## Penalty Kill Save Percentage

I expanded my look at save percentages to penalty kill data. Once again I calculated logits from the save percentages. I removed goalies with logits that were infinity or undefined. Compared to even strength, the penalty kill data is a real muddle. The best model explains only about 13% of the variability seen. About 87% of the variability remains unexplained.

Penalty Kill versus Even Strength

There is a small correlation between even strength save percentage and penalty kill save percentage. Penalty kill save percentage is converted to "PKLogit" and even strength save percentage is converted to "RawLogit".

`> cor.test(RawLogit, PKLogit, alternative="two.sided", method="pearson")`
```Pearson's product-moment correlationdata: RawLogit and PKLogit
```
`t = 7.4081, df = 868, p-value = 3.035e-13`
```alternative hypothesis: true correlation is not equal to 0
```
```95 percent confidence interval:0.1803148  0.3053741
```
`sample estimates:`
```      cor
0.2438580

> LinearModel.10 <- lm(PKLogit ~
RawLogit, Data=PKxxx, weights=PKSA)```
`> anova(LinearModel.10)`
`Analysis of Variance Table`
`Response: PKLogit`
```                Df Sum Sq Mean Sq F value    Pr(>F)
```
`RawLogit    1  497.5  497.54  48.466 6.629e-12 ***`
`Residuals 868 8910.7   10.27                      `

Year Effect

Unlike even strength, there does not seem to be a year effect. The dotted line is the mean. The solid line is the least squares best fit.

`> LinearModel.11 <- lm(PKLogit ~ Year, Data=PKxxx, weights=PKSA)`
`> anova(LinearModel.11)`
`Analysis of Variance Table`
`Response: PKLogit`
`             Df Sum Sq Mean Sq F value Pr(>F)`
`Year         1    9.2  9.1984  0.8495 0.3570`
`Residuals  868 9399.1 10.8284 `

Team Effect

Taken by itself, there is a small team effect.

`> LinearModel.12 <- lm(PKLogit ~ Team, Data=PKxxx, weights=PKSA)`
`> anova(LinearModel.12)`

`Analysis of Variance Table`
`Response: PKLogit`
`            Df Sum Sq Mean Sq F value   Pr(>F) `
`Team        29  566.1  19.521  1.8545 0.004252 **`
`Residuals  840 8842.1  10.526 `

Goalie Effect

Taken by itself, there does not seem to be a goalie effect.

`> LinearModel.13 <- lm(PKLogit ~ GoalieName, Data=PKxxx, weights=PKSA)`
`> anova(LinearModel.13)`

`Analysis of Variance Table`
`Response: PKLogit`
`                 Df Sum Sq Mean Sq F value Pr(>F)`
`GoalieName      220 2535.4  11.525  1.0883 0.2148`
`Residuals       649 6872.8  10.590 `

Multiple Effects

Looking at Team, Year, and Goalie.

`> LinearModel.16 <- lm(PKLogit ~ Year + Team + lastfirst, data=PKData, weights=PKSA)`
`> anova(LinearModel.16)`

`Analysis of Variance Table`
`Response: PKLogit`
`           Df Sum Sq Mean Sq F value   Pr(>F) `
`Year        1    9.2  9.1984  0.9051 0.341786 `
`Team       29  566.3 19.5272  1.9215 0.002828 **`
`lastfirst 220 2542.1 11.5548  1.1370 0.118023 `
`Residuals 619 6290.7 10.1627 `

Since goalie doesn't add to the model, let's take it out.

Looking at Team and Year.

`> LinearModel.14 <- lm(PKLogit ~ Year+Team, data=PKData, weights=PKSA)`
`> anova(LinearModel.14)`
`Analysis of Variance Table`

`Response: PKLogit`
`           Df Sum Sq Mean Sq F value   Pr(>F) `
`Year        1    9.2  9.1984  0.8737 0.350194 `
`Team       29  566.3 19.5272  1.8548 0.004243 **`
`Residuals 839 8832.8 10.5277 `

Finally, looking at Team, Year, and Team*Year interaction.

`> LinearModel.15 <- lm(PKLogit ~ Year*Team, data=PKData, weights=PKSA)`
`> anova(LinearModel.15)`

`Analysis of Variance Table`
`Response: PKLogit`
`           Df Sum Sq Mean Sq F value    Pr(>F) `
`Year        1    9.2  9.1984  0.9124 0.3397687 `
`Team       29  566.3 19.5272  1.9369 0.0023447 ** `
`Year:Team  29  666.6 22.9845  2.2798 0.0001598 ***`
`Residuals 810 8166.2 10.0817 `

For the coefficients of this model, see the Appendix below.

Comparing the two models shows we have not lost anything.

`> anova(LinearModel.15,LinearModel.16)`
`Analysis of Variance Table`

`Model 1: PKLogit ~ Year * Team`
`Model 2: PKLogit ~ Year + Team + lastfirst    Res.Df    RSS  Df Sum of Sq      F Pr(>F)`
`1    810 8166.2 `
`2    590 5870.4 220    2295.8 1.0488 0.3283`

Conclusions

