All Star NBA Model (Trained with 2000-16 Data)
Paul Kellar
03/31/2020
R Environment Preparation
Read in .csv and bring in necessary libraries (NBA player data 2000-16)
setwd("~/Documents/Spring 2019/Data Mining/R Files")
load("seasonstats.Rdata")
#seasonstats <- seasonstats
library(forecast)
library(gains)
library(caret)
library(e1071)Dataset: Must have played more than 10 games and at least 20 minutes/game
Delete non-numeric columns
seasonstats <- seasonstats[,c(6:52)]Deleting records with few N/As and where median wouldn’t be logical
dim(seasonstats[( is.na(seasonstats$AST) |
is.na(seasonstats$PTS)), ])## [1] 0 47seasonstats <- (seasonstats[!(is.na(seasonstats$TwoPP) |
is.na(seasonstats$ThreePP)), ])Imputing the median for FT%if null as deleting/puttiong 0s doesn’t make sense
seasonstats$FTp[is.na(seasonstats$FTp)] <-
median(seasonstats$FTp, na.rm = TRUE)
summary(seasonstats)## Tm G GS FG
## TOT : 323 Min. :11.00 Min. : 0.00 Min. : 12.0
## CHI : 146 1st Qu.:55.00 1st Qu.:19.00 1st Qu.:187.0
## MIL : 144 Median :71.00 Median :46.00 Median :279.0
## DEN : 143 Mean :64.34 Mean :44.43 Mean :304.8
## NYK : 142 3rd Qu.:79.00 3rd Qu.:72.00 3rd Qu.:400.0
## TOR : 140 Max. :85.00 Max. :83.00 Max. :978.0
## (Other):3128
## FGA ThreeP ThreePA TwoP
## Min. : 31.0 Min. : 0.0 Min. : 1.0 Min. : 8.0
## 1st Qu.: 427.0 1st Qu.: 7.0 1st Qu.: 27.0 1st Qu.:137.0
## Median : 624.5 Median : 45.0 Median :132.0 Median :218.0
## Mean : 675.9 Mean : 55.4 Mean :154.1 Mean :249.4
## 3rd Qu.: 882.0 3rd Qu.: 89.0 3rd Qu.:245.0 3rd Qu.:333.8
## Max. :2173.0 Max. :402.0 Max. :886.0 Max. :956.0
##
## TwoPA FT FTA ORB
## Min. : 26.0 Min. : 3.0 Min. : 5.0 Min. : 0.00
## 1st Qu.: 299.0 1st Qu.: 75.0 1st Qu.: 99.0 1st Qu.: 30.00
## Median : 464.0 Median :125.0 Median :164.5 Median : 58.00
## Mean : 521.7 Mean :155.8 Mean :201.5 Mean : 79.53
## 3rd Qu.: 694.8 3rd Qu.:206.0 3rd Qu.:268.0 3rd Qu.:111.00
## Max. :1664.0 Max. :756.0 Max. :972.0 Max. :440.00
##
## DRB TRB AST STL
## Min. : 15.0 Min. : 17.0 Min. : 8.0 Min. : 2.00
## 1st Qu.:136.0 1st Qu.: 171.2 1st Qu.: 84.0 1st Qu.: 37.00
## Median :206.0 Median : 267.0 Median :142.0 Median : 56.00
## Mean :235.1 Mean : 314.7 Mean :187.8 Mean : 61.55
## 3rd Qu.:303.0 3rd Qu.: 410.8 3rd Qu.:247.0 3rd Qu.: 80.00
## Max. :894.0 Max. :1226.0 Max. :925.0 Max. :225.00
##
## BLK TOV PF PTS
## Min. : 0.00 Min. : 5.0 Min. : 12.0 Min. : 34.0
## 1st Qu.: 10.00 1st Qu.: 68.0 1st Qu.:107.0 1st Qu.: 497.0
## Median : 20.00 Median :103.0 Median :152.0 Median : 749.0
## Mean : 34.01 Mean :112.5 Mean :151.1 Mean : 820.7
## 3rd Qu.: 42.00 3rd Qu.:148.0 3rd Qu.:194.0 3rd Qu.:1073.8
## Max. :294.00 Max. :374.0 Max. :371.0 Max. :2832.0
##
## MP PER TSP ThreePAr
## Min. : 231 Min. : 3.00 Min. :0.3590 Min. :0.0010
## 1st Qu.:1433 1st Qu.:12.50 1st Qu.:0.5040 1st Qu.:0.0510
## Median :1931 Median :14.90 Median :0.5320 Median :0.2370
## Mean :1901 Mean :15.25 Mean :0.5314 Mean :0.2351
## 3rd Qu.:2427 3rd Qu.:17.50 3rd Qu.:0.5590 3rd Qu.:0.3700
## Max. :3485 Max. :31.70 Max. :0.7080 Max. :0.8730
##
## FTr ORBP DRBP TRBP
## Min. :0.0360 Min. : 0.000 Min. : 4.20 Min. : 2.400
## 1st Qu.:0.2020 1st Qu.: 2.100 1st Qu.: 9.70 1st Qu.: 6.000
## Median :0.2710 Median : 3.600 Median :12.60 Median : 8.200
## Mean :0.2899 Mean : 4.763 Mean :14.01 Mean : 9.381
## 3rd Qu.:0.3570 3rd Qu.: 7.000 3rd Qu.:17.50 3rd Qu.:12.200
## Max. :1.2190 Max. :18.300 Max. :35.90 Max. :25.600
##
## ASTP STLP BLKP TOVP
## Min. : 1.40 Min. :0.100 Min. : 0.000 Min. : 2.60
## 1st Qu.: 8.80 1st Qu.:1.200 1st Qu.: 0.400 1st Qu.:10.70
## Median :13.20 Median :1.600 Median : 0.900 Median :12.80
## Mean :16.17 Mean :1.678 Mean : 1.322 Mean :13.11
## 3rd Qu.:22.18 3rd Qu.:2.000 3rd Qu.: 1.700 3rd Qu.:15.10
## Max. :55.90 Max. :4.800 Max. :10.200 Max. :33.80
##
## USGP OWS DWS WS
## Min. : 6.40 Min. :-3.300 Min. :-0.600 Min. :-2.100
## 1st Qu.:17.00 1st Qu.: 0.800 1st Qu.: 0.900 1st Qu.: 2.000
## Median :20.20 Median : 1.900 Median : 1.600 Median : 3.700
## Mean :20.45 Mean : 2.415 Mean : 1.886 Mean : 4.302
## 3rd Qu.:23.50 3rd Qu.: 3.500 3rd Qu.: 2.600 3rd Qu.: 6.000
## Max. :38.70 Max. :14.800 Max. : 9.100 Max. :20.300
##
## WS48 OBPM DBPM BPM
## Min. :-0.0520 Min. :-7.2000 Min. :-5.4000 Min. :-7.3000
## 1st Qu.: 0.0660 1st Qu.:-1.2000 1st Qu.:-1.4000 1st Qu.:-1.6000
## Median : 0.0990 Median : 0.2000 Median :-0.3000 Median : 0.0000
## Mean : 0.1005 Mean : 0.3267 Mean :-0.1538 Mean : 0.1727
## 3rd Qu.: 0.1330 3rd Qu.: 1.6000 3rd Qu.: 0.9000 3rd Qu.: 1.7000
## Max. : 0.3220 Max. :12.4000 Max. : 7.0000 Max. :13.0000
##
## VORP FGP ThreePP TwoPP
## Min. :-2.10 Min. :0.2860 Min. :0.0000 Min. :0.2870
## 1st Qu.: 0.10 1st Qu.:0.4160 1st Qu.:0.2650 1st Qu.:0.4430
## Median : 0.90 Median :0.4420 Median :0.3370 Median :0.4710
## Mean : 1.27 Mean :0.4475 Mean :0.2965 Mean :0.4721
## 3rd Qu.: 2.00 3rd Qu.:0.4740 3rd Qu.:0.3780 3rd Qu.:0.5000
## Max. :11.60 Max. :0.7100 Max. :1.0000 Max. :0.7130
##
## eFGP FTP isAllStar
## Min. :0.3150 Min. :0.3110 Min. :0.0000
## 1st Qu.:0.4610 1st Qu.:0.7210 1st Qu.:0.0000
## Median :0.4880 Median :0.7820 Median :0.0000
## Mean :0.4896 Mean :0.7674 Mean :0.1049
## 3rd Qu.:0.5160 3rd Qu.:0.8290 3rd Qu.:0.0000
## Max. :0.7110 Max. :1.0000 Max. :1.0000
## Calculated Variables for per-game analysis
seasonstats$TOVGame <- seasonstats$TOV / seasonstats$G
