Relating baseball records Based on the number of runs scored (S) and runs allowed (A), t...

Relating baseball records Based on the number of runs scored (S) and runs allowed (A), the Pythagorean winning percentage estimates what a baseball team’s winning percentage should be. This formula, developed by baseball statistician Bill James, has the form

James determined that x = 1.83 yields the most accurate results. The 1927 New York Yankees are generally regarded as one of the best teams in baseball history. Their record was 110 wins and 44 losses. They scored 975 runs while allowing only 599.

(a) Find their Pythagorean win–loss record.

(b) Estimate the value of x (to the nearest 0.01) that best predicts the 1927 Yankees’ actual win–loss record.