take the following idée reçue. Hypothesis 5: In the final set the player who has won the previous set has the advantage. We investigate this hypothesis by looking at probabilities of winning the final set after winning the pre-final set. These are presented in Table 3 for all matches taken together (total) and for different types of matches. Sd-NSd indicates a match of a seeded (Sd) against a non-seeded (NSd) player, where the first player (Sd) won the pre-final set. Sd-Sd, NSd-Sd and NSd-NSd are similarly defined. As the number of observations is quite small (51 final sets in the men s singles, 57 in the ladies singles in our data set), the standard errors are quite large. TABLE 3 In the men s singles the probability that the same player wins the fourth and fifth sets is estimated to be 50.2% (7.0%). In the ladies singles the estimated probability that the same player wins the second and third sets is 61.2% (6.5%). These percentages are not significantly different from 50% and hence there is no ground for believing hypothesis 5. If we look at the sub-categories, then we see that, when two seeds play against each other, the winner of the 4th (2nd) set will probably lose the match, especially in the men s singles. When a non-seeded women plays against a seed winning the pre-final set is also a disadvantage, as her probability of winning the match is only 14.8% (14.5%). Both results are significant and indicate that, if there is correlation between the final and pre-final sets, this is more likely to be negative than positive. 6

7 6 Conclusion In this paper we have looked at the final set in a tennis match. At Wimbledon, the final set is the fifth in the men s singles and the third set in the ladies singles. Is it true that both players have the same chance of winning the match at the beginning of the final set? This is not the case: the seeded player is still very much the favourite against a non-seed, even though the non-seed has performed unexpectedly well up to the final set. The next two hypotheses concern the difference between men s tennis and ladies tennis. In contrast to what many people believe, it is not more difficult for a non-seeded women than for a non-seeded man to beat a seeded player. It is true, however, that male players are more equal in quality than female players. These results seem contradictory, but one should keep in mind that non-seeded men have to win three sets, whereas non-seeded women have to win only two sets. Therefore, even though non-seeded men win one set more easily, they still find it difficult to beat a seed. Our fourth hypothesis states that the service dominance decreases in long matches. Servers can get tired and receivers learn more about their opponent s service and hence score more points. It appears that winning a point on service is not more difficult in the final set than in other sets, so hypothesis four is false. Finally, we examine whether winning the pre-final set provides an advantage in the final set. Again there is no ground for believing this hypothesis. Acknowledgements: We thank IBM UK and The All England Club at Wimbledon for their kindness in providing the data. We also thank Arthur van Soest and Martin Dufwenberg for useful comments. 7

8 References Hsi, B.P. and D.M. Burych (1971) Games of two players, Applied Statistics, 20, pp Jackson, D.A. (1989) Letter to the Editor on Probability models for tennis scoring systems by L.H. Riddle, Applied Statistics, 38, pp Kemeny, J.G. and J.L. Snell (1976) Finite Markov Chains, New York: Springer Verlag, in particular pp Klaassen, F.J.G.M. and J.R. Magnus (1998) On the independence and identical distribution of points in tennis, CentER, Tilburg University, submitted for publication. Magnus, J.R. and F.J.G.M. Klaassen (1998a) On the advantage of serving first in a tennis set: four years at Wimbledon, The Statistician (Journal of the Royal Statistical Society, Series D), to appear. Magnus, J.R. and F.J.G.M. Klaassen (1998b) The effect of new balls in tennis: four years at Wimbledon, The Statistician (Journal of the Royal Statistical Society, Series D), to appear. Magnus, J.R. and F.J.G.M. Klaassen (1998c) On the existence of big points in tennis: four years at Wimbledon, mimeo, CentER, Tilburg University. Magnus, J.R. and F.J.G.M. Klaassen (1998d) The importance of breaks in tennis: four years at Wimbledon, mimeo, CentER, Tilburg University. Maisel, H. (1966) Best k of 2k-1 comparisons, Journal of the American Statistical Association, 61, pp Miles, R.E. (1984) Symmetric sequential analysis: the efficiencies of sports scoring systems (with particular reference to those of tennis), Journal of the Royal Statistical Society, Series B, 46, pp McFadden, D. (1984) Econometric analysis of qualitative choice models, in: Z. Griliches and M.D. Intriligator (eds), Handbook of Econometrics, Vol. II, Chapter 24, Amsterdam: North-Holland Publishing Company. Pollard, G.H. (1983) An analysis of classical and tie-breaker tennis, Australian Journal of Statistics, 25, pp Riddle, L.H. (1988) Probability models for tennis scoring systems, Applied Statistics, 37, pp (Corrigendum in Applied Statistics, 37, p. 490.) Riddle, L.H. (1989) Reply to D.A. Jackson, Applied Statistics, 38, pp

9 Number of... MS LS Matches Non-final sets Final sets Games Tiebreaks Points Sets in match Final sets in match Games in non-final set Games in final set Tiebreaks in non-final set Points in match Points in game Points in tiebreak , , , , Table 1 - Number of matches, sets, games, tiebreaks and points in the data set. dummy 3/2 sets match dummy 4/3 sets match dummy 5 sets match dummy final set set number MS 0.589* (0.022) 0.662* (0.027) 0.618* (0.030) (0.048) (0.010) LS 0.326* (0.041) 0.245* (0.044) (0.057) (0.025) Table 2 - Probability of winning a point on service: logit estimation results. Sd-Sd Sd-NSd NSd-Sd NSd-NSd Total MS 10.7 (10.3) 40.8 (11.3) 76.4 (15.0) 57.6 (12.8) 50.2 (7.0) LS 33.7 (15.8) 62.3 (8.9) 14.8 (14.5) 68.5 (13.4) 61.2 (6.5) Table 3 - Estimated probabilities of winning 5th (3rd) set after winning 4th (2nd) set in men s singles (ladies singles). 9

First-Server Advantage in Tennis Matches

First-Server Advantage in Tennis Matches First-Server Advantage in Tennis Matches Iain MacPhee and Jonathan Rougier Department of Mathematical Sciences University of Durham, U.K. Abstract We show that the advantage that can accrue to the server

More information

Revisiting the Hot Hand Theory with Free Throw Data in a Multivariate Framework

Revisiting the Hot Hand Theory with Free Throw Data in a Multivariate Framework Calhoun: The NPS Institutional Archive DSpace Repository Faculty and Researchers Faculty and Researchers Collection 2010 Revisiting the Hot Hand Theory with Free Throw Data in a Multivariate Framework

More information

A point-based Bayesian hierarchical model to predict the outcome of tennis matches

A point-based Bayesian hierarchical model to predict the outcome of tennis matches A point-based Bayesian hierarchical model to predict the outcome of tennis matches Martin Ingram, Silverpond September 21, 2017 Introduction Predicting tennis matches is of interest for a number of applications:

More information

Analysis of performance at the 2007 Cricket World Cup

Analysis of performance at the 2007 Cricket World Cup Analysis of performance at the 2007 Cricket World Cup Petersen, C., Pyne, D.B., Portus, M.R., Cordy, J. and Dawson, B Cricket Australia, Department of Physiology, Australian Institute of Sport, Human Movement,

More information

Grand Slam Tennis Computer Game (Version ) Table of Contents

Grand Slam Tennis Computer Game (Version ) Table of Contents Grand Slam Tennis Computer Game (Version 2010.3) Table of Contents 1. Introduction - What is the grand slam tennis program? 2 2. Options - What are the available playing options? 3 3. History - How has

More information

HOW THE TENNIS COURT SURFACE AFFECTS PLAYER PERFORMANCE AND INJURIES. Tristan Barnett Swinburne University. Graham Pollard University of Canberra

HOW THE TENNIS COURT SURFACE AFFECTS PLAYER PERFORMANCE AND INJURIES. Tristan Barnett Swinburne University. Graham Pollard University of Canberra HOW THE TENNIS COURT SURFACE AFFECTS PLAYER PERFORMANCE AND INJURIES Tristan Barnett Swinburne University Graham Pollard University of Canberra Introduction There are four major Grand Slam tennis events

More information

First Server Advantage in Tennis. Michelle Okereke

First Server Advantage in Tennis. Michelle Okereke First Server Advantage in Tennis Michelle Okereke Overview! Background! Research Question! Methodology! Results! Conclusion Background! Scoring! Advantage Set: First player to win 6 games by a margin of

More information

Should bonus points be included in the Six Nations Championship?

Should bonus points be included in the Six Nations Championship? Should bonus points be included in the Six Nations Championship? Niven Winchester Joint Program on the Science and Policy of Global Change Massachusetts Institute of Technology 77 Massachusetts Avenue,

More information

ECO 199 GAMES OF STRATEGY Spring Term 2004 Precept Materials for Week 3 February 16, 17

ECO 199 GAMES OF STRATEGY Spring Term 2004 Precept Materials for Week 3 February 16, 17 ECO 199 GAMES OF STRATEGY Spring Term 2004 Precept Materials for Week 3 February 16, 17 Illustration of Rollback in a Decision Problem, and Dynamic Games of Competition Here we discuss an example whose

More information

Predictors for Winning in Men s Professional Tennis

Predictors for Winning in Men s Professional Tennis Predictors for Winning in Men s Professional Tennis Abstract In this project, we use logistic regression, combined with AIC and BIC criteria, to find an optimal model in R for predicting the outcome of

More information

Home Team Advantage in English Premier League

Home Team Advantage in English Premier League Patrice Marek* and František Vávra** *European Centre of Excellence NTIS New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia, Czech Republic: patrke@kma.zcu.cz

More information

ADVANCED TACTICS: CONCEPTS, FEATURES AND 5 GAME SITUATIONS

ADVANCED TACTICS: CONCEPTS, FEATURES AND 5 GAME SITUATIONS ITF Coaches Education Programme Coaching High Performance Players Course ADVANCED TACTICS: CONCEPTS, FEATURES AND 5 GAME SITUATIONS By Miguel Crespo & Machar Reid By the end of this session you should

More information

Using Actual Betting Percentages to Analyze Sportsbook Behavior: The Canadian and Arena Football Leagues

Using Actual Betting Percentages to Analyze Sportsbook Behavior: The Canadian and Arena Football Leagues Syracuse University SURFACE College Research Center David B. Falk College of Sport and Human Dynamics October 2010 Using Actual Betting s to Analyze Sportsbook Behavior: The Canadian and Arena Football

More information

THE UPA MANUAL OF CHAMPIONSHIP SERIES TOURNAMENT FORMATS

THE UPA MANUAL OF CHAMPIONSHIP SERIES TOURNAMENT FORMATS THE UPA MANUAL OF CHAMPIONSHIP SERIES TOURNAMENT FORMATS Version 4.3 January 17, 2008 Original submitted by Eric Simon Revised in 8/2003 by: Brian Canniff Jin Ding Hank Ibser AJ Iwaszko Florian Pfender

More information

The probability of winning a high school football game.