seasonstats$STLGame <- seasonstats$STL / seasonstats$G
seasonstats$BLKGame <- seasonstats$BLK / seasonstats$G
seasonstats$PTSGame <- seasonstats$PTS / seasonstats$G
seasonstats$TRBGame <- seasonstats$TRB / seasonstats$G
seasonstats$ASTGame <- seasonstats$AST / seasonstats$G
seasonstats$FTGame <- seasonstats$FT / seasonstats$G
seasonstats$FTAGame <- seasonstats$FTA / seasonstats$G
seasonstats$PFGame <- seasonstats$PF / seasonstats$G
seasonstats$TwoPGame <- seasonstats$TwoP / seasonstats$G
seasonstats$TwoPAGame <- seasonstats$TwoPA / seasonstats$G
seasonstats$ThreePAGame <- seasonstats$ThreePA / seasonstats$G
seasonstats$ThreePGame <- seasonstats$ThreeP / seasonstats$GUpdated to per game stats and deleted G and GS (would skew data so use USG% instead)
seasonstats <- seasonstats[,c(19:60)]
seasonstats <- seasonstats[,c(1,4:42)]
seasonstatsmodel <- seasonstatsLogistic Model - focus on high sensitivity (positivity accuracy) vs high specificity
set.seed(2016)
train.rows <- sample(nrow(seasonstatsmodel), nrow(seasonstatsmodel) * 0.6)
seasonstatsmodel.train <- seasonstatsmodel[train.rows, ]
seasonstatsmodel.valid <- seasonstatsmodel[-train.rows, ]
seasonstatsmodel.glm <- glm(isAllStar ~ ., family = "binomial", data = seasonstatsmodel.train)
summary(seasonstatsmodel.glm)##
## Call:
## glm(formula = isAllStar ~ ., family = "binomial", data = seasonstatsmodel.train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.15460 -0.23592 -0.09018 -0.03491 2.85729
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.603e+01 6.770e+00 -2.369 0.01786 *
## PF -9.122e-03 5.289e-03 -1.725 0.08456 .
## PER -2.196e-01 3.193e-01 -0.688 0.49168
## TSP -7.048e+00 2.617e+01 -0.269 0.78769
## ThreePAr -2.687e+01 1.849e+01 -1.453 0.14615
## FTr 6.886e+00 3.810e+00 1.807 0.07072 .
## ORBP 3.826e-01 4.082e-01 0.937 0.34869
## DRBP 2.592e-01 4.073e-01 0.636 0.52454
## TRBP -7.867e-01 8.166e-01 -0.963 0.33538
## ASTP -2.197e-01 8.550e-02 -2.570 0.01017 *
## STLP -3.523e-01 1.282e+00 -0.275 0.78342
## BLKP 1.726e-01 5.848e-01 0.295 0.76786
## TOVP 7.690e-02 1.460e-01 0.527 0.59852
## USGP 5.509e-01 1.860e-01 2.961 0.00307 **
## OWS -1.173e-01 1.936e+00 -0.061 0.95170
## DWS 2.684e-01 1.939e+00 0.138 0.88990
## WS 3.685e-01 1.938e+00 0.190 0.84919
## WS48 -7.825e+00 1.454e+01 -0.538 0.59042
## OBPM -1.426e+00 1.899e+00 -0.751 0.45272
## DBPM -1.556e+00 1.901e+00 -0.819 0.41287
## BPM 1.847e+00 1.893e+00 0.976 0.32918
## VORP -3.100e-01 3.797e-01 -0.816 0.41425
## FGP -1.395e+02 9.575e+01 -1.457 0.14515
## ThreePP 7.663e-01 9.057e-01 0.846 0.39748
## TwoPP 1.404e+01 1.318e+01 1.065 0.28680
## eFGP 1.380e+02 9.057e+01 1.524 0.12759
## FTP 2.198e-02 3.724e+00 0.006 0.99529
## TOVGame -1.333e+00 8.094e-01 -1.647 0.09958 .
## STLGame 6.993e-01 1.911e+00 0.366 0.71443
## BLKGame 1.441e-01 1.246e+00 0.116 0.90793
## PTSGame -3.955e-01 8.994e-01 -0.440 0.66009
## TRBGame 5.941e-01 3.745e-01 1.586 0.11265
## ASTGame 1.565e+00 3.897e-01 4.016 5.91e-05 ***
## FTGame 1.368e+00 1.242e+00 1.101 0.27092
## FTAGame -9.181e-01 6.801e-01 -1.350 0.17705
## PFGame 1.518e-01 4.475e-01 0.339 0.73439
## TwoPGame 1.277e+00 2.079e+00 0.614 0.53903
## TwoPAGame -2.842e-01 4.632e-01 -0.614 0.53951
## ThreePAGame 4.180e-01 1.099e+00 0.380 0.70369
## ThreePGame NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1769.64 on 2498 degrees of freedom
## Residual deviance: 794.89 on 2460 degrees of freedom
## AIC: 872.89
##
## Number of Fisher Scoring iterations: 8pred.glm.train <- predict(seasonstatsmodel.glm, type = "response")
pred.glm.valid <- predict(seasonstatsmodel.glm, newdata = seasonstatsmodel.valid, type = "response")## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleadingconfusionMatrix(as.factor(ifelse(pred.glm.train >= 0.5, "1", "0")), as.factor(seasonstatsmodel.train$isAllStar),
positive = "1")## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 2164 123
## 1 51 161
##
## Accuracy : 0.9304
## 95% CI : (0.9197, 0.94)
## No Information Rate : 0.8864
## P-Value [Acc > NIR] : 8.990e-14
##
## Kappa : 0.6114
##
## Mcnemar's Test P-Value : 7.346e-08
##
## Sensitivity : 0.56690
## Specificity : 0.97698
## Pos Pred Value : 0.75943
## Neg Pred Value : 0.94622
## Prevalence : 0.11365
## Detection Rate : 0.06443
## Detection Prevalence : 0.08483
## Balanced Accuracy : 0.77194
##
## 'Positive' Class : 1
## Logistic Model - focus on high sensitivity (positivity accuracy) vs high specificity
set.seed(2016)
train.rows <- sample(nrow(seasonstatsmodel), nrow(seasonstatsmodel) * 0.6)
seasonstatsmodel.train <- seasonstatsmodel[train.rows, ]
seasonstatsmodel.valid <- seasonstatsmodel[-train.rows, ]
seasonstatsmodel.glm <- glm(isAllStar ~ ., family = "binomial", data = seasonstatsmodel.train)
summary(seasonstatsmodel.glm)##
## Call:
## glm(formula = isAllStar ~ ., family = "binomial", data = seasonstatsmodel.train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.15460 -0.23592 -0.09018 -0.03491 2.85729
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.603e+01 6.770e+00 -2.369 0.01786 *
