Journal of Quantitative Analysis in Sports

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Journal of Quantitative Analysis in Sports"

Transcription

1 Journal of Quantitative Analysis in Sports Volume 7, Issue Article 5 Stratified Odds Ratios for Evaluating NBA Players Based on their Plus/Minus Statistics Douglas M. Okamoto, Data to Information to Knowledge Recommended Citation: Okamoto, Douglas M. (2011) "Stratified Odds Ratios for Evaluating NBA Players Based on their Plus/Minus Statistics," Journal of Quantitative Analysis in Sports: Vol. 7: Iss. 2, Article 5. Available at: DOI: / American Statistical Association. All rights reserved.

2 Stratified Odds Ratios for Evaluating NBA Players Based on their Plus/Minus Statistics Douglas M. Okamoto Abstract In this paper, I estimate adjusted odds ratios by fitting stratified logistic regression models to binary response variables, games won or lost, with plus/minus statistics as explanatory variables. Adapted from ice hockey, the plus/minus statistic credits an NBA player one or more points whenever his team scores while he is on the basketball court. Conversely, the player is debited minus one or more points whenever the opposing team scores. Throughout the NBA season, the league s better players are likely to have positive plus/minus statistics as reported by Yahoo!Sports and 82games.com. Crude or unadjusted odds ratios estimate the relative probabilities of a player having a positive plus/minus in a win, versus a negative plus/minus in a loss. Home and away games are twin strata with teams playing 41 home games and 41 road games during an 82-game regular season. Stratum-specific odds ratios vary because some players perform better at home than on the road and vice versa. In order to adjust for home court advantage, stratified odds ratios and their 95 percent confidence intervals are estimated for each of the Los Angeles Lakers during the regular season. KEYWORDS: plus/minus statistic, odds ratio, logistic regression model

3 Okamoto: Stratified Odds Ratios for Evaluating NBA Players 1. Introduction Adapted from ice hockey, the plus/minus statistic credits an NBA player one or more points whenever his team scores while he is on the basketball court. Conversely, the player is debited one or more points whenever the opposing team scores. At the end of the game, a player s pluses and minuses are totaled to get his plus/minus (+/-) statistic. The Lakers won the Pacific Division of the Western Conference with a win/loss record during the regular season. In Figure 1, blue circles indicate Laker wins and red circles indicate Laker losses. Each dot corresponds to an ordered pair (x, y), with the x-coordinate equal to Kobe Bryant s +/- and the y-coordinate equal to the winning or losing margin. When Kobe is a plus, {X > 0}, a minus, {X < 0}; when the Lakers win, {Y>0}, they lose, {Y<0} LA Laker Winning or Losing Margin Kobe Bryant Plus/Minus Win Loss Figure 1. Scatterplot of Los Angeles Laker Winning or Losing Margin vs. Kobe Bryant Plus/Minus: NBA Regular Season (73 Games) Kobe was a plus in 48 of 51 Laker wins (NE quadrant) and 5 of 22 losses (SE quadrant). He was a minus in 3 Laker wins (NW quadrant), and 17 losses (SW quadrant). Not shown in the scatterplot are 9 Laker games (6 wins, 3 losses) in which Kobe did not play. Published by Berkeley Electronic Press,

4 Journal of Quantitative Analysis in Sports, Vol. 7 [2011], Iss. 2, Art Odds Ratios The relative odds of the Lakers winning or losing when Kobe was a plus or minus are defined in terms of the conditional probabilities of Y given X, where the joint probability distribution of two binary random variables is as follows: a) {X=1} if Kobe was a plus, {X=0} if Kobe was a minus; and b) {Y=1} if the Lakers won, {Y=0} if the Lakers lost. The odds ratio (OR) is the relative probability of a Laker win when Kobe is a plus divided by the relative probability of a Laker win when he is a minus: equals [(48)(17)]/[(5)(3)] = 54 or 54:1, calculated from the cross product of four cell counts in the following two-by-two contingency table. Table 1. Laker Wins/Losses vs. Kobe Bryant Plus/Minus Minus Plus Totals Win Loss Totals The Los Angeles Lakers were 54 times more likely to have won when Kobe was plus in a win. Conversely, the Lakers were 54 times more likely to have lost when he was minus in a loss. Despite his 54:1 odds ratio, Kobe Bryant ranked second to Laker forward Pau Gasol whose [(40)(14)]/[(4)(2)] = 70 or 70:1 odds ratio calculated from Table 2 led the team in the regular season. Table 2. Laker Wins/Losses vs. Pau Gasol Plus/Minus Minus Plus Totals Win Loss Totals Odds ratios and 95 percent confidence intervals for Kobe Bryant, Pau Gasol and eight of their Laker teammates are shown in Figure 2. DOI: /

5 Okamoto: Stratified Odds Ratios for Evaluating NBA Players Pau Gasol 70 Kobe Bryant 54 Ron Artest 31 Derek Fisher 27 Lamar Odom 16 Andrew Bynum 10 Luke Walton 7.8 Jordan Farmar 6.2 Shannon Brown 3.4 Sasha Vujacic Figure 2. Odds Ratio Chart for the Los Angeles Lakers: NBA Regular Season (82 Games) 3. Logistic Regression Models Fitting a logistic regression model to the logit transform of relative probabilities of the Los Angeles Lakers winning or losing, logit log Pr Y 1 / Pr{ Y 0} X where X is a Laker player s plus/minus statistic and α an intercept term, yields a maximum likelihood estimate of the logistic regression coefficient,, or a log odds ratio that is the antilogarithm of his odds ratio as calculated in Section 2, e.g., exp(3.996) = 54 or 54:1, for Kobe Bryant. Fitting a second logistic multiple regression model to the logit transform of relative probabilities of the Los Angeles Lakers winning or losing, Y Y 1 X 1 2 X 2 logit log Pr 1 / Pr{ 0} Published by Berkeley Electronic Press,