The probability of winning a high school football game. Columbus State University CSU epress Faculty Bibliography 2008 The probability of winning a high school football game. Jennifer Brown Follow this and additional works at: http://csuepress.columbusstate.edu/bibliography_faculty

More information

INSIDE VOLLEY TENNIS

INSIDE VOLLEY TENNIS INSIDE VOLLEY TENNIS WWW.INSIDESPORTSGAME.ORG INSIDE VOLLEY TENNIS RULES GETTING STARTED You will need 2 six-sided dice (2d6) of different colors and 2 ten-sided dice (2d10). Layout the game board with

More information

THE PLAYING PATTERN OF WORLD S TOP SINGLE BADMINTON PLAYERS

THE PLAYING PATTERN OF WORLD S TOP SINGLE BADMINTON PLAYERS THE PLAYING PATTERN OF WORLD S TOP SINGLE BADMINTON PLAYERS Yuen-Ming Tong and Youlian Hong Department of Sports Science and Physical Education, The Chinese University of Hong Kong, Hong Kong SAR A total

More information

MATHEMATICAL MODELLING IN HIERARCHICAL GAMES WITH SPECIFIC REFERENCE TO TENNIS

MATHEMATICAL MODELLING IN HIERARCHICAL GAMES WITH SPECIFIC REFERENCE TO TENNIS MTHEMTICL MODELLING IN HIERRCHICL GMES WITH SPECIFIC REFERENCE TO TENNIS y Tristan J. arnett THESIS SUMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY T SWINURNE UNIVERSITY MRCH 2006 c Copyright by Tristan

More information

106 S. R. Clarke and P. Norton 2 Selection of statisticians The human resources personnel handle the selection and employment of tennis statisticians

106 S. R. Clarke and P. Norton 2 Selection of statisticians The human resources personnel handle the selection and employment of tennis statisticians COLLECTING STATISTICS AT THE AUSTRALIAN OPEN TENNIS CHAMPIONSHIP Stephen R. Clarke Λ School of Mathematical Sciences Swinburne University of Technology PO Box 218, Hawthorn Victoria 3122, Australia sclarke@groupwise.swin.edu.au

More information

The Effect of Pressure on Mixed-Strategy Play in Tennis: The Effect of Court Surface on Service Decisions

The Effect of Pressure on Mixed-Strategy Play in Tennis: The Effect of Court Surface on Service Decisions International Journal of Business and Social Science Vol. 3 No. 20 [Special Issue October 2012] The Effect of Pressure on Mixed-Strategy Play in Tennis: The Effect of Court Surface on Service Decisions

More information

Artificial Pitches and Unfair Home Advantage in Professional Football

Artificial Pitches and Unfair Home Advantage in Professional Football TI 2017-093/V Tinbergen Institute Discussion Paper Artificial Pitches and Unfair Home Advantage in Professional Football Jan C. van Ours 1 1 Erasmus School of Economics, Erasmus University Rotterdam; Tinbergen

More information

An Analysis of Factors Contributing to Wins in the National Hockey League

An Analysis of Factors Contributing to Wins in the National Hockey League International Journal of Sports Science 2014, 4(3): 84-90 DOI: 10.5923/j.sports.20140403.02 An Analysis of Factors Contributing to Wins in the National Hockey League Joe Roith, Rhonda Magel * Department

More information

RELATIVE AGE IN ELITE TENNIS

RELATIVE AGE IN ELITE TENNIS Relative age in elite tennis STUDIES IN PHYSICAL CULTURE AND TOURISM Vol. 16, No. 4, 2009 PETER O DONOGHUE University of Wales Institute Cardiff, Wales RELATIVE AGE IN ELITE TENNIS Key words: longitudinal

More information

NCSS Statistical Software

NCSS Statistical Software Chapter 256 Introduction This procedure computes summary statistics and common non-parametric, single-sample runs tests for a series of n numeric, binary, or categorical data values. For numeric data,

More information

LEE COUNTY WOMEN S TENNIS LEAGUE

LEE COUNTY WOMEN S TENNIS LEAGUE In order for the Lee County Women s Tennis League to successfully promote and equitably manage 2,500+ members and give all players an opportunity to play competitive tennis, it is essential to implement

More information

1. OVERVIEW OF METHOD

1. OVERVIEW OF METHOD 1. OVERVIEW OF METHOD The method used to compute tennis rankings for Iowa girls high school tennis http://ighs-tennis.com/ is based on the Elo rating system (section 1.1) as adopted by the World Chess

More information

Analysis of Variance. Copyright 2014 Pearson Education, Inc.

Analysis of Variance. Copyright 2014 Pearson Education, Inc. Analysis of Variance 12-1 Learning Outcomes Outcome 1. Understand the basic logic of analysis of variance. Outcome 2. Perform a hypothesis test for a single-factor design using analysis of variance manually

More information

Journal of Quantitative Analysis in Sports

Journal of Quantitative Analysis in Sports Journal of Quantitative Analysis in Sports Volume 6, Issue 1 21 Article 5 Age and Winning Professional Golf Tournaments Gizachew Tiruneh University of Central Arkansas, gtiruneh@uca.edu Copyright c 21

More information

Choking under Pressure and Gender: Evidence from Professional Tennis

Choking under Pressure and Gender: Evidence from Professional Tennis Discussion Paper Series IZA DP No. 10587 Choking under Pressure and Gender: Evidence from Professional Tennis Danny Cohen-Zada Alex Krumer Mosi Rosenboim Offer Moshe Shapir february 2017 Discussion Paper