## PF -9.122e-03 5.289e-03 -1.725 0.08456 .
## PER -2.196e-01 3.193e-01 -0.688 0.49168
## TSP -7.048e+00 2.617e+01 -0.269 0.78769
## ThreePAr -2.687e+01 1.849e+01 -1.453 0.14615
## FTr 6.886e+00 3.810e+00 1.807 0.07072 .
## ORBP 3.826e-01 4.082e-01 0.937 0.34869
## DRBP 2.592e-01 4.073e-01 0.636 0.52454
## TRBP -7.867e-01 8.166e-01 -0.963 0.33538
## ASTP -2.197e-01 8.550e-02 -2.570 0.01017 *
## STLP -3.523e-01 1.282e+00 -0.275 0.78342
## BLKP 1.726e-01 5.848e-01 0.295 0.76786
## TOVP 7.690e-02 1.460e-01 0.527 0.59852
## USGP 5.509e-01 1.860e-01 2.961 0.00307 **
## OWS -1.173e-01 1.936e+00 -0.061 0.95170
## DWS 2.684e-01 1.939e+00 0.138 0.88990
## WS 3.685e-01 1.938e+00 0.190 0.84919
## WS48 -7.825e+00 1.454e+01 -0.538 0.59042
## OBPM -1.426e+00 1.899e+00 -0.751 0.45272
## DBPM -1.556e+00 1.901e+00 -0.819 0.41287
## BPM 1.847e+00 1.893e+00 0.976 0.32918
## VORP -3.100e-01 3.797e-01 -0.816 0.41425
## FGP -1.395e+02 9.575e+01 -1.457 0.14515
## ThreePP 7.663e-01 9.057e-01 0.846 0.39748
## TwoPP 1.404e+01 1.318e+01 1.065 0.28680
## eFGP 1.380e+02 9.057e+01 1.524 0.12759
## FTP 2.198e-02 3.724e+00 0.006 0.99529
## TOVGame -1.333e+00 8.094e-01 -1.647 0.09958 .
## STLGame 6.993e-01 1.911e+00 0.366 0.71443
## BLKGame 1.441e-01 1.246e+00 0.116 0.90793
## PTSGame -3.955e-01 8.994e-01 -0.440 0.66009
## TRBGame 5.941e-01 3.745e-01 1.586 0.11265
## ASTGame 1.565e+00 3.897e-01 4.016 5.91e-05 ***
## FTGame 1.368e+00 1.242e+00 1.101 0.27092
## FTAGame -9.181e-01 6.801e-01 -1.350 0.17705
## PFGame 1.518e-01 4.475e-01 0.339 0.73439
## TwoPGame 1.277e+00 2.079e+00 0.614 0.53903
## TwoPAGame -2.842e-01 4.632e-01 -0.614 0.53951
## ThreePAGame 4.180e-01 1.099e+00 0.380 0.70369
## ThreePGame NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1769.64 on 2498 degrees of freedom
## Residual deviance: 794.89 on 2460 degrees of freedom
## AIC: 872.89
##
## Number of Fisher Scoring iterations: 8pred.glm.train <- predict(seasonstatsmodel.glm, type = "response")
pred.glm.valid <- predict(seasonstatsmodel.glm, newdata = seasonstatsmodel.valid, type = "response")## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleadingconfusionMatrix(as.factor(ifelse(pred.glm.train >= 0.5, "1", "0")), as.factor(seasonstatsmodel.train$isAllStar),
positive = "1")## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 2164 123
## 1 51 161
##
## Accuracy : 0.9304
## 95% CI : (0.9197, 0.94)
## No Information Rate : 0.8864
## P-Value [Acc > NIR] : 8.990e-14
##
## Kappa : 0.6114
##
## Mcnemar's Test P-Value : 7.346e-08
##
## Sensitivity : 0.56690
## Specificity : 0.97698
## Pos Pred Value : 0.75943
## Neg Pred Value : 0.94622
## Prevalence : 0.11365
## Detection Rate : 0.06443
## Detection Prevalence : 0.08483
## Balanced Accuracy : 0.77194
##
## 'Positive' Class : 1
## #Initial model has low sensitivity so need to change that:
#Define a cost function with input "obs" being the observed response,
# "pred.p" being predicted probability, and "pcut" being the threshold
#Allows us to weight getting high sensitivity vs high specficity
costfunc <- function(obs, pred.p, pcut){
weight1 <- 10 # define the weight for "true=1 but pred=0" (false negative)
weight0 <- 1 # define the weight for "true=0 but pred=1" (false positive)
c1 <- (obs == 1) & (pred.p < pcut) # count for "true=1 but pred=0" (false negative)
c0 <- (obs == 0) & (pred.p >= pcut) # count for "true=0 but pred=1" (false positive)
cost <- mean(weight1 * c1 + weight0 * c0) # misclassification with weight
return(cost)
}
#Define a sequence from 0.01 to 1 by 0.01
p.seq <- seq(from = 0.01, to = 1, by = 0.01)
# Loop for all potential cutoff values to see which provides the smallest cost
# Define a 0 vector first to save the values of cost from all cutoffs
cost <- rep(0, length(p.seq))
for (i in 1:length(p.seq)) {cost[i] <- costfunc(obs = seasonstatsmodel$isAllStar, pred.p = pred.glm.train, pcut = p.seq[i])
}## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 1) & (pred.p < pcut): longer object length is not a multiple
## of shorter object length## Warning in (obs == 0) & (pred.p >= pcut): longer object length is not a multiple
## of shorter object length#Find optimal pcut
optimal.pcut.glm <- p.seq[which(cost == min(cost))]
#Higher sensitivity seen - will try this cutoff with logistic model(s)
confusionMatrix(as.factor(ifelse(pred.glm.train >= optimal.pcut.glm, "1", "0")), as.factor(seasonstatsmodel.train$isAllStar),
positive = "1")## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 1273 0
## 1 942 284
##
## Accuracy : 0.623
## 95% CI : (0.6037, 0.6421)
## No Information Rate : 0.8864
## P-Value [Acc > NIR] : 1
##
## Kappa : 0.235
##
## Mcnemar's Test P-Value : <2e-16
##
## Sensitivity : 1.0000
## Specificity : 0.5747
## Pos Pred Value : 0.2316
## Neg Pred Value : 1.0000
## Prevalence : 0.1136
## Detection Rate : 0.1136
## Detection Prevalence : 0.4906
## Balanced Accuracy : 0.7874
##
## 'Positive' Class : 1
## cost <- costfunc(obs = seasonstatsmodel.train$isAllStar, pred.p = pred.glm.train, pcut = optimal.pcut.glm)Perform forward selection,backward selection, and stepwise selection
#Forward regression - 2nd best
seasonstatsmodel.glm.null <- glm(isAllStar ~ 1, data = seasonstatsmodel.train, family = "binomial")
seasonstatsmodel.glm.full <- glm(isAllStar ~ ., data = seasonstatsmodel.train, family = "binomial")
seasonstatsmodel.glm.fwd <- step(seasonstatsmodel.glm.null, scope = list(seasonstatsmodel.glm.null, upper = seasonstatsmodel.glm), direction = "forward")## Start: AIC=1771.64
## isAllStar ~ 1
##
## Df Deviance AIC
## + PER 1 980.61 984.61
## + PTSGame 1 1065.55 1069.55
## + VORP 1 1138.59 1142.59
## + WS 1 1142.93 1146.93
## + FTAGame 1 1170.56 1174.56
## + FTGame 1 1173.40 1177.40
## + TwoPGame 1 1187.60 1191.60
## + BPM 1 1197.55 1201.55
## + OWS 1 1220.61 1224.61
## + TwoPAGame 1 1234.21 1238.21
## + WS48 1 1259.83 1263.83
## + USGP 1 1276.25 1280.25
## + OBPM 1 1287.65 1291.65
## + TOVGame 1 1356.88 1360.88
## + DWS 1 1470.20 1474.20
## + ASTGame 1 1557.47 1561.47
## + TRBGame 1 1579.00 1583.00
## + STLGame 1 1595.39 1599.39
## + ASTP 1 1631.79 1635.79
## + FTr 1 1637.62 1641.62
## + TSP 1 1652.17 1656.17
## + BLKGame 1 1688.22 1692.22
## + FGP 1 1692.92 1696.92
## + TwoPP 1 1704.34 1708.34
## + DRBP 1 1707.67 1711.67
## + DBPM 1 1715.46 1719.46
## + PF 1 1715.58 1719.58
## + TRBP 1 1728.75 1732.75
## + ThreePAr 1 1735.75 1739.75
## + eFGP 1 1736.56 1740.56
## + BLKP 1 1746.57 1750.57
## + PFGame 1 1746.83 1750.83
## + STLP 1 1751.43 1755.43
## + FTP 1 1752.65 1756.65
## + ThreePAGame 1 1754.87 1758.87
## + ThreePGame 1 1755.28 1759.28
## + ORBP 1 1763.93 1767.93
## + TOVP 1 1765.41 1769.41
## <none> 1769.64 1771.64
## + ThreePP 1 1768.02 1772.02
##
## Step: AIC=984.61
## isAllStar ~ PER
##
## Df Deviance AIC
## + TOVGame 1 916.99 922.99
## + PTSGame 1 921.55 927.55
## + VORP 1 937.50 943.50
## + ASTGame 1 940.73 946.73
## + FTGame 1 943.60 949.60
## + FTAGame 1 944.22 950.22
## + TwoPAGame 1 948.22 954.22
## + DWS 1 951.60 957.60
## + STLGame 1 953.69 959.69
## + WS 1 954.31 960.31
## + TwoPGame 1 959.31 965.31
## + ASTP 1 960.28 966.28
## + FGP 1 960.29 966.29
## + TwoPP 1 960.59 966.59
## + ORBP 1 960.93 966.93
## + USGP 1 960.93 966.93
## + eFGP 1 965.13 971.13
## + BPM 1 967.17 973.17
## + ThreePAGame 1 967.67 973.67
## + ThreePGame 1 970.32 976.32
## + TSP 1 971.05 977.05
## + TRBP 1 971.12 977.12
## + BLKP 1 971.21 977.21
## + ThreePP 1 971.33 977.33
## + OWS 1 973.62 979.62
## + TOVP 1 974.30 980.30
## + OBPM 1 974.35 980.35
## + DRBP 1 976.25 982.25
## + PF 1 976.79 982.79
## + ThreePAr 1 977.77 983.77
## + STLP 1 977.83 983.83
## + BLKGame 1 978.28 984.28
## <none> 980.61 984.61
## + WS48 1 978.62 984.62
## + FTP 1 979.26 985.26
## + DBPM 1 979.78 985.78
## + FTr 1 980.08 986.08
## + PFGame 1 980.56 986.56
## + TRBGame 1 980.61 986.61
##
## Step: AIC=922.99
## isAllStar ~ PER + TOVGame
##
## Df Deviance AIC
## + WS 1 882.31 890.31
## + DWS 1 884.29 892.29
## + VORP 1 885.76 893.76
## + PTSGame 1 900.48 908.48
## + BPM 1 903.15 911.15
## + TOVP 1 904.89 912.89
## + OWS 1 905.87 913.87
## + WS48 1 907.76 915.76
## + TwoPAGame 1 909.40 917.40
## + DBPM 1 910.57 918.57
## + TwoPGame 1 912.03 920.03
## + FTGame 1 912.20 920.20
## + STLGame 1 912.66 920.66
## + FTAGame 1 913.00 921.00
## + ThreePP 1 913.47 921.47
## + ThreePGame 1 913.64 921.64
## + ThreePAGame 1 913.75 921.75
## + TwoPP 1 913.81 921.81
## + ASTGame 1 914.03 922.03
## + ORBP 1 914.03 922.03
## + FGP 1 914.23 922.23
## + TRBGame 1 914.88 922.88
## <none> 916.99 922.99
## + PF 1 915.58 923.58
## + eFGP 1 915.94 923.94
## + TSP 1 916.09 924.09
## + OBPM 1 916.16 924.16
## + ThreePAr 1 916.16 924.16
## + PFGame 1 916.23 924.23
## + BLKP 1 916.57 924.57
## + FTP 1 916.61 924.61
## + FTr 1 916.80 924.80
## + TRBP 1 916.82 924.82
## + USGP 1 916.88 924.88
## + BLKGame 1 916.90 924.90
## + DRBP 1 916.92 924.92
## + STLP 1 916.99 924.99
## + ASTP 1 916.99 924.99
##
## Step: AIC=890.31
## isAllStar ~ PER + TOVGame + WS
##
## Df Deviance AIC
## + TOVP 1 867.57 877.57
## + PTSGame 1 867.65 877.65
## + TwoPAGame 1 868.09 878.09
## + TwoPGame 1 873.37 883.37
## + TSP 1 874.17 884.17
## + USGP 1 874.61 884.61
## + OWS 1 875.20 885.20
## + DWS 