Measuring Batting Performance

Transcription

1 Measuring Batting Performance Authors: Samantha Attar, Hannah Dineen, Andy Fullerton, Nora Hanson, Cam Kelso, Katie McLaughlin, and Caitlyn Nolan Introduction: The following analysis compares slugging percentage, on-base percentage, and batting average to runs scored from the Steroid Era and the post-steroid Era. Due to the effects of steroids, our group hypothesized that all three batting performance statistics would result in a greater number of runs scored during the Steroid Era compared to the post-steroid Era. Methods: We relied on the Lahman data frame to make the comparisons between slugging percentage, on-base percentage, and batting average and runs scored. To determine if there was a difference between the Steroid Era and the post-steroid Era, we investigated years and We used dplyr to manipulate the data and we used ggplot to make figures to compare the data. We then tested the significance of the null hypothesis to see if there were relationships between the batting performance statistics and runs scored using covariance. We then performed a linear regression to compare the slopes of the lines. Findings: The slugging percentage covariance indicated that there is no significance in the relationship between eras. The p-value was In contrast, the on-base percentage covariance and batting average covariance indicated that there is significance in the relationship between era. The p-value for on-base percentage was and the p-value for batting average was , which are both less than There is significance between the eras for these two batting performance statistics. Therefore, we can reject the null hypothesis - that the two slopes for the two eras are the same - for on-base percentage and batting average, but not slugging percentage. During the Steroid Era, the slope of onbase percentage vs. runs was while the slope was during the post-steroid Era. During the Steroid Era, the slope of batting average vs. runs was while the slope was during the post-steroid Era. Discussion/overview/implications The steeper slopes of the regression lines for on-base percentage and batting average in the Steroid Era indicate that players taking steroids yielded more runs than those not taking

2 steroids. Players taking steroids were likely stronger than those not taking steroids in the post-steroid Era, so they may have been getting more hits due to the ability to hit the ball farther and harder. As a result of greater batting average, on-base percentages would also increase. Perhaps we cannot reject the null hypothesis for slugging percentage because players who would normally hit a high number of homeruns simply would hit them farther with the help of steroids. head(teams) yearid lgid teamid franchid divid Rank G Ghome W L DivWin WCWin LgWin NA BS1 BNA <NA> 3 31 NA <NA> <NA> N NA CH1 CNA <NA> 2 28 NA 19 9 <NA> <NA> N NA CL1 CFC <NA> 8 29 NA <NA> <NA> N NA FW1 KEK <NA> 7 19 NA 7 12 <NA> <NA> N NA NY2 NNA <NA> 5 33 NA <NA> <NA> N NA PH1 PNA <NA> 1 28 NA 21 7 <NA> <NA> Y WSWin R AB H X2B X3B HR BB SO SB CS HBP SF RA ER ERA CG SHO SV 1 <NA> NA NA NA <NA> NA NA NA <NA> NA NA NA <NA> NA NA NA <NA> NA NA NA <NA> NA NA NA IPouts HA HRA BBA SOA E DP FP name NA 0.83 Boston Red Stockings NA 0.82 Chicago White Stockings NA 0.81 Cleveland Forest Citys NA 0.80 Fort Wayne Kekiongas NA 0.83 New York Mutuals NA 0.84 Philadelphia Athletics park attendance BPF PPF teamidbr teamidlahman45 1 South End Grounds I NA BOS BS1 2 Union Base-Ball Grounds NA CHI CH1 3 National Association Grounds NA CLE CL1 4 Hamilton Field NA KEK FW1 5 Union Grounds (Brooklyn) NA NYU NY2 6 Jefferson Street Grounds NA ATH PH1 teamidretro 1 BS1 2 CH1 3 CL1 4 FW1 5 NY2 6 PH1 tm.batting <- Teams %>% select(-(rank:wswin),-(ra:teamidretro)) %>% filter(yearid>1980,yearid<2014) %>% filter(!is.na(hbp),!is.na(sf),!is.na(cs)) %>% group_by(yearid,teamid) %>% summarize(ba=round(h/ab,3),

3 head(tm.batting) PA=AB+BB+HBP+SF, OBP=(H+BB+HBP)/PA, X1B = H-X2B-X3B-HR, TB= X1B+2*X2B+3*X3B+4*HR/AB, SLG= round(tb/ab,3), OPS=OBP+SLG, ISO=SLG-BA, TAv=(TB+HBP+BB+SB)-CS/(AB-H)+CS, RC=(H+BB-CS)*(TB+0.55*SB)/(AB+BB), BRA=OBP*SLG, SoR=SO/PA, WR=BB/PA, R) Source: local data frame [6 x 16] Groups: yearid [1] yearid teamid BA PA OBP X1B TB SLG OPS ISO (int) (fctr) (dbl) (int) (dbl) (int) (dbl) (dbl) (dbl) (dbl) ANA ARI ATL BAL BOS CHA Variables not shown: TAv (dbl), RC (dbl), BRA (dbl), SoR (dbl), WR (dbl), R (int) tm.batting$era <- ifelse(tm.batting$yearid<2006,"steroid","post") ggplot(tm.batting,aes(slg,r))+geom_point()+stat_smooth(method="lm") + facet_g rid(era~.)

4 ggplot(tm.batting,aes(obp,r))+geom_point()+stat_smooth(method="lm") + facet_g rid(era~.)

