Editing Pythagorean expectation (section)

{{short description|Sports formula}}
'''Pythagorean expectation''' is a [[sports analytics]] formula devised by [[Bill James]] to estimate the percentage of games a [[baseball]] team "should" have won based on the number of [[run (baseball)|runs]] they scored and allowed.  Comparing a team's actual and Pythagorean winning percentage can be used to make predictions and evaluate which teams are over-performing and under-performing. The name comes from the formula's resemblance to the [[Pythagorean theorem]].<ref>{{cite web|url=http://thegamedesigner.blogspot.com/2012/05/pythagoras-explained.html|title=The Game Designer: Pythagoras Explained|date=29 May 2012 |access-date=7 May 2016}}</ref>

The basic formula is:

:<math>\mathrm{Win\ Ratio} = \frac{\text{runs scored}^2}{\text{runs scored}^2 + \text{runs allowed}^2} = \frac{1}{1+(\text{runs allowed}/\text{runs scored})^2}</math>

where Win Ratio is the winning ratio generated by the formula. The expected number of wins would be the expected winning ratio multiplied by the number of games played.