1 875.21 885.21
## + PF 1 875.47 885.47
## + TwoPP 1 876.34 886.34
## + eFGP 1 876.71 886.71
## + FGP 1 877.95 887.95
## + FTAGame 1 879.65 889.65
## + FTGame 1 879.93 889.93
## + DBPM 1 880.25 890.25
## <none> 882.31 890.31
## + VORP 1 880.34 890.34
## + TRBGame 1 880.36 890.36
## + WS48 1 880.37 890.37
## + PFGame 1 880.85 890.85
## + ThreePP 1 881.01 891.01
## + ThreePAGame 1 881.05 891.05
## + FTr 1 881.18 891.18
## + ThreePGame 1 881.32 891.32
## + STLGame 1 881.40 891.40
## + ORBP 1 881.48 891.48
## + BPM 1 881.51 891.51
## + OBPM 1 881.67 891.67
## + DRBP 1 881.74 891.74
## + ASTGame 1 881.86 891.86
## + BLKGame 1 881.91 891.91
## + STLP 1 881.99 891.99
## + ASTP 1 882.19 892.19
## + FTP 1 882.24 892.24
## + TRBP 1 882.28 892.28
## + BLKP 1 882.30 892.30
## + ThreePAr 1 882.30 892.30
##
## Step: AIC=877.57
## isAllStar ~ PER + TOVGame + WS + TOVP
##
## Df Deviance AIC
## + OWS 1 858.95 870.95
## + DWS 1 859.01 871.01
## + PF 1 859.17 871.17
## + DBPM 1 860.42 872.42
## + ASTGame 1 863.84 875.84
## + BPM 1 864.37 876.37
## + TSP 1 864.82 876.82
## + VORP 1 865.29 877.29
## + TwoPAGame 1 865.32 877.32
## + TRBGame 1 865.40 877.40
## <none> 867.57 877.57
## + PFGame 1 865.62 877.62
## + DRBP 1 865.87 877.87
## + OBPM 1 866.01 878.01
## + TwoPP 1 866.40 878.40
## + eFGP 1 866.48 878.48
## + BLKGame 1 866.48 878.48
## + ASTP 1 866.52 878.52
## + FTP 1 866.55 878.55
## + TRBP 1 866.82 878.82
## + TwoPGame 1 866.84 878.84
## + STLGame 1 866.88 878.88
## + BLKP 1 866.89 878.89
## + PTSGame 1 866.98 878.98
## + WS48 1 867.05 879.05
## + FGP 1 867.12 879.12
## + ThreePP 1 867.21 879.21
## + FTGame 1 867.36 879.36
## + ThreePAr 1 867.42 879.42
## + USGP 1 867.42 879.42
## + ThreePAGame 1 867.53 879.53
## + ThreePGame 1 867.54 879.54
## + ORBP 1 867.54 879.54
## + FTr 1 867.54 879.54
## + FTAGame 1 867.55 879.55
## + STLP 1 867.57 879.57
##
## Step: AIC=870.95
## isAllStar ~ PER + TOVGame + WS + TOVP + OWS
##
## Df Deviance AIC
## + PF 1 845.48 859.48
## + ASTGame 1 848.58 862.58
## + ASTP 1 854.41 868.41
## + PFGame 1 854.42 868.42
## + PTSGame 1 854.69 868.69
## + ThreePP 1 856.54 870.54
## + ORBP 1 856.63 870.63
## <none> 858.95 870.95
## + BPM 1 857.75 871.75
## + ThreePGame 1 857.83 871.83
## + TwoPP 1 857.84 871.84
## + TRBP 1 857.86 871.86
## + BLKP 1 857.91 871.91
## + FGP 1 857.96 871.96
## + ThreePAGame 1 858.05 872.05
## + OBPM 1 858.10 872.10
## + BLKGame 1 858.37 872.37
## + ThreePAr 1 858.38 872.38
## + VORP 1 858.44 872.44
## + WS48 1 858.47 872.47
## + USGP 1 858.51 872.51
## + DRBP 1 858.57 872.57
## + TwoPAGame 1 858.65 872.65
## + FTP 1 858.71 872.71
## + STLGame 1 858.78 872.78
## + STLP 1 858.78 872.78
## + TSP 1 858.80 872.80
## + DBPM 1 858.82 872.82
## + eFGP 1 858.83 872.83
## + FTr 1 858.89 872.89
## + TRBGame 1 858.91 872.91
## + FTGame 1 858.92 872.92
## + DWS 1 858.93 872.93
## + FTAGame 1 858.93 872.93
## + TwoPGame 1 858.95 872.95
##
## Step: AIC=859.48
## isAllStar ~ PER + TOVGame + WS + TOVP + OWS + PF
##
## Df Deviance AIC
## + PTSGame 1 841.17 857.17
## + ASTGame 1 842.33 858.33
## + TwoPAGame 1 842.52 858.52
## + PFGame 1 842.80 858.80
## <none> 845.48 859.48
## + TRBGame 1 843.80 859.80
## + TwoPGame 1 843.97 859.97
## + STLP 1 844.44 860.44
## + DRBP 1 844.82 860.82
## + WS48 1 844.96 860.96
## + DBPM 1 844.96 860.96
## + TRBP 1 845.01 861.01
## + ASTP 1 845.08 861.08
## + ThreePAr 1 845.09 861.09
## + ThreePP 1 845.16 861.16
## + BLKGame 1 845.20 861.20
## + FTAGame 1 845.21 861.21
## + OBPM 1 845.22 861.22
## + FTr 1 845.28 861.28
## + FTGame 1 845.29 861.29
## + TwoPP 1 845.30 861.30
## + FTP 1 845.30 861.30
## + ThreePAGame 1 845.35 861.35
## + USGP 1 845.36 861.36
## + BLKP 1 845.37 861.37
## + TSP 1 845.38 861.38
## + ORBP 1 845.39 861.39
## + STLGame 1 845.42 861.42
## + DWS 1 845.44 861.44
## + eFGP 1 845.44 861.44
## + ThreePGame 1 845.45 861.45
## + VORP 1 845.46 861.46
## + FGP 1 845.47 861.47
## + BPM 1 845.47 861.47
##
## Step: AIC=857.17
## isAllStar ~ PER + TOVGame + WS + TOVP + OWS + PF + PTSGame
##
## Df Deviance AIC
## + ASTGame 1 833.42 851.42
## + ASTP 1 838.76 856.76
## + TwoPAGame 1 839.11 857.11
## <none> 841.17 857.17
## + PFGame 1 839.19 857.19
## + TSP 1 839.40 857.40
## + TRBGame 1 839.62 857.62
## + DBPM 1 840.00 858.00
## + eFGP 1 840.19 858.19
## + USGP 1 840.22 858.22
## + ThreePAr 1 840.34 858.34
## + TwoPP 1 840.47 858.47
## + TwoPGame 1 840.50 858.50
## + DRBP 1 840.56 858.56
## + ThreePAGame 1 840.56 858.56
## + WS48 1 840.57 858.57
## + TRBP 1 840.59 858.59
## + STLP 1 840.68 858.68
## + FTP 1 840.69 858.69
## + ThreePGame 1 840.69 858.69