More information

Saturation Flow Rate, Start-Up Lost Time, and Capacity for Bicycles at Signalized Intersections

Saturation Flow Rate, Start-Up Lost Time, and Capacity for Bicycles at Signalized Intersections Transportation Research Record 1852 105 Paper No. 03-4180 Saturation Flow Rate, Start-Up Lost Time, and Capacity for Bicycles at Signalized Intersections Winai Raksuntorn and Sarosh I. Khan A review of

More information

Agood tennis player knows instinctively how hard to hit a ball and at what angle to get the ball over the. Ball Trajectories

Agood tennis player knows instinctively how hard to hit a ball and at what angle to get the ball over the. Ball Trajectories 42 Ball Trajectories Factors Influencing the Flight of the Ball Nathalie Tauziat, France By Rod Cross Introduction Agood tennis player knows instinctively how hard to hit a ball and at what angle to get

More information

TOURNAMENT PROCEDURE. in Flight 1 singles or doubles and those reaching the finals in Flights 2, 3, or 4 singles and Flights 2 and 3 doubles

TOURNAMENT PROCEDURE. in Flight 1 singles or doubles and those reaching the finals in Flights 2, 3, or 4 singles and Flights 2 and 3 doubles TENNIS 52 (GIRLS) TOURNAMENT PROCEDURE 1. ASSIGNMENT OF SCHOOLS WILL BE ON A GEOGRAPHICAL BASIS IN TWO DIVISIONS (1-2) a. The smallest 72 schools sponsoring tennis are in Division 2 with the remaining

More information

a) List and define all assumptions for multiple OLS regression. These are all listed in section 6.5

a) List and define all assumptions for multiple OLS regression. These are all listed in section 6.5 Prof. C. M. Dalton ECN 209A Spring 2015 Practice Problems (After HW1, HW2, before HW3) CORRECTED VERSION Question 1. Draw and describe a relationship with heteroskedastic errors. Support your claim with

More information

Will the New Low Emission Zone Reduce the Amount of Motor Vehicles in London?

Will the New Low Emission Zone Reduce the Amount of Motor Vehicles in London? Will the New Low Emission Zone Reduce the Amount of Motor Vehicles in London? Philip Osborne I. INTRODUCTION An initiative of the 2016 London Mayor s election campaign was to improve engagement with Londoners

More information

A Markov Decision Process-based handicap system for. tennis. T.C.Y. Chan 1,2 and R. Singal,1,3. January 3, 2017

A Markov Decision Process-based handicap system for. tennis. T.C.Y. Chan 1,2 and R. Singal,1,3. January 3, 2017 A Markov Decision Process-based handicap system for tennis T.C.Y. Chan 1,2 and R. Singal,1,3 1 Department of Mechanical and Industrial Engineering, University of Toronto 2 Centre for Healthcare Engineering,

More information

DEVELOPMENT OF A SET OF TRIP GENERATION MODELS FOR TRAVEL DEMAND ESTIMATION IN THE COLOMBO METROPOLITAN REGION

DEVELOPMENT OF A SET OF TRIP GENERATION MODELS FOR TRAVEL DEMAND ESTIMATION IN THE COLOMBO METROPOLITAN REGION DEVELOPMENT OF A SET OF TRIP GENERATION MODELS FOR TRAVEL DEMAND ESTIMATION IN THE COLOMBO METROPOLITAN REGION Ravindra Wijesundera and Amal S. Kumarage Dept. of Civil Engineering, University of Moratuwa

More information

Are differences in ranks good predictors for Grand Slam tennis matches?

Are differences in ranks good predictors for Grand Slam tennis matches? International Journal of Forecasting 26 (2010) 551 563 www.elsevier.com/locate/ijforecast Are differences in ranks good predictors for Grand Slam tennis matches? Julio del Corral a,, Juan Prieto-Rodríguez

More information

Name Date Period. E) Lowest score: 67, mean: 104, median: 112, range: 83, IQR: 102, Q1: 46, SD: 17

Name Date Period. E) Lowest score: 67, mean: 104, median: 112, range: 83, IQR: 102, Q1: 46, SD: 17 Chapter 6 Review Standards: 4, 7, 8, and 11 Name Date Period Write complete answers, using complete sentences where necessary. Show your work when possible. MULTIPLE CHOICE. Choose the one alternative

More information

Spring Doubles Tennis Rules

Spring Doubles Tennis Rules Spring Doubles Tennis Rules USTA Tennis Rules Condensed USTA Rules may be modified for IM Play at the discretion of the Intramural Sports Office RULE 1: The Court The court shall be a rectangle, 78 feet

More information

Volume 37, Issue 3. Are Forfeitures of Olympic Medals Predictable? A Test of the Efficiency of the International Anti-Doping System

Volume 37, Issue 3. Are Forfeitures of Olympic Medals Predictable? A Test of the Efficiency of the International Anti-Doping System Volume 37, Issue 3 Are Forfeitures of Olympic Medals Predictable? A Test of the Efficiency of the International Anti-Doping System Eike Emrich Saarland University Freya Gassmann Saarland University Christian

More information

The relationship between payroll and performance disparity in major league baseball: an alternative measure. Abstract

The relationship between payroll and performance disparity in major league baseball: an alternative measure. Abstract The relationship between payroll and performance disparity in major league baseball: an alternative measure Daniel Mizak Frostburg State University Anthony Stair Frostburg State University Abstract This

