To estimate the number of wins for a baseball team based on runs scored and runs allowed, you can use the Pythagorean theorem for baseball, which is often expressed in the following formula:
\[ \text{Winning Percentage} = \frac{\text{Runs Scored}^2}{\text{Runs Scored}^2 + \text{Runs Allowed}^2} \]
In this case, the team scored 763 runs and allowed 667 runs. Let's calculate the winning percentage:
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Calculate \( \text{Runs Scored}^2 \): \[ 763^2 = 581,369 \]
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Calculate \( \text{Runs Allowed}^2 \): \[ 667^2 = 444,889 \]
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Calculate the denominator: \[ 763^2 + 667^2 = 581,369 + 444,889 = 1,026,258 \]
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Now calculate the winning percentage: \[ \text{Winning Percentage} = \frac{581,369}{1,026,258} \approx 0.566 \]
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To find the expected number of wins over a 162-game season: \[ \text{Expected Wins} = \text{Winning Percentage} \times \text{Total Games} = 0.566 \times 162 \approx 91.8 \]
Rounding to the nearest whole number, you would expect the team to win 92 games in a 162-game season.
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