## + BLKGame 1 840.76 858.76
## + ORBP 1 840.84 858.84
## + BLKP 1 840.93 858.93
## + VORP 1 840.96 858.96
## + OBPM 1 840.96 858.96
## + BPM 1 841.03 859.03
## + FGP 1 841.09 859.09
## + FTr 1 841.10 859.10
## + DWS 1 841.11 859.11
## + FTGame 1 841.12 859.12
## + ThreePP 1 841.13 859.13
## + STLGame 1 841.17 859.17
## + FTAGame 1 841.17 859.17
##
## Step: AIC=851.42
## isAllStar ~ PER + TOVGame + WS + TOVP + OWS + PF + PTSGame +
## ASTGame
##
## Df Deviance AIC
## + ASTP 1 824.05 844.05
## + TRBGame 1 825.48 845.48
## + TRBP 1 825.64 845.64
## + ORBP 1 825.80 845.80
## + DRBP 1 828.39 848.39
## + OBPM 1 829.60 849.60
## + BLKGame 1 829.76 849.76
## + DBPM 1 829.78 849.78
## + BLKP 1 830.11 850.11
## + STLP 1 830.14 850.14
## + ThreePAr 1 830.37 850.37
## + ThreePAGame 1 830.51 850.51
## + FTr 1 830.66 850.66
## + PFGame 1 830.98 850.98
## + ThreePGame 1 831.15 851.15
## + TwoPAGame 1 831.32 851.32
## <none> 833.42 851.42
## + STLGame 1 831.92 851.92
## + TwoPGame 1 832.03 852.03
## + FTAGame 1 832.05 852.05
## + USGP 1 832.18 852.18
## + FGP 1 832.38 852.38
## + FTP 1 832.43 852.43
## + FTGame 1 832.81 852.81
## + WS48 1 833.07 853.07
## + ThreePP 1 833.32 853.32
## + BPM 1 833.37 853.37
## + eFGP 1 833.38 853.38
## + TwoPP 1 833.40 853.40
## + VORP 1 833.40 853.40
## + TSP 1 833.41 853.41
## + DWS 1 833.42 853.42
##
## Step: AIC=844.05
## isAllStar ~ PER + TOVGame + WS + TOVP + OWS + PF + PTSGame +
## ASTGame + ASTP
##
## Df Deviance AIC
## + STLGame 1 821.15 843.15
## + STLP 1 821.24 843.24
## + FTr 1 821.63 843.63
## + ORBP 1 821.93 843.93
## + USGP 1 822.00 844.00
## + TRBP 1 822.01 844.01
## <none> 824.05 844.05
## + TRBGame 1 822.14 844.14
## + ThreePAGame 1 822.28 844.28
## + ThreePAr 1 822.32 844.32
## + TwoPAGame 1 822.68 844.68
## + FTAGame 1 822.72 844.72
## + ThreePGame 1 822.76 844.76
## + DRBP 1 822.95 844.95
## + FTGame 1 823.05 845.05
## + OBPM 1 823.09 845.09
## + PFGame 1 823.10 845.10
## + DBPM 1 823.25 845.25
## + BLKGame 1 823.27 845.27
## + BLKP 1 823.37 845.37
## + TwoPGame 1 823.54 845.54
## + eFGP 1 823.70 845.70
## + WS48 1 823.85 845.85
## + TwoPP 1 823.86 845.86
## + FTP 1 823.94 845.94
## + FGP 1 823.94 845.94
## + VORP 1 823.99 845.99
## + TSP 1 824.01 846.01
## + BPM 1 824.03 846.03
## + ThreePP 1 824.04 846.04
## + DWS 1 824.04 846.04
##
## Step: AIC=843.15
## isAllStar ~ PER + TOVGame + WS + TOVP + OWS + PF + PTSGame +
## ASTGame + ASTP + STLGame
##
## Df Deviance AIC
## + FTr 1 818.49 842.49
## <none> 821.15 843.15
## + FTAGame 1 819.64 843.64
## + DBPM 1 819.70 843.70
## + FTGame 1 819.92 843.92
## + USGP 1 819.93 843.93
## + ORBP 1 819.98 843.98
## + PFGame 1 820.01 844.01
## + TRBGame 1 820.27 844.27
## + ThreePAr 1 820.30 844.30
## + ThreePAGame 1 820.34 844.34
## + TRBP 1 820.39 844.39
## + TwoPAGame 1 820.53 844.53
## + ThreePGame 1 820.58 844.58
## + eFGP 1 820.61 844.61
## + BPM 1 820.75 844.75
## + TwoPP 1 820.80 844.80
## + DRBP 1 820.86 844.86
## + VORP 1 820.89 844.89
## + WS48 1 820.95 844.95
## + BLKGame 1 820.95 844.95
## + BLKP 1 821.03 845.03
## + OBPM 1 821.05 845.05
## + FTP 1 821.06 845.06
## + TSP 1 821.07 845.07
## + ThreePP 1 821.07 845.07
## + TwoPGame 1 821.08 845.08
## + FGP 1 821.14 845.14
## + DWS 1 821.15 845.15
## + STLP 1 821.15 845.15
##
## Step: AIC=842.49
## isAllStar ~ PER + TOVGame + WS + TOVP + OWS + PF + PTSGame +
## ASTGame + ASTP + STLGame + FTr
##
## Df Deviance AIC
## <none> 818.49 842.49
## + USGP 1 816.97 842.97
## + ORBP 1 817.27 843.27
## + DBPM 1 817.29 843.29
## + TRBGame 1 817.51 843.51
## + TwoPAGame 1 817.60 843.60
## + TRBP 1 817.65 843.65
## + FTAGame 1 817.80 843.80
## + WS48 1 817.85 843.85
## + PFGame 1 817.90 843.90
## + VORP 1 818.03 844.03
## + BPM 1 818.03 844.03
## + ThreePAr 1 818.10 844.10
## + ThreePAGame 1 818.14 844.14
## + DRBP 1 818.16 844.16
## + ThreePP 1 818.19 844.19
## + FTGame 1 818.25 844.25
## + TwoPGame 1 818.25 844.25
## + TwoPP 1 818.29 844.29
## + TSP 1 818.30 844.30
## + BLKGame 1 818.34 844.34
## + ThreePGame 1 818.36 844.36
## + BLKP 1 818.41 844.41
## + eFGP 1 818.41 844.41
## + OBPM 1 818.46 844.46
## + DWS 1 818.47 844.47
## + STLP 1 818.49 844.49
## + FGP 1 818.49 844.49
## + FTP 1 818.49 844.49summary(seasonstatsmodel.glm.fwd)##
## Call:
## glm(formula = isAllStar ~ PER + TOVGame + WS + TOVP + OWS + PF +
## PTSGame + ASTGame + ASTP + STLGame + FTr, family = "binomial",
## data = seasonstatsmodel.train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.20927 -0.23958 -0.10281 -0.04741 3.00470
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -12.650194 1.609283 -7.861 3.82e-15 ***