More information

LEE COUNTY WOMEN S TENNIS LEAGUE

LEE COUNTY WOMEN S TENNIS LEAGUE In order for the Lee County Women s Tennis League to successfully promote and equitably manage 2,500+ members and give all players an opportunity to play competitive tennis, it is essential to implement

More information

RULES OF THE COURT 2016 SUMMARY OF MODIFICATIONS

RULES OF THE COURT 2016 SUMMARY OF MODIFICATIONS RULES OF THE COURT 2016 SUMMARY OF MODIFICATIONS For 2016, the following changes have been made: Rules of Tennis The following substantive modifications have been made to the Rules of Tennis: In Appendix

More information

Consolidation of the Haavelmo- Cowles Commission Paradigm

Consolidation of the Haavelmo- Cowles Commission Paradigm Consolidation of the Haavelmo- Cowles Commission Paradigm (based on Chapter 1 of my book draft: The Reformation of Econometrics: A Historical Perspective) Duo Qin SOAS, London, UK December 2011 Coverage

More information

Modern volleyball aspects

Modern volleyball aspects Modern volleyball aspects Table of contents Aims 3 Introduction 4 Part 1 Men s volleyball of top level. Main indicators 5 Part 2 Women s volleyball of top level. Main indicators 29 Part 3 Men s and Women

More information

Racetrack Betting: Do Bettors Understand the Odds?

Racetrack Betting: Do Bettors Understand the Odds? University of Pennsylvania ScholarlyCommons Statistics Papers Wharton Faculty Research 1994 Racetrack Betting: Do Bettors Understand the Odds? Lawrence D. Brown University of Pennsylvania Rebecca D'Amato

More information

College Teaching Methods & Styles Journal First Quarter 2007 Volume 3, Number 1

College Teaching Methods & Styles Journal First Quarter 2007 Volume 3, Number 1 The Economics Of The Duration Of The Baseball World Series Alexander E. Cassuto, (E-mail: aleaxander.cassuto@csueastbay.edu), California State University, Hayward Franklin Lowenthal, (E-mail: frabklin.lowenthal@csueastbay.edu),

More information

On Probabilistic Excitement of Sports Games

On Probabilistic Excitement of Sports Games On Probabilistic Excitement of Sports Games Jan Vecer, Tomoyuki Ichiba, Mladen Laudanovic, Columbia University, Department of Statistics, New York, NY 0027, USA May 8, 2007 Abstract In this paper we introduce

More information

DISCUSSION BY CHARLES C. HEWITT, JR.

DISCUSSION BY CHARLES C. HEWITT, JR. 78 CREDIBILITY Substituting these values in equations (F) and (E) we obtain A = 35,287 and 33,258 respectively. The introduction of the third moment here increases the credibility requirement by 6%. The

More information

Major League Baseball Offensive Production in the Designated Hitter Era (1973 Present)

Major League Baseball Offensive Production in the Designated Hitter Era (1973 Present) Major League Baseball Offensive Production in the Designated Hitter Era (1973 Present) Jonathan Tung University of California, Riverside tung.jonathanee@gmail.com Abstract In Major League Baseball, there

More information

Chapter 13. Factorial ANOVA. Patrick Mair 2015 Psych Factorial ANOVA 0 / 19

Chapter 13. Factorial ANOVA. Patrick Mair 2015 Psych Factorial ANOVA 0 / 19 Chapter 13 Factorial ANOVA Patrick Mair 2015 Psych 1950 13 Factorial ANOVA 0 / 19 Today s Menu Now we extend our one-way ANOVA approach to two (or more) factors. Factorial ANOVA: two-way ANOVA, SS decomposition,

More information

Journal of the American Statistical Association, Vol. 89, No (Sep., 1994), pp

Journal of the American Statistical Association, Vol. 89, No (Sep., 1994), pp A Brownian Motion Model for the Progress of Sports Scores Hal S. Stern Journal of the American Statistical Association, Vol. 89, No. 427. (Sep., 1994), pp. 1128-1134. Stable URL: http://links.jstor.org/sici?sici=0162-1459%28199409%2989%3a427%3c1128%3aabmmft%3e2.0.co%3b2-w

More information

Improving the Serving Motion in a Volleyball Game: A Design of Experiment Approach

Improving the Serving Motion in a Volleyball Game: A Design of Experiment Approach www.ijcsi.org 206 Improving the Serving Motion in a Volleyball Game: A Design of Experiment Approach Maryam Mohammadi 1 and Afagh Malek 2 1&2 Department of Manufacturing and Industrial Engineering, Universiti

More information

Potential, Prizes and Performance: Testing Tournament Theory with Professional Tennis Data

Potential, Prizes and Performance: Testing Tournament Theory with Professional Tennis Data DISCUSSION PAPER SERIES IZA DP No. 947 Potential, Prizes and Performance: Testing Tournament Theory with Professional Tennis Data Uwe Sunde December 2003 Forschungsinstitut zur Zukunft der Arbeit Institute

More information

Use of Additional Through Lanes at Signalized Intersections

Use of Additional Through Lanes at Signalized Intersections Transportation Research Record 869 1 Use of Additional Through Lanes at Signalized Intersections PATRICK T. McCOY AND JOHN R. TOBIN One method sometimes used to increase the capacity of signalized intersections

More information

PREDICTING the outcomes of sporting events

PREDICTING the outcomes of sporting events CS 229 FINAL PROJECT, AUTUMN 2014 1 Predicting National Basketball Association Winners Jasper Lin, Logan Short, and Vishnu Sundaresan Abstract We used National Basketball Associations box scores from 1991-1998

