In-class activity #7: Predicting the Number of Wins

getwd()

[1] "/cloud/project"

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 ...

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 ...

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 ...

plot(moneyball$RD, moneyball$W)

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-16

In-class activity 7

#If a baseball team scores 763 runs and allows 614 runs, how many games do we expect the team to win?

NumberofWins=80.88+0.106*(763-614)
NumberofWins

[1] 96.674

A team with a runs difference of 149 is expected to win around 97 games.

RunsReg = lm(RS ~ OBP + SLG + BA, data=moneyball)
summary(RunsReg)

Call:
lm(formula = RS ~ OBP + SLG + BA, data = moneyball)

Residuals:
    Min      1Q  Median      3Q     Max 
-70.941 -17.247  -0.621  16.754  90.998 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -788.46      19.70 -40.029  < 2e-16 ***
OBP          2917.42     110.47  26.410  < 2e-16 ***
SLG          1637.93      45.99  35.612  < 2e-16 ***
BA           -368.97     130.58  -2.826  0.00482 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 24.69 on 898 degrees of freedom
Multiple R-squared:  0.9302,    Adjusted R-squared:   0.93 
F-statistic:  3989 on 3 and 898 DF,  p-value: < 2.2e-16

cor(moneyball$BA, moneyball$OBP)

[1] 0.8540549

# Regression model to predict runs scored again but removing the batting average
RunsReg = lm(RS ~ OBP + SLG, data=moneyball)
summary(RunsReg)

Call:
lm(formula = RS ~ OBP + SLG, data = moneyball)

Residuals:
    Min      1Q  Median      3Q     Max 
-70.838 -17.174  -1.108  16.770  90.036 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -804.63      18.92  -42.53   <2e-16 ***
OBP          2737.77      90.68   30.19   <2e-16 ***
SLG          1584.91      42.16   37.60   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 24.79 on 899 degrees of freedom
Multiple R-squared:  0.9296,    Adjusted R-squared:  0.9294 
F-statistic:  5934 on 2 and 899 DF,  p-value: < 2.2e-16

In-class activity 8: Part 1

If a baseball team’s OBP is 0.361 and SLG is 0.409, how many runs do we expect the team to score?

ExpectedRuns= -804.63 + 2737.77 * (0.361) + 1584.91 * (0.409)
ExpectedRuns

[1] 831.9332

Based on the calculations, we expect the team to score around 832 runs.

install.packages("car")

Installing package into ‘/cloud/lib/x86_64-pc-linux-gnu-library/4.4’
(as ‘lib’ is unspecified)
also installing the dependencies ‘fansi’, ‘pkgconfig’, ‘cpp11’, ‘utf8’, ‘withr’, ‘gtable’, ‘isoband’, ‘rbibutils’, ‘backports’, ‘generics’, ‘purrr’, ‘tibble’, ‘tidyr’, ‘pillar’, ‘tidyselect’, ‘cowplot’, ‘Deriv’, ‘ggplot2’, ‘modelr’, ‘microbenchmark’, ‘Rdpack’, ‘colorspace’, ‘broom’, ‘dplyr’, ‘numDeriv’, ‘doBy’, ‘SparseM’, ‘MatrixModels’, ‘minqa’, ‘nloptr’, ‘reformulas’, ‘Rcpp’, ‘RcppEigen’, ‘farver’, ‘labeling’, ‘munsell’, ‘RColorBrewer’, ‘viridisLite’, ‘carData’, ‘abind’, ‘Formula’, ‘pbkrtest’, ‘quantreg’, ‘lme4’, ‘scales’

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The downloaded source packages are in
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#install.packages("carData")

library(car)

vif(RunsReg)

     OBP      SLG       BA 
4.271126 3.426472 4.433501 

RunsAllowedReg = lm(RA ~ OOBP + OSLG, data=moneyball)
summary(RunsAllowedReg)

Call:
lm(formula = RA ~ OOBP + OSLG, data = moneyball)

Residuals:
    Min      1Q  Median      3Q     Max 
-82.397 -15.178  -0.129  17.679  60.955 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -837.38      60.26 -13.897  < 2e-16 ***
OOBP         2913.60     291.97   9.979 4.46e-16 ***
OSLG         1514.29     175.43   8.632 2.55e-13 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 25.67 on 87 degrees of freedom
  (812 observations deleted due to missingness)
Multiple R-squared:  0.9073,    Adjusted R-squared:  0.9052 
F-statistic: 425.8 on 2 and 87 DF,  p-value: < 2.2e-16

In-class activity 8: Part 2

If a baseball team’s opponents OBP (OOBP) is 0.267 and opponents SLG (OSLG) is 0.392, how many runs do we expect the team to allow?

ExpectedRunsAllowed = -837.38 + 2913.60 * (0.267) + 1514.29 * (0.392)
ExpectedRunsAllowed

[1] 534.1529

The team is expected to allow around 534 runs.

vif(RunsAllowedReg)

    OOBP     OSLG 
2.735629 2.735629