6 Journal of Quantitative Analysis in Sports, Vol. 7 [2011], Iss. 2, Art. 5 where X 1 and X 2 are plus/minus statistics for two Laker players, say Kobe Bryant and Pau Gasol, yields maximum likelihood estimates of two logistic regression coefficients, 1 and 2. Taking antilogarithms of these two log odds ratios, exp(2.553) = 13 or 13:1, for Kobe Bryant and exp(3.733) = 42 or 42:1, for Pau Gasol. During the regular seasons, Bryant and Gasol only played together in 56 of 82 Laker regular season games, winning 41 and losing 15 games. Table 3a. Kobe Bryant Plus/Minus vs. Pau Gasol Plus/Minus Laker Wins BRYANT+/- GASOL +/- Plus Minus Totals Plus Zero Minus Totals Table 3b. Kobe Bryant Plus/Minus vs. Pau Gasol Plus/Minus Laker Losses BRYANT+/- GASOL +/- Plus Minus Totals Plus Zero Minus Totals In Table 3a, there are 5 Laker wins in which Bryant is a minus, but Gasol is not; whereas, in 4 Laker wins Bryant is a plus and Gasol a minus. Similarly, in Table 3b there are 2 Laker losses in which Bryant is a plus and Gasol a minus; whereas, in 1 Laker loss Bryant is a minus and Gasol a plus. 4. Stratified Odds Ratios The relative odds of the Lakers winning a home game when Kobe was a plus equals [(30)(5)]/[(1)(1)] = 150 or 150:1, calculated from Table 4a. The relative odds of the Lakers winning an away game when Kobe was a plus equals [(18)(12)]/[(4)(2)] = 27 or 27:1, calculated from Table 4b. DOI: /

7 Okamoto: Stratified Odds Ratios for Evaluating NBA Players Table 4a. Laker Wins/Losses vs. Kobe Bryant Plus/Minus Home Games Minus Plus Totals Win Loss Totals Table 4b. Laker Wins/Losses vs. Kobe Bryant Plus/Minus Away Games Minus Plus Totals Win Loss Totals Dividing Kobe Bryant s home odds ratio by his away odds ratio, the Lakers were five-and-a-half times more likely to have won at home than on the road when Kobe Bryant was a plus. Consequently, the estimation of stratified odds ratios or adjusted odds ratios that take into account stratification is a necessary refinement. Figure 3 shows the odds ratios for Kobe Bryant and eight of his Laker teammates, with home games represented in gold and away games represented in purple. Odds Ratio (Hom e and Away) Odds Ratio (Home and Away) Sasha Shannon Jordan Andrew Lamar Derek Ron Kobe Pau 1.0 Sasha Vujacic Shanno Brow n Jordan Farmar Andrew By num Lamar Odom Fisher Derek Artest Ron Bry Kobe ant Gasol Pau Vujacic n Brown Farmar Bynum Odom Fisher Artest Bryant Gasol Home OR Home OR Away ay OR OR Figure 3. Odds Ratio Chart for the Los Angeles Lakers: NBA Regular Season (41 Home Games, 41 Away Games) Published by Berkeley Electronic Press,

8 Journal of Quantitative Analysis in Sports, Vol. 7 [2011], Iss. 2, Art. 5 The logit transform of relative probabilities of the Lakers winning or losing as a function of a player s common log odds ratio for both home and away games is modeled as follows: 2 1 logit log Pr Y 1 / Pr{ Y 0} X or X where and are stratum-specific, nuisance parameters. Fitting a stratified logistic regression model yields a conditional likelihood estimate for the log odds ratio,, conditioned on sufficient statistics for the two nuisance parameters as in Mehta and Patel (1995). For example, Kobe Bryant s stratified odds ratio equals the antilogarithm of his log odds ratio, exp (3.695) = 40 or 40:1. Pau Gasol Kobe Bryant Ron Artest Derek Fisher Lamar Odom Andrew Bynum Jordan Farmar Luke Walton Shannon Brown Sasha Vujacic Figure 4. Stratified Odds Ratio Chart for the Los Angeles Lakers: NBA Regular Season (41 Home Games, 41 Away Games) Pau Gasol led the Lakers during the regular season with a stratified odds ratio, 50:1, which compared to Kobe Bryant s 40:1 stratified odds ratio means the Lakers were 25 percent more likely to win when he was plus (or lose when he was minus) than they were when Kobe was plus (or minus). DOI: /