More information

Journal of Quantitative Analysis in Sports

Journal of Quantitative Analysis in Sports Journal of Quantitative Analysis in Sports Volume 1, Issue 1 2005 Article 5 Determinants of Success in the Olympic Decathlon: Some Statistical Evidence Ian Christopher Kenny Dan Sprevak Craig Sharp Colin

More information

2016 USTA Georgia Adult Tournament Regulations & Point Ranking System

2016 USTA Georgia Adult Tournament Regulations & Point Ranking System 2016 USTA Georgia Adult Tournament Regulations & A. Residency Requirements for Closed Tournaments Only players who have established a legal residency in Georgia, hold a current USTA membership card assigned

More information

Fit to Be Tied: The Incentive Effects of Overtime Rules in Professional Hockey

Fit to Be Tied: The Incentive Effects of Overtime Rules in Professional Hockey Fit to Be Tied: The Incentive Effects of Overtime Rules in Professional Hockey Jason Abrevaya Department of Economics, Purdue University 43 West State St., West Lafayette, IN 4797-256 This version: May

More information

FIFA Foe Fun! Mark Kozek! Whittier College. Tim Chartier! Davidson College. Michael Mossinghoff! Davidson College

FIFA Foe Fun! Mark Kozek! Whittier College. Tim Chartier! Davidson College. Michael Mossinghoff! Davidson College FIFA Foe Fun! Tim Chartier! Davidson College Mark Kozek! Whittier College Michael Mossinghoff! Davidson College Group E: Switzerland, Ecuador, France, Honduras. Switzerland is the top seed, based on FIFA

More information

Bhagwant N. Persaud* Richard A. Retting Craig Lyon* Anne T. McCartt. May *Consultant to the Insurance Institute for Highway Safety

Bhagwant N. Persaud* Richard A. Retting Craig Lyon* Anne T. McCartt. May *Consultant to the Insurance Institute for Highway Safety Review of The Impact of Red Light Cameras (Photo-Red Enforcement) on Crashes in Virginia by Nicholas J. Garber, John S. Miller, R. Elizabeth Abel, Saeed Eslambolchi, and Santhosh K. Korukonda Bhagwant

More information

An early warning system to predict house price bubbles

An early warning system to predict house price bubbles An early warning system to predict house price bubbles Christian Dreger, Konstantin Kholodilin DIW Berlin Why is the topic relevant? Bubbles in housing prices can impede the real economic evolution Prices

More information

An Econometric Evaluation of the Performance of the Greek National Football Team

An Econometric Evaluation of the Performance of the Greek National Football Team Athens Journal of Sports December 2014 An Econometric Evaluation of the Performance of the Greek National Football Team By Gregory T. Papanikos This paper uses a Cobb-Douglas production function to account

More information

Discussion Paper Series. Take a Chance on ABBA. IZA DP No Danny Cohen-Zada Alex Krumer Offer Moshe Shapir

Discussion Paper Series. Take a Chance on ABBA. IZA DP No Danny Cohen-Zada Alex Krumer Offer Moshe Shapir Discussion Paper Series IZA DP No. 10878 Take a Chance on ABBA Danny Cohen-Zada Alex Krumer Offer Moshe Shapir july 2017 Discussion Paper Series IZA DP No. 10878 Take a Chance on ABBA Danny Cohen-Zada

More information

Navigate to the golf data folder and make it your working directory. Load the data by typing

Navigate to the golf data folder and make it your working directory. Load the data by typing Golf Analysis 1.1 Introduction In a round, golfers have a number of choices to make. For a particular shot, is it better to use the longest club available to try to reach the green, or would it be better

More information

Optimal Weather Routing Using Ensemble Weather Forecasts

Optimal Weather Routing Using Ensemble Weather Forecasts Optimal Weather Routing Using Ensemble Weather Forecasts Asher Treby Department of Engineering Science University of Auckland New Zealand Abstract In the United States and the United Kingdom it is commonplace

More information

Chapter 9 Progress in Performance

Chapter 9 Progress in Performance Chapter 9 Progress in Performance To become a better player you must play competitive games. Match play against weaker opponents enables you to consolidate and develop the work you have done in practice.

More information

Insurance. The practical application. of credibility models in the rating of Health

Insurance. The practical application. of credibility models in the rating of Health The practical application of credibility models in the rating of Health Insurance In an increasingly competitive market, fixing insurance premiums is becoming an essential task for insurance companies.

More information

Journal of Quantitative Analysis in Sports

Journal of Quantitative Analysis in Sports Journal of Quantitative Analysis in Sports Volume 2, Issue 1 2006 Article 5 The Effects of Home-Away Sequencing on the Length of Best-of-Seven Game Playoff Series Christopher M. Rump Bowling Green State

More information

SCIENTIFIC COMMITTEE SECOND REGULAR SESSION August 2006 Manila, Philippines

SCIENTIFIC COMMITTEE SECOND REGULAR SESSION August 2006 Manila, Philippines SCIENTIFIC COMMITTEE SECOND REGULAR SESSION 7-18 August 2006 Manila, Philippines MEASUREMENT-POINTS EXAMINATION OF CIRCLE HOOKS FOR PELAGIC LONGLINE FISHERY TO EVALUATE EFFECTS OF HOOK DESIGN WCPFC-SC2-2006/EB

More information

Journal of Quantitative Analysis in Sports Manuscript 1039

Journal of Quantitative Analysis in Sports Manuscript 1039 An Article Submitted to Journal of Quantitative Analysis in Sports Manuscript 1039 A Simple and Flexible Rating Method for Predicting Success in the NCAA Basketball Tournament Brady T. West University

More information

TECHNICAL STUDY 2 with ProZone

TECHNICAL STUDY 2 with ProZone A comparative performance analysis of games played on artificial (Football Turf) and grass from the evaluation of UEFA Champions League and UEFA Cup. Introduction Following on from our initial technical

More information

Rules and Regulations Excerpt from the Rules, Regulations and Standing Orders of USTA Eastern, Inc.

Rules and Regulations Excerpt from the Rules, Regulations and Standing Orders of USTA Eastern, Inc. In addition to the Rules of Tennis of the ITF and USTA Tournament Regulations, which are hereby adopted as being applicable to all Eastern sanctioned tournaments, the following additional regulations will

More information

Determinants of college hockey attendance

Determinants of college hockey attendance University of Northern Iowa UNI ScholarWorks Honors Program Theses University Honors Program 2014 Determinants of college hockey attendance Max Martino University of Northern Iowa Copyright 2014 Max Martino

More information

Was John Adams more consistent his Junior or Senior year of High School Wrestling?

Was John Adams more consistent his Junior or Senior year of High School Wrestling? Was John Adams more consistent his Junior or Senior year of High School Wrestling? An investigation into my Dad s high school Wrestling Career Amanda Adams Period 1 Statistical Reasoning in Sports December

More information

Game Theory (MBA 217) Final Paper. Chow Heavy Industries Ty Chow Kenny Miller Simiso Nzima Scott Winder

Game Theory (MBA 217) Final Paper. Chow Heavy Industries Ty Chow Kenny Miller Simiso Nzima Scott Winder Game Theory (MBA 217) Final Paper Chow Heavy Industries Ty Chow Kenny Miller Simiso Nzima Scott Winder Introduction The end of a basketball game is when legends are made or hearts are broken. It is what

More information

Is Home-Field Advantage Driven by the Fans? Evidence from Across the Ocean. Anne Anders 1 John E. Walker Department of Economics Clemson University

Is Home-Field Advantage Driven by the Fans? Evidence from Across the Ocean. Anne Anders 1 John E. Walker Department of Economics Clemson University Is Home-Field Advantage Driven by the Fans? Evidence from Across the Ocean Anne Anders 1 John E. Walker Department of Economics Clemson University Kurt W. Rotthoff Stillman School of Business Seton Hall

More information

RACING RULES / RACE OFFICIALS

RACING RULES / RACE OFFICIALS RACING RULES / RACE OFFICIALS RYA GUIDANCE REDRESS WHAT IS REDRESS? It is compensation awarded to a boat when, in the words of rule 62, a boat s score in a race or series has been, or may be, through no

More information

Building System Dynamics Models

Building System Dynamics Models Building System Dynamics Models Stella Guide 6 Overshoot and Collapse Deer Population Vegetation 7000.00 90000.00 3500.00 45000.00 0.00 0.00 0.00 5.00 0.00 5.00 0.00 Graph p () Years 4:0 pm Mon, Feb 6,

More information

Figure 1. Winning percentage when leading by indicated margin after each inning,

Figure 1. Winning percentage when leading by indicated margin after each inning, The 7 th Inning Is The Key By David W. Smith Presented June, 7 SABR47, New York, New York It is now nearly universal for teams with a 9 th inning lead of three runs or fewer (the definition of a save situation

More information

SIX NATIONS 2015 STATISTICAL REPORT WORLD RUGBY GAME ANALYSIS

SIX NATIONS 2015 STATISTICAL REPORT WORLD RUGBY GAME ANALYSIS SIX NATIONS 2015 STATISTICAL REPORT FINAL RESULTS & STANDINGS P W D L PF PA PD TF TA PTS Ireland 5 4 0 1 119 56 +63 8 3 8 England 5 4 0 1 157 100 +57 18 11 8 Wales 5 4 0 1 146 93 +53 13 8 8 France 5 2

More information

How predictable are the FIFA worldcup football outcomes? An empirical analysis

How predictable are the FIFA worldcup football outcomes? An empirical analysis Applied Economics Letters, 2008, 15, 1171 1176 How predictable are the FIFA worldcup football outcomes? An empirical analysis Saumik Paul* and Ronita Mitra Department of Economics, Claremont Graduate University,

More information

ScienceDirect. Quantitative and qualitative benchmarks in volleyball game at girls "cadets" level (15-16 years old) Doina Croitoru * ICSPEK 2013

ScienceDirect. Quantitative and qualitative benchmarks in volleyball game at girls cadets level (15-16 years old) Doina Croitoru * ICSPEK 2013 Available online at www.sciencedirect.com ScienceDirect Procedia - Social and Behavioral Scienc es 117 ( 2014 ) 383 388 ICSPEK 2013 Quantitative and qualitative benchmarks in volleyball game at girls "cadets"

More information

IS POINT SHAVING IN COLLEGE BASKETBALL WIDESPREAD?

