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Using Relationships to Make Predictions

Using Relationships to Make Predictions. Pythagorean Formula: Predicted Winning Percentage. Try this …. How do we find the winning percentage of a team ? Which is used to calculate standard deviation: actual PERFORMANCE – mean PERFORMANCE OR mean PERFORMANCE – actual PERFORMANCE

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Using Relationships to Make Predictions

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  1. Using Relationships to Make Predictions Pythagorean Formula: Predicted Winning Percentage

  2. Try this … • How do we find the winning percentage of a team? • Which is used to calculate standard deviation: actual PERFORMANCE – mean PERFORMANCE OR mean PERFORMANCE – actual PERFORMANCE (Note: We followed the same order for MAD & standardized score.) ___Wins___ Wins + Loss

  3. Model for Predicting Winning Percentage What is the predicted winning percentage of the Philadelphia Phillies? • A math geek (I can say that) named Bill James was interested in answering this type of question. Bill James found the following formula will produce a __________ that can be used to help predict the number of wins: where RS = runs scored and RA = runs allowed. percentage

  4. Make a Prediction During the 2008 season, the Philadelphia Phillies scored a total of 779 runs and gave up 680 runs. Predict how many games the Phillies won that year. • Winning percentage: = • Predicted # games won (162 games in the season): ___7792___ 7792 + 6802 = 0.568 = 56.8% 0.568 (162) = 92.016 games

  5. Residual • How far off we are from our prediction is called a _______. Residual = • The 2008 Philadelphia Phillies actually won 92 games that year. What is the residual? Residual = The Phillies won 0.016_____ games than expected! residual actual - predicted 92 – 92.016= -0.016wins fewer

  6. Example In 2008, the Los Angeles Angels scored 765 runs and allowed 697 runs. • What percentage can be used to predict how many games the Angels will win? • Predict how many of the 162 games the Angels will win. • They actually won 100 games that year. Find the residual. The Angles won 11.548 _____ games than expected! ___7652___ 7652 + 6972 = 0.546 = 54.6% 0.546 (162) = 88.452 games 100 – 88.452 = 11.548 more

  7. Sum it Up • The Pythagorean formula used to predict the winning percentage in baseball is: Predicted winning percentage = • The difference between the actual value of a variable and the predicted value of that variable is known as a _______. RS2___ RS2 + RA2 residual Residual = - actual predicted AP

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