9 Okamoto: Stratified Odds Ratios for Evaluating NBA Players NBA Playoffs The Lakers won their second straight NBA Championship with an overall record of 16 wins and 7 losses in the 2010 NBA Playoffs. In Figure 5, Kobe Bryant was plus in 14 of 16 Laker playoff wins (blue circles) and minus in 6 of 7 Laker playoff losses (red circles). He was neither plus nor minus in 1 playoff win (white circle), minus in another playoff win, and plus in 1 playoff loss LA Laker Winning or Losing Margin Kobe Bryant Plus/Minus Win Loss Figure 5. Scatterplot of Los Angeles Laker Winning or Losing Margin vs. Kobe Bryant Plus/Minus: 2010 NBA Championship Playoffs (23 Games) If the single playoff game in which Kobe Bryant was neither plus nor minus is excluded, then his odds ratio was [(14)(6)/(1)(1)] = 84 or 84:1. The Lakers were 84 times more likely to have won when Kobe was plus than they were when he was minus in a win. Table 5. Laker Wins/Losses vs. Kobe Bryant Plus/Minus Minus Plus Totals Win Loss Totals Published by Berkeley Electronic Press,

10 Journal of Quantitative Analysis in Sports, Vol. 7 [2011], Iss. 2, Art. 5 K. Bryant 84 P. Gasol 39 L. Odom 39 J. Farmar 15 L. Walton 10 D. Fisher 5.5 S. Brown 4.4 R. Artest 3.0 A. Bynum 2.4 J. Powell Figure 6. Odds Ratio Chart for the Los Angeles Lakers: 2010 NBA Championship Playoffs (23 Games) With his 84:1 odds ratio more than twice the odds ratio of any of his teammates, Kobe Bryant led the Los Angeles Lakers to their second consecutive NBA Championship and earned his second straight Larry O Brien trophy as the Finals MVP. His stratified odds ratio could not be calculated because he was minus in the single Laker playoff loss at home against the Boston Celtics, and plus in all 5 of their playoff wins away from home. Pau Gasol and Lamar Odom whose 39:1 odds ratio during the playoffs tied them for second, had stratified odds ratios of 23:1 and 29:1, respectively. Unlike Kobe Bryant, Pau Gasol and Lamar Odom were minuses in one of the 5 playoff games the Lakers won on the road. References Mehta C.R. and Patel N.R. (1995). Exact logistic regression: theory and examples, Statistics in Medicine, 14: pp Rosenbaum, Dan T. (2004). Measuring how NBA players help their teams win, 82games.com, DOI: /

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

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

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

On Estimating the Ability of NBA Players

On Estimating the Ability of NBA Players On Estimating the Ability of NBA Players Paul Fearnhead and Benjamin M. Taylor August 5, 2010 Abstract arxiv:1008.0705v1 [stat.ap] 4 Aug 2010 This paper introduces a new model and methodology for estimating

More information

A Novel Approach to Predicting the Results of NBA Matches

A Novel Approach to Predicting the Results of NBA Matches A Novel Approach to Predicting the Results of NBA Matches Omid Aryan Stanford University aryano@stanford.edu Ali Reza Sharafat Stanford University sharafat@stanford.edu Abstract The current paper presents

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

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

Pierce 0. Measuring How NBA Players Were Paid in the Season Based on Previous Season Play

Pierce 0. Measuring How NBA Players Were Paid in the Season Based on Previous Season Play Pierce 0 Measuring How NBA Players Were Paid in the 2011-2012 Season Based on Previous Season Play Alex Pierce Economics 499: Senior Research Seminar Dr. John Deal May 14th, 2014 Pierce 1 Abstract This

More information

Predicting the Total Number of Points Scored in NFL Games

Predicting the Total Number of Points Scored in NFL Games Predicting the Total Number of Points Scored in NFL Games Max Flores (mflores7@stanford.edu), Ajay Sohmshetty (ajay14@stanford.edu) CS 229 Fall 2014 1 Introduction Predicting the outcome of National Football

More information

Predicting Results of March Madness Using the Probability Self-Consistent Method

Predicting Results of March Madness Using the Probability Self-Consistent Method International Journal of Sports Science 2015, 5(4): 139-144 DOI: 10.5923/j.sports.20150504.04 Predicting Results of March Madness Using the Probability Self-Consistent Method Gang Shen, Su Hua, Xiao Zhang,

More information

Home Team Advantage in the NBA: The Effect of Fan Attendance on Performance

Home Team Advantage in the NBA: The Effect of Fan Attendance on Performance MPRA Munich Personal RePEc Archive Home Team Advantage in the NBA: The Effect of Fan on Performance Vincent La Dartmouth College 14 March 2014 Online at https://mpra.ub.uni-muenchen.de/54579/ MPRA Paper

More information

Modeling Fantasy Football Quarterbacks

Modeling Fantasy Football Quarterbacks Augustana College Augustana Digital Commons Celebration of Learning Modeling Fantasy Football Quarterbacks Kyle Zeberlein Augustana College, Rock Island Illinois Myles Wallin Augustana College, Rock Island

More information

THERE S NO I IN TEAM

THERE S NO I IN TEAM THERE S NO I IN TEAM But there is an m and an e After concluding that defense doesn t necessarily win championships, we decided to examine another shopworn bit of sports wisdom. Before young athletes are

More information

Journal of Quantitative Analysis in Sports

Journal of Quantitative Analysis in Sports Journal of Quantitative Analysis in Sports Volume 7, Issue 3 2011 Article 14 Are NFL Coaches Risk and Loss Averse? Evidence from Their Use of Kickoff Strategies John D. Urschel, State University of New

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

STANDARDIZED CATCH RATES OF BLUEFIN TUNA, THUNNUS THYNNUS, FROM THE ROD AND REEL/HANDLINE FISHERY OFF THE NORTHEAST UNITED STATES DURING

