# Players with a good OBP (on base percentage) is very important
# OBP - On Base Percentage (Percentage of time a player gets on base, including walks)
# OOBP - opponent on base percentage - you do not want the opponent to get on base ()
# SLG - Slugging Percentage (How far a player gets around the bases on his turn (measures power)
# BA - Batting Average (getting on base by hitting the ball)##Exercise 1:
If a baseball team’s OBP is 0.361, SLG is 0.409, and BA is 0.257, how many runs do we expect the team to score?
Using the linear regression model constructed during the lecture (the one that uses OBP, SLG, and BA as independent variables), find the number of runs we expect the team to score:
# Read in data
baseball = read.csv("C:/Users/17862/Documents/SPORTS_ANALYTICS/Intro_to_R/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$RAstr(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 ...# Regression model to predict runs scored
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# OBP is 0.361, SLG is 0.409, and BA is 0.257
#runs_Scored = Intercept_value + OBP_value*(OBP)+SLG_value*(SLG)+BA_value*(BA)
Runs_Scored = -788.46 + 2917.42*(0.361)+1637.93*(0.409)-368.97*(0.257)
Runs_Scored## [1] 839.8167The team is expected to score around 840 runs.
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? Using the linear regression model discussed during the lecture (the one on the last slide of the previous video), find the number of runs we expect the team to allow.
# Regression model to predict runs allowed
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#team’s opponents OBP (OOBP) is 0.267 and opponents SLG (OSLG) is 0.392
RunsAllowedReg = -837.38 + 2913.60*(0.267)+ 1514.29*(0.392)
RunsAllowedReg## [1] 534.1529The team expect to allow around 534 runs.