## PER 0.287937 0.054005 5.332 9.73e-08 ***
## TOVGame -0.332723 0.606091 -0.549 0.58303
## WS 0.545897 0.083794 6.515 7.28e-11 ***
## TOVP 0.060048 0.107118 0.561 0.57508
## OWS -0.584125 0.108786 -5.369 7.90e-08 ***
## PF -0.004080 0.002345 -1.740 0.08187 .
## PTSGame 0.248910 0.086470 2.879 0.00399 **
## ASTGame 0.884862 0.211441 4.185 2.85e-05 ***
## ASTP -0.133102 0.042741 -3.114 0.00184 **
## STLGame -0.452017 0.256846 -1.760 0.07843 .
## FTr 1.645029 1.001094 1.643 0.10033
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1769.64 on 2498 degrees of freedom
## Residual deviance: 818.49 on 2487 degrees of freedom
## AIC: 842.49
##
## Number of Fisher Scoring iterations: 7sum.fwd <- summary(seasonstatsmodel.glm.fwd)
dim(sum.fwd$coefficients)## [1] 12 4AIC(seasonstatsmodel.glm.fwd)## [1] 842.488pred.glm.train2 <- predict(seasonstatsmodel.glm.fwd, type = "response")
pred.glm.valid2 <- predict(seasonstatsmodel.glm.fwd, newdata = seasonstatsmodel.valid, type = "response")
confusionMatrix(as.factor(ifelse(pred.glm.train2 >= optimal.pcut.glm, "1", "0")), as.factor(seasonstatsmodel.train$isAllStar),
positive = "1")## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 1224 0
## 1 991 284
##
## Accuracy : 0.6034
## 95% CI : (0.5839, 0.6227)
## No Information Rate : 0.8864
## P-Value [Acc > NIR] : 1
##
## Kappa : 0.2192
##
## Mcnemar's Test P-Value : <2e-16
##
## Sensitivity : 1.0000
## Specificity : 0.5526
## Pos Pred Value : 0.2227
## Neg Pred Value : 1.0000
## Prevalence : 0.1136
## Detection Rate : 0.1136
## Detection Prevalence : 0.5102
## Balanced Accuracy : 0.7763
##
## 'Positive' Class : 1
## #0.8455 accuracy
#Perform backward elimination - Best
seasonstatsmodel.glm.back <- step(seasonstatsmodel.glm.full, direction = "backward")## Start: AIC=872.89
## isAllStar ~ PF + PER + TSP + ThreePAr + FTr + ORBP + DRBP + TRBP +
## ASTP + STLP + BLKP + TOVP + USGP + OWS + DWS + WS + WS48 +
## OBPM + DBPM + BPM + VORP + FGP + ThreePP + TwoPP + eFGP +
## FTP + TOVGame + STLGame + BLKGame + PTSGame + TRBGame + ASTGame +
## FTGame + FTAGame + PFGame + TwoPGame + TwoPAGame + ThreePAGame +
## ThreePGame
##
##
## Step: AIC=872.89
## isAllStar ~ PF + PER + TSP + ThreePAr + FTr + ORBP + DRBP + TRBP +
## ASTP + STLP + BLKP + TOVP + USGP + OWS + DWS + WS + WS48 +
## OBPM + DBPM + BPM + VORP + FGP + ThreePP + TwoPP + eFGP +
## FTP + TOVGame + STLGame + BLKGame + PTSGame + TRBGame + ASTGame +
## FTGame + FTAGame + PFGame + TwoPGame + TwoPAGame + ThreePAGame
##
## Df Deviance AIC
## - FTP 1 794.89 870.89
## - OWS 1 794.89 870.89
## - BLKGame 1 794.90 870.90
## - DWS 1 794.91 870.91
## - WS 1 794.93 870.93
## - TSP 1 794.96 870.96
## - STLP 1 794.97 870.97
## - BLKP 1 794.98 870.98
## - PFGame 1 795.00 871.00
## - STLGame 1 795.03 871.03
## - ThreePAGame 1 795.03 871.03
## - PTSGame 1 795.08 871.08
## - TOVP 1 795.17 871.17
## - WS48 1 795.18 871.18
## - TwoPGame 1 795.26 871.26
## - TwoPAGame 1 795.27 871.27
## - DRBP 1 795.30 871.30
## - PER 1 795.36 871.36
## - OBPM 1 795.46 871.46
## - DBPM 1 795.56 871.56
## - VORP 1 795.56 871.56
## - ThreePP 1 795.60 871.60
## - ORBP 1 795.77 871.77
## - TRBP 1 795.82 871.82
## - BPM 1 795.85 871.85
## - TwoPP 1 796.03 872.03
## - FTGame 1 796.08 872.08
## - FTAGame 1 796.63 872.63
## <none> 794.89 872.89
## - FGP 1 796.96 872.96
## - ThreePAr 1 796.99 872.99
## - eFGP 1 797.15 873.15
## - TRBGame 1 797.52 873.52
## - TOVGame 1 797.60 873.60
## - PF 1 797.74 873.74
## - FTr 1 798.00 874.00
## - ASTP 1 801.86 877.86
## - USGP 1 803.87 879.87
## - ASTGame 1 812.53 888.53
##
## Step: AIC=870.89
## isAllStar ~ PF + PER + TSP + ThreePAr + FTr + ORBP + DRBP + TRBP +
## ASTP + STLP + BLKP + TOVP + USGP + OWS + DWS + WS + WS48 +
## OBPM + DBPM + BPM + VORP + FGP + ThreePP + TwoPP + eFGP +
## TOVGame + STLGame + BLKGame + PTSGame + TRBGame + ASTGame +
## FTGame + FTAGame + PFGame + TwoPGame + TwoPAGame + ThreePAGame
##
## Df Deviance AIC
## - OWS 1 794.89 868.89
## - BLKGame 1 794.90 868.90
## - DWS 1 794.91 868.91
## - WS 1 794.93 868.93
## - STLP 1 794.97 868.97
## - BLKP 1 794.98 868.98
## - TSP 1 794.98 868.98
## - PFGame 1 795.00 869.00
## - STLGame 1 795.03 869.03
## - ThreePAGame 1 795.03 869.03
## - PTSGame 1 795.08 869.08
## - TOVP 1 795.17 869.17
## - WS48 1 795.18 869.18
## - TwoPGame 1 795.26 869.26
## - TwoPAGame 1 795.27 869.27
## - DRBP 1 795.30 869.30
## - PER 1 795.36 869.36
## - OBPM 1 795.46 869.46
## - DBPM 1 795.56 869.56
## - VORP 1 795.56 869.56
## - ThreePP 1 795.60 869.60
## - ORBP 1 795.78 869.78
## - TRBP 1 795.82 869.82
## - BPM 1 795.85 869.85
## - TwoPP 1 796.06 870.06
## - FTGame 1 796.14 870.14
## <none> 794.89 870.89
## - FGP 1 796.97 870.97
## - FTAGame 1 796.99 870.99
## - ThreePAr 1 796.99 870.99
## - eFGP 1 797.18 871.18
## - TRBGame 1 797.56 871.56
## - TOVGame 1 797.62 871.62
## - PF 1 797.74 871.74
## - FTr 1 798.00 872.00
## - ASTP 1 801.87 875.87
## - USGP 1 803.87 877.87
## - ASTGame 1 812.59 886.59
##
## Step: AIC=868.89
## isAllStar ~ PF + PER + TSP + ThreePAr + FTr + ORBP + DRBP + TRBP +
## ASTP + STLP + BLKP + TOVP + USGP + DWS + WS + WS48 + OBPM +
## DBPM + BPM + VORP + FGP + ThreePP + TwoPP + eFGP + TOVGame +
## STLGame + BLKGame + PTSGame + TRBGame + ASTGame + FTGame +
## FTAGame + PFGame + TwoPGame + TwoPAGame + ThreePAGame
##
## Df Deviance AIC
## - BLKGame 1 794.91 866.91
## - STLP 1 794.97 866.97
## - BLKP 1 794.98 866.98
## - TSP 1 794.99 866.99
## - PFGame 1 795.01 867.01
## - STLGame 1 795.03 867.03
## - ThreePAGame 1 795.04 867.04
## - PTSGame 1 795.09 867.09
## - TOVP 1 795.17 867.17
## - WS48 1 795.19 867.19
## - TwoPGame 1 795.27 867.27
## - TwoPAGame 1 795.27 867.27
## - DRBP 1 795.30 