STANDARDIZED CATCH RATES OF BLUEFIN TUNA, THUNNUS THYNNUS, FROM THE ROD AND REEL/HANDLINE FISHERY OFF THE NORTHEAST UNITED STATES DURING SCRS/2008/088 STANDARDIZED CATCH RATES OF BLUEFIN TUNA, THUNNUS THYNNUS, FROM THE ROD AND REEL/HANDLINE FISHERY OFF THE NORTHEAST UNITED STATES DURING 1980-2007 by Craig A. Brown 1 Sustainable Fisheries

More information

The Van Exel Effect: Adjusting for Scorekeeper Bias in NBA Box Scores

The Van Exel Effect: Adjusting for Scorekeeper Bias in NBA Box Scores The Van Exel Effect: Adjusting for Scorekeeper Bias in NBA Box Scores Matthew van Bommel and Luke Bornn Simon Fraser University mvanbomm@sfu.ca lbornn@sfu.ca 1 Introduction Box score statistics are the

More information

2016 Scoresheet Hockey Drafting Packet (for web draft leagues) Player Lists Explanation

2016 Scoresheet Hockey Drafting Packet (for web draft leagues) Player Lists Explanation 2016 Scoresheet Hockey Drafting Packet (for web draft leagues) The game rules are the same no matter how you draft your team. But if you are in a league that is using the web draft system then you can

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

Determining Occurrence in FMEA Using Hazard Function

Determining Occurrence in FMEA Using Hazard Function Determining Occurrence in FMEA Using Hazard Function Hazem J. Smadi Abstract FMEA has been used for several years and proved its efficiency for system s risk analysis due to failures. Risk priority number

More information

Slam-dunk Activities and Projects for Grades 4 8

Slam-dunk Activities and Projects for Grades 4 8 Slam-dunk Activities and Projects for Grades 4 8 Third Edition Jack A. Coffland and David A. Coffland Good Year Books Tucson, Arizona This book is not sponsored or endorsed by, or otherwise affiliated

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

The Dilemma of Choosing Talent: Michael Jordans are Hard to Find

The Dilemma of Choosing Talent: Michael Jordans are Hard to Find The Dilemma of Choosing Talent: Michael Jordans are Hard to Find by Peter A. Groothuis Associate Professor 3093 Raley Hall Appalachian State University Boone, NC 28608 (828) 262-6077 J. Richard Hill Professor

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

4-3 Rate of Change and Slope. Warm Up. 1. Find the x- and y-intercepts of 2x 5y = 20. Describe the correlation shown by the scatter plot. 2.

4-3 Rate of Change and Slope. Warm Up. 1. Find the x- and y-intercepts of 2x 5y = 20. Describe the correlation shown by the scatter plot. 2. Warm Up 1. Find the x- and y-intercepts of 2x 5y = 20. Describe the correlation shown by the scatter plot. 2. Objectives Find rates of change and slopes. Relate a constant rate of change to the slope of

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

Electronic Supplementary Material: Goals as Reference Points in Marathon Running: A Novel Test of Reference Dependence

Electronic Supplementary Material: Goals as Reference Points in Marathon Running: A Novel Test of Reference Dependence Electronic Supplementary Material: Goals as Reference Points in Marathon Running: A Novel Test of Reference Dependence Alex Markle George Wu Rebecca White Aaron Sackett This document provides additional

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

Salary in the National Basketball Association

Salary in the National Basketball Association University of Pennsylvania ScholarlyCommons Joseph Wharton Scholars Wharton School 2016 Salary in the National Basketball Association Jason Huang University of Pennsylvania Follow this and additional works

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

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

Analyzing NBA Champions and the Player Efficiency Rating

Analyzing NBA Champions and the Player Efficiency Rating Analyzing NBA Champions and the Player Efficiency Rating Hitesh Maidasani hitmai@cs.umd.edu November 13, 2013 1 Introduction The National Basketball Association is a very competitive and widely followed

More information

Expanding Plus-Minus for Visual and Statistical Analysis of NBA Box-Score Data

Expanding Plus-Minus for Visual and Statistical Analysis of NBA Box-Score Data Expanding Plus-Minus for Visual and Statistical Analysis of NBA Box-Score Data Robert Sisneros and Mark Van Moer Abstract In this work we present an augmentation of the plus-minus statistic as well as

More information

WIND DATA REPORT. Swan s Island, ME

WIND DATA REPORT. Swan s Island, ME WIND DATA REPORT Swan s Island, ME June 1, 2009 August 31, 2009 Prepared for US Department of Energy by Daniel T. Grip Utama Abdulwahid James F. Manwell Anthony F. Ellis September 17, 2009 Report template

More information

Effects of Automated Speed Enforcement in Montgomery County, Maryland, on Vehicle Speeds, Public Opinion, and Crashes

Effects of Automated Speed Enforcement in Montgomery County, Maryland, on Vehicle Speeds, Public Opinion, and Crashes Effects of Automated Speed Enforcement in Montgomery County, Maryland, on Vehicle Speeds, Public Opinion, and Crashes August 2015 Wen Hu Insurance Institute for Highway Safety Anne T. McCartt Insurance

More information

ICES Advice on fishing opportunities, catch, and effort Celtic Seas and Greater North Sea Ecoregions Published 24 October 2017

ICES Advice on fishing opportunities, catch, and effort Celtic Seas and Greater North Sea Ecoregions Published 24 October 2017 ICES Advice on fishing opportunities, catch, and effort Celtic Seas and Greater North Sea Ecoregions Published 24 October 2017 DOI: 10.17895/ices.pub.3334 Seabass (Dicentrarchus labrax) in divisions 4.b

