Using Relationships to Make Predictions

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# Using Relationships to Make Predictions - PowerPoint PPT Presentation

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

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

(Note: We followed the same order for MAD & standardized score.)

___Wins___

Wins + Loss

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

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

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

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

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