Pythagorean Theorem Of Baseball Handout Renowned Baseball Statistician Bill James Devised A Model For Predicting A Team 1 (53.28 KiB) Viewed 93 times
Pythagorean Theorem of Baseball Handout Renowned baseball statistician Bill James devised a model for predicting a team's winning percentage. Dubbed the "Pythagorean Theorem of Baseball," this model predicts a team's winning percentage as (runs ? Winning percentage = (runs scoredja + (runs against )2 * 100 +€ a. Use this model to predict the winning percentage for the New York Yankees, who scored 915 runs and allowed 753 runs in the 2009 season. b. The New York Yankees actually won 103 games and lost 59 in the 2009 season. Determine the winning percentage, and also determine the residual from the Pythagorean model (by taking the observed winning percentage minus the predicted winning percentage). c. Interpret what this residual value means for the 2009 Yankees. (Hints: Did the team do better or worse than expected, given their runs scored and runs allowed? By how much?) d. Repeat (a-c) for the 2009 San Diego Padres, who scored 638 runs and allowed 769 runs, while winning 75 games and losing 87 games. e. Which team (Yankees or Padres) exceeded their Pythagorean expectations by more? Table 0.4 provides data, predictions, and residuals for all 30 Major League Baseball teams in 2009. f. Which team exceeded their Pythagorean expectations the most? Describe how this team's winning percentage compares to what is predicted by their runs scores and runs allowed. g. Which team fell furthest below their Pythagorean expectations? Describe how this team's winning percentage compares to what is predicted by their runs scored and runs allowed.
0.4. EXERCISES 21 Table 0.4: Winning percentage and Pythagorean predictions for baseball teams in 2009 TEAM w L WinPct Run Scored Runs Against Predicted Residual Arizona Diamondbacks 70 92 43.21 720 782 45.88 -2.67 Atlanta Braves 86 76 53.09 735 641 56.80 -3.71 Baltimore Orioles 64 98 39.51 741 876 41.71 -2.20 Boston Red Sox 95 67 58.64 872 736 58.40 0.24 Chicago Cubs 83 78 51.55 707 672 52.54 -0.98 Chicago White Sox 79 83 48.77 724 732 49.45 -0.69 Cincinnati Reds 78 84 48.15 673 723 46.42 1.73 Cleveland Indians 65 97 40.12 773 865 44.40 -428 Colorado Rockies 92 70 56.79 804 715 55.84 0.96 Detroit Tigers 86 77 52.76 743 745 49.87 2.90 Florida Marlins 87 75 53.70 772 706 50.39 3.31 Houston Astros 74 88 45.68 643 770 41.08 4.59 Kansas City Royals 65 97 40.12 686 842 39.90 0.23 Los Angeles Angels 97 65 59.88 883 761 57.38 2.50 Los Angeles Dodgers 95 67 58.64 780 611 61.97 -3.33 Milwaukee Brewers 80 82 49.38 785 818 47.94 1.44 Minnesota Twins 87 76 53.37 817 765 53.28 0.09 New York Mets 70 92 43.21 671 757 41.00 -0.79 New York Yankees 103 59 63.58 915 753 Oakland Athletics 75 87 46.30 759 761 49.87 -3.57 Philadelphia Phillies 93 09 57.41 820 709 57.22 0.19 Pittsburgh Pirates 62 99 38.51 6:36 768 40.68 -2.17 San Diego Padres 75 87 46.30 638 769 San Francisco Giants 88 74 54.32 657 611 83.62 0.70 Seattle Mariners 85 77 52.47 640 692 46.10 6.37 St. Louis Cardinals 91 71 56.17 730 640 56.54 -0.37 Tampa Bay Rays 84 78 51.85 803 754 13.14 -1.29 Texas Rangers 87 75 53.70 784 740 52.88 0.82 Toronto Blue Jays 75 87 46.30 798 771 51.72 -5.42 Washington Nationals 59 103 36.42 710 874 39.76 -3.34 Source: www.laseball - reference.com
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