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

ANALYSIS AND COMPARISON OF COMPETITIVE BALANCE IN THE SPANISH ACB BASKETBALL LEAGUE: A PRELIMINARY STUDY

ANALYSIS AND COMPARISON OF COMPETITIVE BALANCE IN THE SPANISH ACB BASKETBALL LEAGUE: A PRELIMINARY STUDY Revista de Psicología del Deporte 2009. Vol. 18 - suppl., pp. 397-401 ISSN: 1132-239X Universitat de les Illes Balears Universitat Autònoma de Barcelona ANALYSIS AND COMPARISON OF COMPETITIVE BALANCE IN

More information

In Search of Sure Things An Analysis of Market Efficiency in the NFL Betting Market

In Search of Sure Things An Analysis of Market Efficiency in the NFL Betting Market In Search of Sure Things An Analysis of Market Efficiency in the NFL Betting Market By: Rick Johnson Advisor: Professor Eric Schulz Submitted for Honors in Mathematical Methods in the Social Sciences Spring,

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

Client Interview Competition Rules

Client Interview Competition Rules Client Interview Competition Rules Approved by ALSA Executive 4/04/2017 1. COMPETITION NAME 1.1 This competition will be known as the Australian Law Students' Association (ALSA) Client Interview Competition.

More information

download.file("http://www.openintro.org/stat/data/kobe.rdata", destfile = "kobe.rdata")

download.file(http://www.openintro.org/stat/data/kobe.rdata, destfile = kobe.rdata) Lab 2: Probability Hot Hands Basketball players who make several baskets in succession are described as having a hot hand. Fans and players have long believed in the hot hand phenomenon, which refutes

More information

STRATFORD CITY SOCCER LEAGUE

STRATFORD CITY SOCCER LEAGUE STRATFORD CITY SOCCER LEAGUE CONSTITUTION PURPOSE: To promote, develop and organize adult soccer in the City of Stratford. It is understood that teams from outside of Stratford may participate in the league,

More information

A Study of Olympic Winning Times

A Study of Olympic Winning Times Connecting Algebra 1 to Advanced Placement* Mathematics A Resource and Strategy Guide Updated: 05/15/ A Study of Olympic Winning Times Objective: Students will graph data, determine a line that models

More information

BEST WINNING STREAKS OF ALL TIME. Best Winning Streaks Of All Time

BEST WINNING STREAKS OF ALL TIME. Best Winning Streaks Of All Time BEST WINNING STREAKS OF ALL TIME Best Winning Streaks Of All Time Contents Introduction: SHHH!! The game s on! Published at Petitcodiac Regional School May 2016 #5 Pittsburgh Steelers #4 Boston Celtics

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

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

The final set in a tennis match: four years at Wimbledon 1 Published as: Journal of Applied Statistics, Vol. 26, No. 4, 1999, 461-468. The final set in a tennis match: four years at Wimbledon 1 Jan R. Magnus, CentER, Tilburg University, the Netherlands and Franc

More information

An analysis of strategy in the first three innings in test cricket: declaration and the follow-on

An analysis of strategy in the first three innings in test cricket: declaration and the follow-on An analysis of strategy in the first three innings in test cricket: declaration and the follow-on Philip Scarf* and Sohail Akhtar* *Centre for Operations Management, Management Science and Statistics,

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

SportsBettingChamp.com MLB Betting System. Here s the MLB betting system in detail. As long as you strictly follow my betting

SportsBettingChamp.com MLB Betting System. Here s the MLB betting system in detail. As long as you strictly follow my betting SportsBettingChamp.com MLB Betting System Here s the MLB betting system in detail. As long as you strictly follow my betting guidelines below, you will be winning almost all of your MLB bets. In a nutshell,

More information

APPENDIX A: TOURNAMENT FORMAT

APPENDIX A: TOURNAMENT FORMAT NORTH AMERICAN HARDCOURT BIKE POLO ASSOCIATION APPENDIX A: TOURNAMENT FORMAT for the 2014 season SECTION 1: Tournament Format.. TABLE OF CONTENTS SECTION 2: Tournament Examples.. Page 5 SECTION 3: Game

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

Wildlife Ad Awareness & Attitudes Survey 2015

Wildlife Ad Awareness & Attitudes Survey 2015 Wildlife Ad Awareness & Attitudes Survey 2015 Contents Executive Summary 3 Key Findings: 2015 Survey 8 Comparison between 2014 and 2015 Findings 27 Methodology Appendix 41 2 Executive Summary and Key Observations

More information

Market Efficiency and Behavioral Biases in the WNBA Betting Market

Market Efficiency and Behavioral Biases in the WNBA Betting Market Int. J. Financial Stud. 2014, 2, 193 202; doi:10.3390/ijfs2020193 Article OPEN ACCESS International Journal of Financial Studies ISSN 2227-7072 www.mdpi.com/journal/ijfs Market Efficiency and Behavioral

More information

Journal of Human Sport and Exercise E-ISSN: Universidad de Alicante España

Journal of Human Sport and Exercise E-ISSN: Universidad de Alicante España Journal of Human Sport and Exercise E-ISSN: 1988-5202 jhse@ua.es Universidad de Alicante España SOÓS, ISTVÁN; FLORES MARTÍNEZ, JOSÉ CARLOS; SZABO, ATTILA Before the Rio Games: A retrospective evaluation