IS POINT SHAVING IN COLLEGE BASKETBALL WIDESPREAD? UNC CHARLOTTE ECONOMICS WORKING PAPER SERIES IS POINT SHAVING IN COLLEGE BASKETBALL WIDESPREAD? Jason P. Berkowitz Craig A. Depken, II John M. Gandar Working Paper No. 2016-012 THE UNIVERSITY OF NORTH

More information

2013 Australian open women s singles champion and runner-up technical and tactics features research based on mathematical statistic analysis

2013 Australian open women s singles champion and runner-up technical and tactics features research based on mathematical statistic analysis ISSN : 0974-7435 Volume 0 Issue 3 BTAIJ, 0(3), 04 [6-60] 03 Australian open women s singles champion and runner-up technical and tactics features research based on mathematical statistic analysis Feng

More information

Traffic safety developments in Poland

Traffic safety developments in Poland Traffic safety developments in Poland Siem Oppe D-2001-8 Traffic safety developments in Poland A research note D-2001-8 Siem Oppe Leidschendam, 2001 SWOV Institute for Road Safety Research, The Netherlands

More information

Available online at ScienceDirect. Procedia Engineering 112 (2015 )

Available online at  ScienceDirect. Procedia Engineering 112 (2015 ) Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 112 (2015 ) 540 545 7th Asia-Pacific Congress on Sports Technology, APCST 2015 Movement variability of professional pool billiards

More information

The Cold Facts About the "Hot Hand" in Basketball

The Cold Facts About the Hot Hand in Basketball The Cold Facts About the "Hot Hand" in Basketball Do basketball players tend to shoot in streaks? Contrary to the belief of fans and commentators, analysis shows that the chances of hitting a shot are

More information

Nonlife Actuarial Models. Chapter 7 Bühlmann Credibility

Nonlife Actuarial Models. Chapter 7 Bühlmann Credibility Nonlife Actuarial Models Chapter 7 Bühlmann Credibility Learning Objectives 1. Basic framework of Bühlmann credibility 2. Variance decomposition 3. Expected value of the process variance 4. Variance of

More information

A IMPROVED VOGEL S APPROXIMATIO METHOD FOR THE TRA SPORTATIO PROBLEM. Serdar Korukoğlu 1 and Serkan Ballı 2.

A IMPROVED VOGEL S APPROXIMATIO METHOD FOR THE TRA SPORTATIO PROBLEM. Serdar Korukoğlu 1 and Serkan Ballı 2. Mathematical and Computational Applications, Vol. 16, No. 2, pp. 370-381, 2011. Association for Scientific Research A IMPROVED VOGEL S APPROXIMATIO METHOD FOR THE TRA SPORTATIO PROBLEM Serdar Korukoğlu

More information

This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and

This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution

More information

Oregon School Activities Association SW Parkway Avenue, Suite 1 Wilsonville, OR fax:

Oregon School Activities Association SW Parkway Avenue, Suite 1 Wilsonville, OR fax: Oregon School Activities Association 25200 SW Parkway Avenue, Suite 1 Wilsonville, OR 97070 503.682.6722 fax: 503.682.0960 http://www.osaa.org August 2, 2016 TO: FROM: SUBJECT: Superintendents, Principals

More information

Introduction. Mode Choice and Urban Form. The Transportation Planner s Approach. The problem

Introduction. Mode Choice and Urban Form. The Transportation Planner s Approach. The problem Introduction The table below shows transit s share in the urban US (all trip purposes) and the 10 urban areas where it is most popular (2008 data): Mode Choice and Urban Form Philip A. Viton April 4, 2014

More information

propose creative solutions and constitute good presentations T E A M S

propose creative solutions and constitute good presentations T E A M S M A T H E M A T I C A L B A T T L E S S E T O F G U I D E L I N E S Math battle is a combination of problem-solving competition and debate. It is a team contest which aims to challenge the academic ability

More information

Ups and Downs: Team Performance in Best-of-Seven Playoff Series

Ups and Downs: Team Performance in Best-of-Seven Playoff Series Ups and Downs: Team Performance in Best-of-Seven Playoff Series Tim B. Swartz, Aruni Tennakoon, Farouk Nathoo, Parminder S. Sarohia and Min Tsao Abstract This paper explores the impact of the status of

More information

CAROLINA REGION USA VOLLEYBALL JUNIOR BEACH TOUR GUIDELINES 2018

CAROLINA REGION USA VOLLEYBALL JUNIOR BEACH TOUR GUIDELINES 2018 CAROLINA REGION USA VOLLEYBALL JUNIOR BEACH TOUR GUIDELINES 2018 (Based on the USA Volleyball Junior Beach Tour Handbook with slight adaptations relevant to the region s tour) Carolina Region Jr Beach

More information

Minimax Play at Wimbledon

Minimax Play at Wimbledon Minimax Play at Wimbledon By MARK WALKER AND JOHN WOODERS* In many strategic situations it is important that one s actions not be predictable by one s opponent, or by one s opponents. Indeed, the origins

More information

Efficiency Wages in Major League Baseball Starting. Pitchers Greg Madonia

Efficiency Wages in Major League Baseball Starting. Pitchers Greg Madonia Efficiency Wages in Major League Baseball Starting Pitchers 1998-2001 Greg Madonia Statement of Problem Free agency has existed in Major League Baseball (MLB) since 1974. This is a mechanism that allows

More information

Driver Behavior at Highway-Rail Grade Crossings With Passive Traffic Controls

Driver Behavior at Highway-Rail Grade Crossings With Passive Traffic Controls 2014 Global Level Crossing Symposium August 2014, Urbana, IL, USA Driver Behavior at Highway-Rail Grade Crossings With Passive Traffic Controls - A Driving Simulator Study Presenter: Dr. Asad J. Khattak

More information

Low-intensity wheelchair training in inactive people with long-term spinal cord injury van der Scheer, Jan

Low-intensity wheelchair training in inactive people with long-term spinal cord injury van der Scheer, Jan University of Groningen Low-intensity wheelchair training in inactive people with long-term spinal cord injury van der Scheer, Jan IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's

More information