For this activity we wil continue to use the baseball dataset from in class activity #7 and compute a linear regression model using OBP, SLG, and BA as independent variables. This is because we will use those variables to predict runs.
Information on the variables:
BA= In baseball, batting average (BA) is determined by dividing a player’s hits by their total at-bats.
OBP= OBP refers to how frequently a batter reaches base per plate appearance. Times on base include hits, walks and hit-by-pitches, but do not include errors, times reached on a fielder’s choice or a dropped third strike.
SLG= In baseball statistics, slugging percentage ( SLG) is a measure of the batting productivity of a hitter. It is calculated as total bases divided by at bats, through the following formula, where AB is the number of at bats for a given player, and 1B, 2B, 3B, and HR are the number of singles, doubles, triples, and home runs, respectively:
First we must load the data
# 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 ...# 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-16As we can see the OBP,SLG,and BA are statistically significant since the p value is less than alpha. The formula to predict runs using the coefficients and intercept would be.
Predicted_runs= round(-788.46+2917.42obp+1637.93slg -368.97*ba)
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:
obp = 0.361
slg = 0.409
ba = 0.257
Predicted_runs= round(-788.46+2917.42*obp+1637.93*slg -368.97*ba)
Predicted_runs## [1] 840Based on the results, we are expected to score 840 runs
Notes from Moneyball: The A’s claimed that:
On-Base Percentage was the most important for scoring runs. Slugging Percentage was important . Batting Average was overvalued.
Exercise 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? 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 using OBP and SLG
RunsAllowed = lm(RA ~ OOBP + OSLG, data=moneyball)
summary(RunsAllowed)##
## 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-16For this model we decided to eliminate batting average due to the high correlation with obp. In addition, we can see that both oobp and oslg are statistically significant because the pv is less than alpha.
Based on the results using the linear regression model the formula to calculate predicted runs allow is the following:
OOBP = 0.267
OSLG = 0.392
predicted_ra=round(-837.38+ 2913.60*OOBP + 1514.29*OSLG )
predicted_ra## [1] 534As we can see we expect the team to allow 534 runs.