Penalty kill save percentage is best predicted by Team and a Team*Year interaction term. Goaltenders do not seem to differ significantly and do not add resolving power to the model. The model predicts only about 13% of the total variability seen in the data.

Appendix

`> summary(LinearModel.15)`

`Call:`
`lm(formula = PKData\$PKLogit ~ Year * Team, data = PKData, weights = PKSA)`

`Residuals:`
`Min      1Q  Median      3Q     Max `
`-8.0952 -2.3457 -0.5473  1.7953  9.7120 `

`Coefficients:`
`Estimate Std. Error t value Pr(>|t|) `
`(Intercept)      -23.986591  22.206924  -1.080  0.28040 `
`Year               0.012944   0.011086   1.168  0.24329 `
`Team[T.ATL]      -10.523932  35.026909  -0.300  0.76391 `
`Team[T.BOS]       14.805245  32.815465   0.451  0.65199 `
`Team[T.BUF]       27.982456  31.241862   0.896  0.37069 `
`Team[T.CAR]       71.411711  32.527856   2.195  0.02842 * `
`Team[T.CBJ]       29.715859  39.199665   0.758  0.44863 `
`Team[T.CGY]      -11.023374  30.860942  -0.357  0.72104 `
`Team[T.CHI]        6.342364  32.909471   0.193  0.84723 `
`Team[T.COL]       83.106082  31.357718   2.650  0.00820 **`
`Team[T.DAL]       77.805340  33.163387   2.346  0.01921 * `
`Team[T.DET]       78.066731  32.214720   2.423  0.01560 * `
`Team[T.EDM]       23.276299  31.503776   0.739  0.46022 `
`Team[T.FLA]       -5.228478  31.574171  -0.166  0.86852 `
`Team[T.LAK]       75.850056  31.358441   2.419  0.01579 * `
`Team[T.MIN]      -31.303930  40.540374  -0.772  0.44024 `
`Team[T.MTL]       20.734570  32.961644   0.629  0.52949 `
`Team[T.NJD]       11.933600  33.733418   0.354  0.72361 `
`Team[T.NSH]       25.535574  34.270177   0.745  0.45641 `
`Team[T.NYI]       49.159100  33.088931   1.486  0.13776 `
`Team[T.NYR]      -21.016443  32.208480  -0.653  0.51426 `
`Team[T.OTT]       33.700302  32.921507   1.024  0.30630 `
`Team[T.PHI]       39.878339  33.149079   1.203  0.22933 `
`Team[T.PHX]       20.381213  33.090162   0.616  0.53811 `
`Team[T.PIT]       24.266255  31.996114   0.758  0.44842 `
`Team[T.SJS]      -14.503204  32.040726  -0.453  0.65092 `
`Team[T.STL]      -15.382665  32.119666  -0.479  0.63213 `
`Team[T.TBL]       35.760341  32.690079   1.094  0.27432 `
`Team[T.TOR]       98.249645  32.546095   3.019  0.00262 **`
`Team[T.VAN]       29.383455  32.439625   0.906  0.36532 `
`Team[T.WSH]       89.971782  30.869225   2.915  0.00366 **`
`Year:Team[T.ATL]   0.005163   0.017480   0.295  0.76781 `
`Year:Team[T.BOS]  -0.007405   0.016381  -0.452  0.65137 `
`Year:Team[T.BUF]  -0.013926   0.015597  -0.893  0.37221 `
`Year:Team[T.CAR]  -0.035679   0.016237  -2.197  0.02828 * `
`Year:Team[T.CBJ]  -0.014835   0.019559  -0.758  0.44839 `
`Year:Team[T.CGY]   0.005478   0.015407   0.356  0.72227 `
`Year:Team[T.CHI]  -0.003197   0.016428  -0.195  0.84574 `
`Year:Team[T.COL]  -0.041499   0.015656  -2.651  0.00819 **`
`Year:Team[T.DAL]  -0.038867   0.016556  -2.348  0.01913 * `
`Year:Team[T.DET]  -0.038944   0.016083  -2.421  0.01568 * `
`Year:Team[T.EDM]  -0.011641   0.015727  -0.740  0.45939 `
`Year:Team[T.FLA]   0.002624   0.015761   0.166  0.86783 `
`Year:Team[T.LAK]  -0.037921   0.015655  -2.422  0.01564 * `
`Year:Team[T.MIN]   0.015664   0.020228   0.774  0.43893 `
`Year:Team[T.MTL]  -0.010338   0.016453  -0.628  0.52996 `
`Year:Team[T.NJD]  -0.005968   0.016839  -0.354  0.72311 `
`Year:Team[T.NSH]  -0.012764   0.017106  -0.746  0.45579 `
`Year:Team[T.NYI]  -0.024568   0.016514  -1.488  0.13722 `
`Year:Team[T.NYR]   0.010468   0.016079   0.651  0.51519 `
`Year:Team[T.OTT]  -0.016838   0.016433  -1.025  0.30583 `
`Year:Team[T.PHI]  -0.019930   0.016547  -1.204  0.22877 `
`Year:Team[T.PHX]  -0.010213   0.016520  -0.618  0.53662 `
`Year:Team[T.PIT]  -0.012158   0.015972  -0.761  0.44673 `
`Year:Team[T.SJS]   0.007222   0.015995   0.452  0.65175 `
`Year:Team[T.STL]   0.007655   0.016033   0.477  0.63319 `
`Year:Team[T.TBL]  -0.017942   0.016318  -1.100  0.27186 `
`Year:Team[T.TOR]  -0.049103   0.016249  -3.022  0.00259 **`
`Year:Team[T.VAN]  -0.014681   0.016193  -0.907  0.36487 `
`Year:Team[T.WSH]  -0.044899   0.015410  -2.914  0.00367 **`

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