Baseball standings dataset:

the data represents MLB standings foe 2018: there are 12 teams with variables explained below:

GLOSSARY of the data:

• W:Wins
• L:Losses
• PCT:Winning Percentage
• GB:Games Back
• HOME:Home Record
• AWAY:Away Record
• RS:Runs scored
• RA:Runs allowed
• DIFF:Run Differential
• STRK:Current Streak
• L10:Record last 10 games
• POFF:% chance of making the playoffs
• * –:Clinched Best League Record
• Y –:Clinched Wild Card
• X –:Clinched Division

Pythagorean Formula and residual plot:

The first graph below is the scatter plot of log (W/L) against log (RS/RA)  which demonstrate the Pythagorean Formula
, and the second plot is the residuals against log (RS/RA).

It seems to have a linear relationship between log (W/L) and log (RS/RA). fitting a linear model log (W/L) ~ log (RS/RA) will yield to: slope =1.4 and intercept almost equals to 0.

With R square is around 82% and pretty small p-value= 5.359e-05, we concede that the model fitted the data pretty well so the best k value is the slope 1.4.

The Colorado Rockies and Milwaukee teams considered lucky teams because they have the highest residual values so their  wins/losses is higher then predicted value.

The Washington Nationals considered unlucky team because it has the least residual values so its  wins/losses is lower then predicted value.