Turn and Face the Strange Changes: Does Throwing Changeups Help Pitchers Sustain Lower BABIP?

I included all starting pitchers with 300+ innings since 2009 and used R v2.12.1 to fit a linear model for babip to fixed effects of flyball-rate, strikeout-rate, changeup frequency, total value by linear weights of all changeups, and value by linear weights per changeup. At Woodman's suggestion (and as justified in the body of the post), I included splitters as changeups.

Keep in mind that the p-values refer to whether the evidence suggests that a factor is significant (the lower the p-value, the more confident we can be that the effect is real) and the R-squared values refer to how well the model describes the variance (the higher the R-squared value, the better the description).

> summary(fit1)

Call:
lm(formula = babip$BABIP ~ babip$fly + babip$K + babip$chfreq + 
    babip$chtot + babip$chperc, data = babip)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.040995 -0.007808 -0.000659  0.008768  0.032989 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)   3.322e-01  8.910e-03  37.283  < 2e-16 ***
babip$fly    -1.213e-01  2.342e-02  -5.179  9.2e-07 ***
babip$K       1.609e-02  3.379e-02   0.476   0.6348    
babip$chfreq  9.532e-03  2.125e-02   0.448   0.6546    
babip$chtot  -5.992e-05  1.570e-04  -0.382   0.7034    
babip$chperc -2.969e-03  1.544e-03  -1.924   0.0568 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.01358 on 119 degrees of freedom
  (1 observation deleted due to missingness)
Multiple R-squared: 0.2564,	Adjusted R-squared: 0.2251 
F-statistic: 8.206 on 5 and 119 DF,  p-value: 1.100e-06

The "1 observation deleted due to missingness" (what a great word, by the way), was Tommy Hanson, who has zero changeups and splitters on record.  Anyway, what we find is that the effects of flyball-rate are highly significant (p = 2 × 10**-16). The effects of value per changeup are moderately significant (p = 0.0568). None of the other effects (including K%!) were significant.  A model including only those two factors actually fit the data slightly better than the initial model, which also included k-rate, changeup frequency and total changeup value.  Here is the output for that model:

> summary(fit2)

Call:
lm(formula = babip$BABIP ~ babip$fly + babip$chperc, data = babip)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.040973 -0.008040 -0.001156  0.008629  0.032851 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)   0.3340417  0.0078308  42.657  < 2e-16 ***
babip$fly    -0.1159427  0.0213364  -5.434 2.87e-07 ***
babip$chperc -0.0031551  0.0008792  -3.589  0.00048 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.01344 on 122 degrees of freedom
  (1 observation deleted due to missingness)
Multiple R-squared: 0.254,	Adjusted R-squared: 0.2418 
F-statistic: 20.77 on 2 and 122 DF,  p-value: 1.726e-08

 

Next, I used the Lindeman, Gold and Merenda (1990) (lgm) method to describe the relative importances of each factor.  Here is the output for the first model:

> calc.relimp(fit1,type=c("lmg","last","first","pratt"), rela=TRUE)
Response variable: babip$BABIP 
Total response variance: 0.0002381301 
Analysis based on 125 observations 

5 Regressors: 
babip$fly babip$K babip$chfreq babip$chtot babip$chperc 
Proportion of variance explained by model: 25.64%
Metrics are normalized to sum to 100% (rela=TRUE). 

Relative importance metrics: 

                    lmg        last      first       pratt
babip$fly    0.66176163 0.862561629 0.48939293  0.72622533
babip$K      0.02597355 0.007290960 0.04968005 -0.02154839
babip$chfreq 0.05245325 0.006468146 0.10981283 -0.03433426
babip$chtot  0.08818158 0.004685193 0.14603247  0.05044396
babip$chperc 0.17162998 0.118994071 0.20508171  0.27921336

Average coefficients for different model sizes: 

                        1X           2Xs           3Xs           4Xs
babip$fly    -0.1141989299 -0.1126788278 -0.1150599466 -1.190098e-01
babip$K      -0.0518129769 -0.0316319422 -0.0157599046  1.072460e-03
babip$chfreq -0.0425860063 -0.0276718376 -0.0142778771 -1.016283e-03
babip$chtot  -0.0002423128 -0.0001693865 -0.0001124105 -7.509733e-05
babip$chperc -0.0030463088 -0.0028538654 -0.0028884462 -3.005977e-03
                       5Xs
babip$fly    -0.1213197877
babip$K       0.0160889358
babip$chfreq  0.0095322944
babip$chtot  -0.0000599228
babip$chperc -0.0029691976

 

In terms of relative importance, flyball-rate was most important but the changeup inputs made important contributions to the model as well. K-rate made the least important contribution (just 2% relative importance).  We can either combine the relative contributions of the changeups here or use this method to calculate relative importances for our second model.  Here is the output for the second model:

> calc.relimp(fit2,type=c("lmg","last","first","pratt"), rela=TRUE)
Response variable: babip$BABIP 
Total response variance: 0.0002381301 
Analysis based on 125 observations 

2 Regressors: 
babip$fly babip$chperc 
Proportion of variance explained by model: 25.4%
Metrics are normalized to sum to 100% (rela=TRUE). 

Relative importance metrics: 

                   lmg      last     first     pratt
babip$fly    0.7004244 0.6963282 0.7046952 0.7005284
babip$chperc 0.2995756 0.3036718 0.2953048 0.2994716

Average coefficients for different model sizes: 

                       1X          2Xs
babip$fly    -0.114198930 -0.115942720
babip$chperc -0.003046309 -0.003155121

Of course, this method has a critical flaw.  The problem with using linear weights pitch value data is that those linear weights values are affected by BABIP, so they aren't independent of one another.  However, changeup frequency should be independent of babip, so we can use a simple model that looks only at flyball-rate and changeup frequency.  Here is the output: