Determining the Necessary Improvement to Move Up in the Standings

In an earlier post, I discussed the Pythagorean formula for estimating winning percentage from runs for and runs against.

In this post, I will use the Pythagorean formula to determine the necessary improvement the last place team in a league would need to make to move up in the standings.

There were seven teams in the league and I found the average and standard deviaton of the winning percentages for the league. Then based on the rank, I found the percentile for the inverse normal distribution. Then based on the percentile and the average and standard deviation, I found the expected winning percentage for each of the teams in the league.

I assumed that the last place team would need to improve their offensive and their defensive equally to move up in the standings. That is, the runs for would need to increase and the runs against would need to decrease by the same amount. 

rank	percentile	win pct	runs for	runs against	change
1	0.88	0.636	119	90	29
2	0.75	0.580	113	96	23
3	0.63	0.538	109	100	19
4	0.50	0.500	105	105	15
5	0.38	0.462	101	108	11
6	0.25	0.420	96	113	6
7	0.13	0.364	90	119	0

Thus if the top four teams of the seven team league make the playoffs, the last place team from 2012 would have to increase their runs for by 15 and decrease their runs against by 15 in 2013.