More information

ScienceDirect. Rebounding strategies in basketball

ScienceDirect. Rebounding strategies in basketball Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 72 ( 2014 ) 823 828 The 2014 conference of the International Sports Engineering Association Rebounding strategies in basketball

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

IN THE MATTER OF SALARY ARBITRATION BETWEEN: LARS FOSGAARD ELLER. - and - THE MONTREAL CANADIENS BRIEF OF LARS FOSGAARD ELLER TEAM 19

IN THE MATTER OF SALARY ARBITRATION BETWEEN: LARS FOSGAARD ELLER. - and - THE MONTREAL CANADIENS BRIEF OF LARS FOSGAARD ELLER TEAM 19 IN THE MATTER OF SALARY ARBITRATION BETWEEN: LARS FOSGAARD ELLER - and - THE MONTREAL CANADIENS BRIEF OF LARS FOSGAARD ELLER TEAM 19 TABLE OF CONTENTS SUMMARY:...1 I) The overall performance, including

More information

Progeny? Performance? What really matters in a stud fee. Charlotte R. Hansen and Sayed Saghaian. University of Kentucky

Progeny? Performance? What really matters in a stud fee. Charlotte R. Hansen and Sayed Saghaian. University of Kentucky Progeny? Performance? What really matters in a stud fee. Charlotte R. Hansen and Sayed Saghaian University of Kentucky Department of Agricultural Economics 314 Charles E. Barnhart Building Lexington, KY

More information

GENETICS OF RACING PERFORMANCE IN THE AMERICAN QUARTER HORSE: II. ADJUSTMENT FACTORS AND CONTEMPORARY GROUPS 1'2

GENETICS OF RACING PERFORMANCE IN THE AMERICAN QUARTER HORSE: II. ADJUSTMENT FACTORS AND CONTEMPORARY GROUPS 1'2 GENETICS OF RACING PERFORMANCE IN THE AMERICAN QUARTER HORSE: II. ADJUSTMENT FACTORS AND CONTEMPORARY GROUPS 1'2 S. T. Buttram 3, R. L. Willham 4 and D. E. Wilson 4 Iowa State University, Ames 50011 ABSTRACT

More information

Player Lists Explanation

Player Lists Explanation Scoresheet Football Drafting Packet (for web draft leagues) The game rules are the same no matter how you draft your team. But if you are in a league that is using the web draft system then you can mostly

More information

2014 United States College and University Curling Championship Guidelines July 2013

2014 United States College and University Curling Championship Guidelines July 2013 2014 United States College and University Curling Championship Guidelines July 2013 June 30, 2013 Mission and Goals The Mission of the United States College and University Curling Championship is to promote

More information

Are Longshots Only for Losers? A New Look at the Last Race Effect

Are Longshots Only for Losers? A New Look at the Last Race Effect Journal of Behavioral Decision Making, J. Behav. Dec. Making, 29: 25 36 (2016) Published online 29 March 2015 in Wiley Online Library (wileyonlinelibrary.com).1873 Are Longshots Only for Losers? A New

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

We can use a 2 2 array to show all four situations that can arise in a single play of this game, and the results of each situation, as follows:

We can use a 2 2 array to show all four situations that can arise in a single play of this game, and the results of each situation, as follows: Two-Person Games Game theory was developed, starting in the 1940 s, as a model of situations of conflict. Such situations and interactions will be called games and they have participants who are called

More information

Wyndemere Bocce Basic Rules of Play & Other Info 2018

Wyndemere Bocce Basic Rules of Play & Other Info 2018 START OF MATCH Umpire flips a coin Team captains call heads/tails. The winner of the coin toss gets the first toss of the pallino and the choice of the color of the balls and throws the first bocce ball.

More information

Lab 3: Pumps in Series & Pumps in Parallel

Lab 3: Pumps in Series & Pumps in Parallel CEE 3620: Water Resources Engineering Spring 2018 Lab 3: Pumps in Series & Pumps in Parallel BACKGROUND Pumps are used to transfer fluid in a system, either at the same elevation or to a new height. The

More information

Applying Hooke s Law to Multiple Bungee Cords. Introduction

Applying Hooke s Law to Multiple Bungee Cords. Introduction Applying Hooke s Law to Multiple Bungee Cords Introduction Hooke s Law declares that the force exerted on a spring is proportional to the amount of stretch or compression on the spring, is always directed

More information

Case Study: How Misinterpreting Probabilities Can Cost You the Game. Kurt W. Rotthoff Seton Hall University Stillman School of Business

Case Study: How Misinterpreting Probabilities Can Cost You the Game. Kurt W. Rotthoff Seton Hall University Stillman School of Business Case Study: How Misinterpreting Probabilities Can Cost You the Game Kurt W. Rotthoff Seton Hall University Stillman School of Business Abstract: Using data to make future decisions can increase the odds

More information

Central Hills Prairie Deer Goal Setting Block G9 Landowner and Hunter Survey Results

Central Hills Prairie Deer Goal Setting Block G9 Landowner and Hunter Survey Results Central Hills Prairie Deer Goal Setting Block G9 Landowner and Hunter Survey Results Table of Contents Public Surveys for Deer Goal Setting... 1 Methods... 1 Hunter Survey... 2 Demographics... 2 Population

