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How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and FootballHow does professional baseball evaluate hitters? Is a singles hitter like Wade Boggs more valuable than a power hitter like David Ortiz? This title shows readers how to use simple mathematics to analyze a range of statistical and probability-related questions in professional baseball, basketball, and football, and in sports gambling."Mathletics" is a remarkably entertaining book that shows readers how to use simple mathematics to analyze a range of statistical and probability-related questions in professional baseball, basketball, and football, and in sports gambling. How does professional baseball evaluate hitters? Is a singles hitter like Wade Boggs more valuable than a power hitter like David Ortiz? Should NFL teams pass or run more often on first downs? Could professional basketball have used statistics to expose the crooked referee Tim Donaghy? Does money buy performance in professional sports? In "Mathletics", Wayne Winston describes the mathematical methods that top coaches and managers use to evaluate players and improve team performance, and gives math enthusiasts the practical tools they need to enhance their understanding and enjoyment of their favorite sports - and maybe even gain the outside edge to winning bets. "Mathletics" blends fun math problems with sports stories of actual games, teams, and players, along with personal anecdotes from Winston's work as a sports consultant.; Winston uses easy-to-read tables and illustrations to illuminate the techniques and ideas he presents, and all the necessary math concepts - such as arithmetic, basic statistics and probability, and Monte Carlo simulations - are fully explained in the examples. After reading "Mathletics", you will understand why baseball teams should almost never bunt, why football overtime systems are unfair, why points, rebounds, and assists aren't enough to determine who's the NBA's best player - and much, much more.Preface xi Acknowledgments xiii List of Abbreviations xv Part I. Baseball 1 Chapter 1: Baseball's Pythagorean Theorem 3 Chapter 2: Who Had a Better Year, Nomar Garciaparra or Ichiro Suzuki? 11 The Runs- Created Approach Chapter 3: Evaluating Hitters by Linear Weights 17 Chapter 4: Evaluating Hitters by Monte Carlo Simulation 30 Chapter 5: Evaluating Baseball Pitchers and Forecasting Future Pitcher Performance 41 Chapter 6: Baseball Decision- Making 52 Chapter 7: Evaluating Fielders 64 Sabermetrics' Last Frontier Chapter 8: Player Win Averages 71 Chapter 9: The Value of Replacement Players 79 Evaluating Trades and Fair Salary Chapter 10: Park Factors 84 Chapter 11: Streakiness in Sports 87 Chapter 12: The Platoon Effect 102 Chapter 13: Was Tony Perez a Great Clutch Hitter? 106 Chapter 14: Pitch Count and Pitcher Effectiveness 110 Chapter 15: Would Ted Williams Hit .406 Today? 113 Chapter 16: Was Joe DiMaggio's 56- Game Hitting Streak the Greatest Sports Record of All Time? 116 Chapter 17: Major League Equivalents 123 Part II. Football 125 Chapter 18: What Makes NFL Teams Win? 127 Chapter 19: Who's Better, Tom Brady or Peyton Manning? 132 Chapter 20: Football States and Values 138 Chapter 21: Football Decision- Making 101 143 Chapter 22: A State and Value Analysis of the 2006 Super Bowl 151 Champion Colts Chapter 23: If Passing Is Better Than Running, Why Don't 158 Teams Always Pass? Chapter 24: Should We Go for a One- Point or Two- Point Conversion? 165 Chapter 25: To Give Up the Ball Is Better Than to Receive 172 The Case of College Football Overtime Chapter 26: Why Is the NFL's Overtime System Fatally Flawed? 175 Chapter 27: How Valuable Are High Draft Picks in the NFL? 180 Part III. Basketball 185 Chapter 28: Basketball Statistics 101 187 The Four- Factor Model Chapter 29: Linear Weights for Evaluating NBA Players 195 Chapter 30: Adjusted_/_Player Ratings 202 Chapter 31: NBA Lineup Analysis 224 Chapter 32: Analyzing Team and Individual Matchups 228 Chapter 33: NBA Players' Salaries and the Draft 233 Chapter 34: Are NBA Officials Prejudiced? 237 Chapter 35: Are College Basketball Games Fixed? 242 Chapter 36: Did Tim Donaghy Fix NBA Games? 244 Chapter 37: End- Game Basketball Strategy 248 Part IV. Playing with Money, and Other Topics for Serious Sports Fans 253 Chapter 38: Sports Gambling 101 255 Chapter 39: Freakonomics Meets the Bookmaker 262 Chapter 40: Rating Sports Teams 266 Chapter 41: Which League Has Greater Parity, The NFL or the NBA? 283 Chapter 42: The Ratings Percentage Index (RPI) 287 Chapter 43: From Point Ratings to Probabilities 290 Chapter 44: Optimal Money Management 298 The Kelly Growth Criteria Chapter 45: Ranking Great Sports Collapses 303 Chapter 46: Can Money Buy Success? 311 Chapter 47: Does Joey Crawford Hate the Spurs? 319 Chapter 48: Does Fatigue Make Cowards of Us All? 321 The Case of NBA Back- to- Back Games and NFL Bye Weeks Chapter 49: Can the Bowl Championship Series Be Saved? 324 Chapter 50: Comparing Players from Different Eras 331 Chapter 51: Conclusions 335 Index of Databases 341 Annotated Bibliography 343 Index 353