The Pythagorean expectation predicted a winning percentage of .512. Use this value to determine the actual number of runs the Cardinals allowed.

Question

Additional Information about the Problem: In the 2006 regular season, the Louis Cardinals won 83 of 161 games and scored 781 runs (They played only games because the September 17 game against the San Francisco Giants was rained out and not rescheduled.)

The Answer is 762 I just don’t know how to show my work !

Answer 1

Hi Jayla,

The formula is: wins = (runs scored)²/[(runs scored)² + (runs allowed)²]

.512 = 781²/(781² + x²)

781² + x² = 781²/.512

x² = (781²/.512) - 781²

You can take it from here. I get x = ±762.4576..., choose +762.

I hope this helps, Joe.