More information

Journal of Human Sport and Exercise E-ISSN: Universidad de Alicante España

Journal of Human Sport and Exercise E-ISSN: Universidad de Alicante España Journal of Human Sport and Exercise E-ISSN: 1988-5202 jhse@ua.es Universidad de Alicante España HRUSA, PETR The dependence of the number of shots and rebounds on the change of rules in the top Czech Basketball

More information

BABE: THE SULTAN OF PITCHING STATS? by. August 2010 MIDDLEBURY COLLEGE ECONOMICS DISCUSSION PAPER NO

BABE: THE SULTAN OF PITCHING STATS? by. August 2010 MIDDLEBURY COLLEGE ECONOMICS DISCUSSION PAPER NO BABE: THE SULTAN OF PITCHING STATS? by Matthew H. LoRusso Paul M. Sommers August 2010 MIDDLEBURY COLLEGE ECONOMICS DISCUSSION PAPER NO. 10-30 DEPARTMENT OF ECONOMICS MIDDLEBURY COLLEGE MIDDLEBURY, VERMONT

More information

NBA Salary Prediction

NBA Salary Prediction NBA Salary Prediction Edbert Puspito Link to codes Imagine You are Lakers GM The team are it worst now, 16-65, last place in Western conference. Kobe will retire, a bunch of player will have their contract

More information

Equation 1: F spring = kx. Where F is the force of the spring, k is the spring constant and x is the displacement of the spring. Equation 2: F = mg

Equation 1: F spring = kx. Where F is the force of the spring, k is the spring constant and x is the displacement of the spring. Equation 2: F = mg 1 Introduction Relationship between Spring Constant and Length of Bungee Cord In this experiment, we aimed to model the behavior of the bungee cord that will be used in the Bungee Challenge. Specifically,

More information

Team Number 25 Case: Cody Franson Club s Representative

Team Number 25 Case: Cody Franson Club s Representative Team Number 25 Case: Cody Franson Club s Representative Introduction It is our position as representatives of the Toronto Maple Leafs, that when Cody Franson s performance, and valid comparable players

More information

THE RELATIONSHIP BETWEEN TRAIN LENGTH AND ACCIDENT CAUSES AND RATES

THE RELATIONSHIP BETWEEN TRAIN LENGTH AND ACCIDENT CAUSES AND RATES THE RELATIONSHIP BETWEEN TRAIN LENGTH AND ACCIDENT CAUSES AND RATES Darwin H. Schafer II Corresponding Author Graduate Research Assistant, Railroad Engineering Program Department of Civil and Environmental

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

This Learning Packet has two parts: (1) text to read and (2) questions to answer.

This Learning Packet has two parts: (1) text to read and (2) questions to answer. BASKETBALL PACKET # 4 INSTRUCTIONS This Learning Packet has two parts: (1) text to read and (2) questions to answer. The text describes a particular sport or physical activity, and relates its history,

More information

MEASURING CONTROL DELAY AT SIGNALIZED INTERSECTIONS: CASE STUDY FROM SOHAG, EGYPT

MEASURING CONTROL DELAY AT SIGNALIZED INTERSECTIONS: CASE STUDY FROM SOHAG, EGYPT MEASURING CONTROL DELAY AT SIGNALIZED INTERSECTIONS: CASE STUDY FROM SOHAG, EGYPT Ibrahim H. Hashim 1, Talaat A. Abdel-Wahed 2 and Ahmed M. Mandor 3 1 Associate Prof., Civil Eng. Dept., Faculty of Engineering,

More information

What variables explain differences in coaching salaries for Division I women's sports?

What variables explain differences in coaching salaries for Division I women's sports? University of Northern Iowa UNI ScholarWorks Honors Program Theses University Honors Program 2014 What variables explain differences in coaching salaries for Division I women's sports? Tyler Lange University

More information

Team Number 6. Tommy Hanson v. Atlanta Braves. Side represented: Atlanta Braves

Team Number 6. Tommy Hanson v. Atlanta Braves. Side represented: Atlanta Braves Team Number 6 Tommy Hanson v. Atlanta Braves Side represented: Atlanta Braves Table of Contents I. Introduction... 1 II. Hanson s career has been in decline since his debut and he has dealt with major

More information

Analysis of Factors Affecting Train Derailments at Highway-Rail Grade Crossings

Analysis of Factors Affecting Train Derailments at Highway-Rail Grade Crossings Chadwick et al TRB 12-4396 1 1 2 3 Analysis of Factors Affecting Train Derailments at Highway-Rail Grade Crossings 4 5 TRB 12-4396 6 7 8 9 Submitted for consideration for presentation and publication at

More information

Season Ticket Basketball 2003

Season Ticket Basketball 2003 Season Ticket Basketball 2003 Season Ticket Basketball 2003 is a text-based basketball simulation modeled after the world of professional basketball. It allows you to take control of a basketball team

More information

Live by the Three, Die by the Three? The Price of Risk in the NBA

Live by the Three, Die by the Three? The Price of Risk in the NBA Live by the Three, Die by the Three? The Price of Risk in the NBA Matthew Goldman, UCSD Dept. of Economics, @mattrgoldman Justin M. Rao, Microsoft Research, @justinmrao Shoot a 2 or a 3? Determining the

More information

Understand, You're Going to Fail.

