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24. Should We Go for a One- Point or Two- Point Conversion

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Mathletics
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24SHOULD WE GO FOR A ONE- POINT OR TWO- POINT CONVERSION?Since 1994, when the NFL began allowing teams to go for a two- pointconversion after a touchdown, it has become important for NFL coaches todetermine whether to go for one or two points after a touchdown. The suc-cess rate for a one- point conversion is over 99%, so we will assume thatthere is a 100% chance that a one- point conversion will be successful. Thesuccess rate for two- point conversions is around 47%.1On average, a one- point conversion try earns one point and a two- point conversion attemptearns 0(.6)2(.47).94 points. So, on average, a one- point conversionearns more points but in some situations it is clear that going for two is theproper choice. For example, if a team scores a touchdown with thirty sec-onds to go and they were down by eight points before the touchdown, theteam needs to go for two to tie the game. Most coaches have a “chart” thattells them whether they should go for one or two points based on the scoreof the game. The idea of the “chart” is believed to have originated withUCLA assistant coach Dick Vermeil during the early 1970s.2The coach’s decision should depend on the amount of time left in thegame as well as the score. For example, if there is a lot of time remaining inthe game, then if the team scores a touchdown and is down by eight pointsthey may not want to choose a play (the two- point conversion) over a playwith higher expected scoring (the one- point conversion). To determinehow the optimal strategy depends on the score of the game and time re-maining we need to use a sophisticated technique, dynamic program-ming, which allows us to work backward from the end of the game to-1Schatz, Football Prospectus.2Vermeil later became a successful NFL coach and NFL TV commentator. Sackrowitz’s“Refining the Point(s)- After- Touchdown Scenario” appears to be the first mathematical studyof the one- or two- point conversion decision.

24SHOULD WE GO FOR A ONE- POINT OR TWO- POINT CONVERSION?Since 1994, when the NFL began allowing teams to go for a two- pointconversion after a touchdown, it has become important for NFL coaches todetermine whether to go for one or two points after a touchdown. The suc-cess rate for a one- point conversion is over 99%, so we will assume thatthere is a 100% chance that a one- point conversion will be successful. Thesuccess rate for two- point conversions is around 47%.1On average, a one- point conversion try earns one point and a two- point conversion attemptearns 0(.6)2(.47).94 points. So, on average, a one- point conversionearns more points but in some situations it is clear that going for two is theproper choice. For example, if a team scores a touchdown with thirty sec-onds to go and they were down by eight points before the touchdown, theteam needs to go for two to tie the game. Most coaches have a “chart” thattells them whether they should go for one or two points based on the scoreof the game. The idea of the “chart” is believed to have originated withUCLA assistant coach Dick Vermeil during the early 1970s.2The coach’s decision should depend on the amount of time left in thegame as well as the score. For example, if there is a lot of time remaining inthe game, then if the team scores a touchdown and is down by eight pointsthey may not want to choose a play (the two- point conversion) over a playwith higher expected scoring (the one- point conversion). To determinehow the optimal strategy depends on the score of the game and time re-maining we need to use a sophisticated technique, dynamic program-ming, which allows us to work backward from the end of the game to-1Schatz, Football Prospectus.2Vermeil later became a successful NFL coach and NFL TV commentator. Sackrowitz’s“Refining the Point(s)- After- Touchdown Scenario” appears to be the first mathematical studyof the one- or two- point conversion decision.

Chapters in this book

  1. Frontmatter i
  2. CONTENTS vii
  3. Preface xi
  4. Acknowledgments xiii
  5. List of Abbreviations xv
  6. PART I. BASEBALL
  7. 1. Baseball’s Pythagorean Theorem 3
  8. 2. Who Had a Better Year, Nomar Garciaparra or Ichiro Suzuki? 11
  9. 3. Evaluating Hitters by Linear Weights 17
  10. 4. Evaluating Hitters by Monte Carlo Simulation 30
  11. 5. Evaluating Baseball Pitchers and Forecasting Future Pitcher Performance 41
  12. 6. Baseball Decision- Making 52
  13. 7. Evaluating Fielders 64
  14. 8. Player Win Averages 71
  15. 9. The Value of Replacement Players 79
  16. 10. Park Factors 84
  17. 11. Streakiness in Sports 87
  18. 12. The Platoon Effect 102
  19. 13. Was Tony Perez a Great Clutch Hitter? 106
  20. 14. Pitch Count and Pitcher Effectiveness 110
  21. 15. Would Ted Williams Hit .406 Today? 113
  22. 16. Was Joe DiMaggio’s 56- Game Hitting Streak the Greatest Sports Record of All Time? 116
  23. 17. Major League Equivalents 123
  24. PART II. FOOTBALL
  25. 18. What Makes NFL Teams Win? 127
  26. 19. Who’s Better, Tom Brady or Peyton Manning? 132
  27. 20. Football States and Values 138
  28. 21. Football Decision- Making 101 143
  29. 22. A State and Value Analysis of the 2006 Super Bowl Champion Colts 151
  30. 23. If Passing Is Better Than Running, Why Don’t Teams Always Pass? 158
  31. 24. Should We Go for a One- Point or Two- Point Conversion 165
  32. 25. To Give Up the Ball Is Better Than to Receive 172
  33. 26. Why Is the NFL’s Overtime System Fatally Flawed? 175
  34. 27. How Valuable Are High Draft Picks in the NFL? 180
  35. PART III. BASKETBALL
  36. 28. Basketball Statistics 101 187
  37. 29. Linear Weights for Evaluating NBA Players 195
  38. 30. Adjusted+/-Player Ratings 202
  39. 31. NBA Lineup Analysis 224
  40. 32. Analyzing Team and Individual Matchups 228
  41. 33. NBA Players’ Salaries and the Draft 233
  42. 34. Are NBA Officials Prejudiced? 237
  43. 35. Are College Basketball Games Fixed? 242
  44. 36. Did Tim Donaghy Fix NBA Games? 244
  45. 37. End- Game Basketball Strategy 248
  46. PART IV. PLAYING WITH MONEY, AND OTHER TOPICS FOR SERIOUS SPORTS FANS
  47. 38. Sports Gambling 101 255
  48. 39. Freakonomics Meets the Bookmaker 262
  49. 40. Rating Sports Teams 266
  50. 41. Which League Has Greater Parity, The NFL or the NBA? 283
  51. 42. The Ratings Percentage Index (RPI) 287
  52. 43. From Point Ratings to Probabilities 290
  53. 44. Optimal Money Management 298
  54. 45. Ranking Great Sports Collapses 303
  55. 46. Can Money Buy Success? 311
  56. 47. Does Joey Crawford Hate the Spurs? 319
  57. 48. Does Fatigue Make Cowards of Us All? 321
  58. 49. Can the Bowl Championship Series Be Saved? 324
  59. 50. Comparing Players from Different Eras 331
  60. 51. Conclusions 335
  61. Epilogue to the Paperback Edition 341
  62. Index of Databases 355
  63. Annotated Bibliography 357
  64. Index 367
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