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): ___779 2 ___ 779 2 + 680 2 = 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 92 – 92.016 = -0.016 wins fewer actual - predicted

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! ___765 2 ___ 765 2 + 697 2 = 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 _______. residual actual predicted RS 2 ___ RS 2 + RA 2 Residual = -