5 ggplot(tm.batting,aes(ba,r))+geom_point()+stat_smooth(method="lm") + facet_gr id(era~.)

6 glimpse(tm.batting) Observations: 420 Variables: 17 $ yearid (int) 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2... $ teamid (fctr) ANA, ARI, ATL, BAL, BOS, CHA, CHN, CIN, CLE, COL, DET,... $ BA (dbl) 0.280, 0.265, 0.271, 0.272, 0.267, 0.286, 0.256, 0.274,... $ PA (int) 6326, 6179, 6188, 6210, 6331, 6351, 6308, 6316, 6471, 6... $ OBP (dbl) , , , , ,... $ X1B (int) 995, 961, 1011, 992, 988, 1041, 948, 1007, 1078, 1130,... $ TB (dbl) , , , , , $ SLG (dbl) 0.305, 0.300, 0.298, 0.302, 0.305, 0.317, 0.280, 0.305,... $ OPS (dbl) , , , , ,... $ ISO (dbl) 0.025, 0.035, 0.027, 0.030, 0.038, 0.031, 0.024, 0.031,... $ TAv (dbl) , , , , , $ RC (dbl) , , , , , $ BRA (dbl) , , , , $ SoR (dbl) , , , , ,... $ WR (dbl) , , , , $ R (int) 864, 792, 810, 794, 792, 978, 764, 825, 950, 968, 823,... $ era (chr) "Steroid", "Steroid", "Steroid", "Steroid", "Steroid",...

7 model.slg <- lm(tm.batting$r~tm.batting$slg+tm.batting$era+tm.batting$slg*tm. batting$era) summary(model.slg) Call: lm(formula = tm.batting$r ~ tm.batting$slg + tm.batting$era + tm.batting$slg * tm.batting$era) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) tm.batting$slg <2e-16 tm.batting$erasteroid tm.batting$slg:tm.batting$erasteroid (Intercept). tm.batting$slg *** tm.batting$erasteroid tm.batting$slg:tm.batting$erasteroid --- Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: on 416 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 3 and 416 DF, p-value: < 2.2e-16 model.obp <- lm(tm.batting$r~tm.batting$obp+tm.batting$era+tm.batting$obp*tm. batting$era) summary(model.obp) Call: lm(formula = tm.batting$r ~ tm.batting$obp + tm.batting$era + tm.batting$obp * tm.batting$era) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) <2e-16 tm.batting$obp <2e-16 tm.batting$erasteroid tm.batting$obp:tm.batting$erasteroid

8 (Intercept) *** tm.batting$obp *** tm.batting$erasteroid * tm.batting$obp:tm.batting$erasteroid * --- Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: on 416 degrees of freedom Multiple R-squared: , Adjusted R-squared: 0.81 F-statistic: on 3 and 416 DF, p-value: < 2.2e-16 model.ba <- lm(tm.batting$r~tm.batting$ba+tm.batting$era+tm.batting$ba*tm.bat ting$era) summary(model.ba) Call: lm(formula = tm.batting$r ~ tm.batting$ba + tm.batting$era + tm.batting$ba * tm.batting$era) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) < 2e-16 tm.batting$ba < 2e-16 tm.batting$erasteroid tm.batting$ba:tm.batting$erasteroid (Intercept) *** tm.batting$ba *** tm.batting$erasteroid ** tm.batting$ba:tm.batting$erasteroid *** --- Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: on 416 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 3 and 416 DF, p-value: < 2.2e-16 steroid <- tm.batting %>% filter(era == "Steroid") post <- tm.batting %>% filter(era == "Post") slg.steroid <- lm(steroid$r~steroid$slg) summary(slg.steroid) Call:

9 lm(formula = steroid$r ~ steroid$slg) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) steroid$slg e-12 *** --- Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: on 178 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 1 and 178 DF, p-value: 4.981e-12 slg.post <- lm(post$r~post$slg) summary(slg.post) Call: lm(formula = post$r ~ post$slg) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) post$slg <2e-16 *** --- Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: on 238 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 1 and 238 DF, p-value: < 2.2e-16 obp.steroid <- lm(steroid$r~steroid$obp) summary(obp.steroid) Call: lm(formula = steroid$r ~ steroid$obp) Residuals: Min 1Q Median 3Q Max Coefficients:

10 Estimate Std. Error t value Pr(> t ) (Intercept) <2e-16 *** steroid$obp <2e-16 *** --- Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: on 178 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 1 and 178 DF, p-value: < 2.2e-16 obp.post <- lm(post$r~post$obp) summary(obp.post) Call: lm(formula = post$r ~ post$obp) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) <2e-16 *** post$obp <2e-16 *** --- Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: on 238 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 1 and 238 DF, p-value: < 2.2e-16 ba.steroid <- lm(steroid$r~steroid$ba) summary(ba.steroid) Call: lm(formula = steroid$r ~ steroid$ba) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) <2e-16 *** steroid$ba <2e-16 *** --- Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: on 178 degrees of freedom

11 Multiple R-squared: , Adjusted R-squared: F-statistic: on 1 and 178 DF, p-value: < 2.2e-16 ba.post <- lm(post$r~post$ba) summary(ba.post) Call: lm(formula = post$r ~ post$ba) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) <2e-16 *** post$ba <2e-16 *** --- Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: on 238 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 1 and 238 DF, p-value: < 2.2e-16