Understand, You're Going to Fail. Understand, You're Going to Fail. Posted on May 16, Posted by Craig Huntington Category Blog Last month one of the best NBA players ever, called it a career. Kobe Bryant of the Los Angeles Lakers played

More information

Available online at ScienceDirect. The 2014 Conference of the International Sports Engineering Association

Available online at  ScienceDirect. The 2014 Conference of the International Sports Engineering Association Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 72 ( 2014 ) 435 440 The 2014 Conference of the International Sports Engineering Association Accuracy performance parameters

More information

Evaluation and further development of car following models in microscopic traffic simulation

Evaluation and further development of car following models in microscopic traffic simulation Urban Transport XII: Urban Transport and the Environment in the 21st Century 287 Evaluation and further development of car following models in microscopic traffic simulation P. Hidas School of Civil and

More information

The Use of Rank-sum Ratio on the Attack and Defensive Ability of the Top 8 Men s Basketball Competition in the 16th Asian Games

The Use of Rank-sum Ratio on the Attack and Defensive Ability of the Top 8 Men s Basketball Competition in the 16th Asian Games Management Science and Engineering Vol. 6, No. 1, 2012, pp. 101-105 DOI:10.3968/j.mse.1913035X20120601.Z5R008 ISSN 1913-0341 [Print] ISSN 1913-035X [Online] www.cscanada.net www.cscanada.org The Use of

More information

The NBA and the Influx of International Basketball Players

The NBA and the Influx of International Basketball Players (Draft) Erick Eschker Department of Economics Humboldt State University Arcata, CA 95521-8299 Phone: 707-826-3216 Email: ee3@humboldt.edu Stephen J. Perez Department of Economics California State University,

More information

RULES AND REGULATIONS OF FIXED ODDS BETTING GAMES

RULES AND REGULATIONS OF FIXED ODDS BETTING GAMES RULES AND REGULATIONS OF FIXED ODDS BETTING GAMES Royalhighgate Public Company Ltd. 04.04.2014 Table of contents SECTION I: GENERAL RULES... 6 ARTICLE 1 - GENERAL REGULATIONS... 6 ARTICLE 2 - THE HOLDING

More information

quotes-motivational.com

quotes-motivational.com Basketball Quotes Receive motivational Quotes! Follow me on Twitter: BASKETBALL QUOTES I would tell players to relax and never think about what s at stake. Just think about the basketball game. If you

More information

TRIP GENERATION RATES FOR SOUTH AFRICAN GOLF CLUBS AND ESTATES

TRIP GENERATION RATES FOR SOUTH AFRICAN GOLF CLUBS AND ESTATES TRIP GENERATION RATES FOR SOUTH AFRICAN GOLF CLUBS AND ESTATES M M Withers and C J Bester Department of Civil Engineering University of Stellenbosch, Private Bag X1, Matieland, 7602 ABSTRACT There has

More information

Principal factors contributing to heavy haul freight train safety improvements in North America: a quantitative analysis

Principal factors contributing to heavy haul freight train safety improvements in North America: a quantitative analysis Principal factors contributing to heavy haul freight train safety improvements in North America: a quantitative analysis B. Wang & C. Barkan University of Illinois At Urbana-Champaign, Urbana Illinois,

More information

NBA Court Realty. Dan Cervone, Luke Bornn and Kirk Goldsberry New York Unversity, Simon Fraser University, and University of Texas (Austin)

NBA Court Realty. Dan Cervone, Luke Bornn and Kirk Goldsberry New York Unversity, Simon Fraser University, and University of Texas (Austin) NBA Court Realty Dan Cervone, Luke Bornn and Kirk Goldsberry New York Unversity, Simon Fraser University, and University of Texas (Austin) 1 Intro: the Basketball Court is a Real Estate Market Continuously

More information

Looking at Spacings to Assess Streakiness

Looking at Spacings to Assess Streakiness Looking at Spacings to Assess Streakiness Jim Albert Department of Mathematics and Statistics Bowling Green State University September 2013 September 2013 1 / 43 The Problem Collect hitting data for all

More information

A Group of Factors Influencing the Development of the Greeks Volleyball Athletes at School Age

A Group of Factors Influencing the Development of the Greeks Volleyball Athletes at School Age Journal of Sports Science 5 (27) 2-37 doi:.725/2332-783/27..3 D DAVID PUBLISHING A Group of Factors Influencing the Development of the Greeks Volleyball Athletes at School Age Achilleopoulos John, Lamprousi

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

Results of mathematical modelling the kinetics of gaseous exchange through small channels in micro dischargers

Results of mathematical modelling the kinetics of gaseous exchange through small channels in micro dischargers Journal of Physics: Conference Series PAPER OPEN ACCESS Results of mathematical modelling the kinetics of gaseous exchange through small channels in micro dischargers Related content - The versatile use

More information

5 Stories On Why Larry Bird Was the Greatest

5 Stories On Why Larry Bird Was the Greatest 5 Stories On Why Larry Bird Was the Greatest When I played, Larry Bird was the only one I feared. A lot of black guys always ask me, Did Larry Bird really play that good? I said, Larry Bird is so good

More information

OKLAHOMA CITY THUNDER at MIAMI HEAT

OKLAHOMA CITY THUNDER at MIAMI HEAT OKLAHOMA CITY THUNDER 2012 PLAYOFF GAME NOTES NBA FINALS ٠ GAME #4 2011-12 SCHEDULE/RESULTS.. OKLAHOMA CITY THUNDER PROBABLE STARTERS NO DATE OPP W/L TV/RECORD 1 12/25 vs. ORL W, 97-89 1-0 2 12/26 @ MIN

More information