##In Class activity 7
getwd()## [1] "C:/Users/USUARIO/Desktop/RESPALDO/Desktop/MDC/Sport Analytics"# Read in data
baseball = read.csv("baseball.csv")
str(baseball)## 'data.frame': 1232 obs. of 15 variables:
## $ Team : chr "ARI" "ATL" "BAL" "BOS" ...
## $ League : chr "NL" "NL" "AL" "AL" ...
## $ Year : int 2012 2012 2012 2012 2012 2012 2012 2012 2012 2012 ...
## $ RS : int 734 700 712 734 613 748 669 667 758 726 ...
## $ RA : int 688 600 705 806 759 676 588 845 890 670 ...
## $ W : int 81 94 93 69 61 85 97 68 64 88 ...
## $ OBP : num 0.328 0.32 0.311 0.315 0.302 0.318 0.315 0.324 0.33 0.335 ...
## $ SLG : num 0.418 0.389 0.417 0.415 0.378 0.422 0.411 0.381 0.436 0.422 ...
## $ BA : num 0.259 0.247 0.247 0.26 0.24 0.255 0.251 0.251 0.274 0.268 ...
## $ Playoffs : int 0 1 1 0 0 0 1 0 0 1 ...
## $ RankSeason : int NA 4 5 NA NA NA 2 NA NA 6 ...
## $ RankPlayoffs: int NA 5 4 NA NA NA 4 NA NA 2 ...
## $ G : int 162 162 162 162 162 162 162 162 162 162 ...
## $ OOBP : num 0.317 0.306 0.315 0.331 0.335 0.319 0.305 0.336 0.357 0.314 ...
## $ OSLG : num 0.415 0.378 0.403 0.428 0.424 0.405 0.39 0.43 0.47 0.402 ...# Subset to only include moneyball years
moneyball = subset(baseball, Year < 2002)
str(moneyball)## 'data.frame': 902 obs. of 15 variables:
## $ Team : chr "ANA" "ARI" "ATL" "BAL" ...
## $ League : chr "AL" "NL" "NL" "AL" ...
## $ Year : int 2001 2001 2001 2001 2001 2001 2001 2001 2001 2001 ...
## $ RS : int 691 818 729 687 772 777 798 735 897 923 ...
## $ RA : int 730 677 643 829 745 701 795 850 821 906 ...
## $ W : int 75 92 88 63 82 88 83 66 91 73 ...
## $ OBP : num 0.327 0.341 0.324 0.319 0.334 0.336 0.334 0.324 0.35 0.354 ...
## $ SLG : num 0.405 0.442 0.412 0.38 0.439 0.43 0.451 0.419 0.458 0.483 ...
## $ BA : num 0.261 0.267 0.26 0.248 0.266 0.261 0.268 0.262 0.278 0.292 ...
## $ Playoffs : int 0 1 1 0 0 0 0 0 1 0 ...
## $ RankSeason : int NA 5 7 NA NA NA NA NA 6 NA ...
## $ RankPlayoffs: int NA 1 3 NA NA NA NA NA 4 NA ...
## $ G : int 162 162 162 162 161 162 162 162 162 162 ...
## $ OOBP : num 0.331 0.311 0.314 0.337 0.329 0.321 0.334 0.341 0.341 0.35 ...
## $ OSLG : num 0.412 0.404 0.384 0.439 0.393 0.398 0.427 0.455 0.417 0.48 ...# Compute Run Difference
moneyball$RD = moneyball$RS - moneyball$RA
str(moneyball)## 'data.frame': 902 obs. of 16 variables:
## $ Team : chr "ANA" "ARI" "ATL" "BAL" ...
## $ League : chr "AL" "NL" "NL" "AL" ...
## $ Year : int 2001 2001 2001 2001 2001 2001 2001 2001 2001 2001 ...
## $ RS : int 691 818 729 687 772 777 798 735 897 923 ...
## $ RA : int 730 677 643 829 745 701 795 850 821 906 ...
## $ W : int 75 92 88 63 82 88 83 66 91 73 ...
## $ OBP : num 0.327 0.341 0.324 0.319 0.334 0.336 0.334 0.324 0.35 0.354 ...
## $ SLG : num 0.405 0.442 0.412 0.38 0.439 0.43 0.451 0.419 0.458 0.483 ...
## $ BA : num 0.261 0.267 0.26 0.248 0.266 0.261 0.268 0.262 0.278 0.292 ...
## $ Playoffs : int 0 1 1 0 0 0 0 0 1 0 ...
## $ RankSeason : int NA 5 7 NA NA NA NA NA 6 NA ...
## $ RankPlayoffs: int NA 1 3 NA NA NA NA NA 4 NA ...
## $ G : int 162 162 162 162 161 162 162 162 162 162 ...
## $ OOBP : num 0.331 0.311 0.314 0.337 0.329 0.321 0.334 0.341 0.341 0.35 ...
## $ OSLG : num 0.412 0.404 0.384 0.439 0.393 0.398 0.427 0.455 0.417 0.48 ...
## $ RD : int -39 141 86 -142 27 76 3 -115 76 17 ...As we can see when we compute the run difference we are creating a new variable that equals the runs scored minus the runs allowed. Therefore, if the RD is negative, that means that the team allowed more runs than the scored. Therefore, the higher the run difference the more wins that team has. For this example, we will plot the relationship between runs difference and wins to see if there is a linear relationship between the two variables.
# Scatterplot to check for linear relationship
plot(moneyball$RD, moneyball$W)
As we can see there is a linear relationship between number of wins and run difference. Therefore, we will build a linear regression model to predict wins using run difference.
# Regression model to predict wins
WinsReg = lm(W ~ RD, data=moneyball)
summary(WinsReg)##
## Call:
## lm(formula = W ~ RD, data = moneyball)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.2662 -2.6509 0.1234 2.9364 11.6570
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 80.881375 0.131157 616.67 <2e-16 ***
## RD 0.105766 0.001297 81.55 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.939 on 900 degrees of freedom
## Multiple R-squared: 0.8808, Adjusted R-squared: 0.8807
## F-statistic: 6651 on 1 and 900 DF, p-value: < 2.2e-16As we can see run difference is statistically significant because the p value is less than alpha. Therefore, we will use this model to answer the following question.
If a baseball team scores 763 runs and allows 614 runs, how many games do we expect the team to win?
Using the linear regression model constructed during the lecture, enter the number of games we expect the team to win:
The first step will be to compute the runs difference.
#Remember RD=Runs Scored - Runs Allowed.
rd = 763 - 614
rd## [1] 149Now that we know that the run difference is 149 we create a formula with the following coefficients: 80.881375(Intercept), 0.105766(RD)
#Remember that we computed the run difference and save it as a object named rd
Predicted_Wins = round(80.881375 + 0.105766*rd)
Predicted_Wins## [1] 97Based on these results, the team is expected to win 97 games.