867.30
## - PER 1 795.37 867.37
## - OBPM 1 795.46 867.46
## - VORP 1 795.57 867.57
## - DBPM 1 795.57 867.57
## - ThreePP 1 795.60 867.60
## - ORBP 1 795.79 867.79
## - TRBP 1 795.83 867.83
## - BPM 1 795.85 867.85
## - TwoPP 1 796.06 868.06
## - FTGame 1 796.16 868.16
## - WS 1 796.43 868.43
## <none> 794.89 868.89
## - FGP 1 796.97 868.97
## - ThreePAr 1 796.99 868.99
## - FTAGame 1 797.03 869.03
## - eFGP 1 797.18 869.18
## - DWS 1 797.26 869.26
## - TRBGame 1 797.56 869.56
## - TOVGame 1 797.63 869.63
## - PF 1 797.76 869.76
## - FTr 1 798.04 870.04
## - ASTP 1 801.88 873.88
## - USGP 1 803.88 875.88
## - ASTGame 1 812.59 884.59
##
## Step: AIC=866.91
## isAllStar ~ PF + PER + TSP + ThreePAr + FTr + ORBP + DRBP + TRBP +
## ASTP + STLP + BLKP + TOVP + USGP + DWS + WS + WS48 + OBPM +
## DBPM + BPM + VORP + FGP + ThreePP + TwoPP + eFGP + TOVGame +
## STLGame + PTSGame + TRBGame + ASTGame + FTGame + FTAGame +
## PFGame + TwoPGame + TwoPAGame + ThreePAGame
##
## Df Deviance AIC
## - STLP 1 794.98 864.98
## - TSP 1 795.00 865.00
## - STLGame 1 795.04 865.04
## - PFGame 1 795.04 865.04
## - ThreePAGame 1 795.05 865.05
## - PTSGame 1 795.10 865.10
## - TOVP 1 795.18 865.18
## - WS48 1 795.23 865.23
## - TwoPGame 1 795.28 865.28
## - TwoPAGame 1 795.30 865.30
## - DRBP 1 795.30 865.30
## - PER 1 795.37 865.37
## - OBPM 1 795.47 865.47
## - DBPM 1 795.58 865.58
## - VORP 1 795.58 865.58
## - ThreePP 1 795.61 865.61
## - ORBP 1 795.79 865.79
## - TRBP 1 795.83 865.83
## - BLKP 1 795.86 865.86
## - BPM 1 795.86 865.86
## - TwoPP 1 796.08 866.08
## - FTGame 1 796.16 866.16
## - WS 1 796.45 866.45
## <none> 794.91 866.91
## - FGP 1 797.00 867.00
## - ThreePAr 1 797.03 867.03
## - FTAGame 1 797.03 867.03
## - eFGP 1 797.21 867.21
## - DWS 1 797.43 867.43
## - TOVGame 1 797.63 867.63
## - PF 1 797.83 867.83
## - FTr 1 798.04 868.04
## - TRBGame 1 798.97 868.97
## - ASTP 1 801.89 871.89
## - USGP 1 803.89 873.89
## - ASTGame 1 812.66 882.66
##
## Step: AIC=864.98
## isAllStar ~ PF + PER + TSP + ThreePAr + FTr + ORBP + DRBP + TRBP +
## ASTP + BLKP + TOVP + USGP + DWS + WS + WS48 + OBPM + DBPM +
## BPM + VORP + FGP + ThreePP + TwoPP + eFGP + TOVGame + STLGame +
## PTSGame + TRBGame + ASTGame + FTGame + FTAGame + PFGame +
## TwoPGame + TwoPAGame + ThreePAGame
##
## Df Deviance AIC
## - TSP 1 795.07 863.07
## - PFGame 1 795.10 863.10
## - STLGame 1 795.10 863.10
## - ThreePAGame 1 795.15 863.15
## - PTSGame 1 795.18 863.18
## - TOVP 1 795.22 863.22
## - WS48 1 795.27 863.27
## - TwoPAGame 1 795.35 863.35
## - DRBP 1 795.37 863.37
## - TwoPGame 1 795.38 863.38
## - PER 1 795.49 863.49
## - OBPM 1 795.54 863.54
## - VORP 1 795.59 863.59
## - DBPM 1 795.65 863.65
## - ThreePP 1 795.68 863.68
## - ORBP 1 795.86 863.86
## - TRBP 1 795.90 863.90
## - BPM 1 795.92 863.92
## - BLKP 1 796.03 864.03
## - TwoPP 1 796.16 864.16
## - FTGame 1 796.28 864.28
## - WS 1 796.46 864.46
## <none> 794.98 864.98
## - FTAGame 1 797.09 865.09
## - FGP 1 797.15 865.15
## - ThreePAr 1 797.20 865.20
## - eFGP 1 797.36 865.36
## - DWS 1 797.55 865.55
## - TOVGame 1 797.63 865.63
## - PF 1 797.90 865.90
## - FTr 1 798.11 866.11
## - TRBGame 1 799.30 867.30
## - ASTP 1 802.60 870.60
## - USGP 1 804.09 872.09
## - ASTGame 1 816.03 884.03
##
## Step: AIC=863.07
## isAllStar ~ PF + PER + ThreePAr + FTr + ORBP + DRBP + TRBP +
## ASTP + BLKP + TOVP + USGP + DWS + WS + WS48 + OBPM + DBPM +
## BPM + VORP + FGP + ThreePP + TwoPP + eFGP + TOVGame + STLGame +
## PTSGame + TRBGame + ASTGame + FTGame + FTAGame + PFGame +
## TwoPGame + TwoPAGame + ThreePAGame
##
## Df Deviance AIC
## - PFGame 1 795.19 861.19
## - STLGame 1 795.21 861.21
## - ThreePAGame 1 795.26 861.26
## - PTSGame 1 795.26 861.26
## - TwoPAGame 1 795.37 861.37
## - WS48 1 795.37 861.37
## - TOVP 1 795.38 861.38
## - TwoPGame 1 795.44 861.44
## - DRBP 1 795.44 861.44
## - PER 1 795.59 861.59
## - OBPM 1 795.62 861.62
## - VORP 1 795.68 861.68
## - DBPM 1 795.73 861.73
## - ThreePP 1 795.78 861.78
## - ORBP 1 795.93 861.93
## - TRBP 1 795.96 861.96
## - BPM 1 796.00 862.00
## - BLKP 1 796.17 862.17
## - TwoPP 1 796.20 862.20
## - FTGame 1 796.53 862.53
## - WS 1 796.59 862.59
## <none> 795.07 863.07
## - FGP 1 797.16 863.16
## - ThreePAr 1 797.23 863.23
## - eFGP 1 797.41 863.41
## - DWS 1 797.69 863.69
## - TOVGame 1 797.97 863.97
## - PF 1 798.10 864.10
## - FTr 1 798.29 864.29
## - FTAGame 1 798.74 864.74
## - TRBGame 1 799.34 865.34
## - ASTP 1 802.63 868.63
## - USGP 1 804.16 870.16
## - ASTGame 1 816.07 882.07
##
## Step: AIC=861.19
## isAllStar ~ PF + PER + ThreePAr + FTr + ORBP + DRBP + TRBP +
## ASTP + BLKP + TOVP + USGP + DWS + WS + WS48 + OBPM + DBPM +
## BPM + VORP + FGP + ThreePP + TwoPP + eFGP + TOVGame + STLGame +
## PTSGame + TRBGame + ASTGame + FTGame + FTAGame + TwoPGame +
## TwoPAGame + ThreePAGame
##
## Df Deviance AIC
## - ThreePAGame 1 795.34 859.34
## - PTSGame 1 795.35 859.35
## - WS48 1 795.37 859.37
## - TOVP 1 795.52 859.52
## - STLGame 1 795.53 859.53
## - TwoPGame 1 795.54 859.54
## - TwoPAGame 1 795.56 859.56
## - DRBP 1 795.61 859.61
## - OBPM 1 795.71 859.71
## - VORP 1 795.74 859.74
## - DBPM 1 795.84 859.84
## - ThreePP 1 795.89 859.89
## - BPM 1 796.08 860.08
## - ORBP 1 796.14 860.14
## - TRBP 1 796.18 860.18
## - PER 1 796.22 860.22
## - TwoPP 1 796.28 860.28
## - FTGame 1 796.60 860.60
## - WS 1 796.67 860.67
## - BLKP 1 796.83 860.83
## <none> 795.19 861.19
## - FGP 1 797.23 861.23
## - ThreePAr 1 797.30 861.30
## - eFGP 1 797.48 861.48
## - DWS 1 797.72 861.72
## - TOVGame 1 798.36 862.36
## - FTr 1 798.38 862.38
## - FTAGame 1 798.93 862.93
## - TRBGame 1 800.55 864.55
## - PF 1 802.04 866.04
## - ASTP 1 802.67 866.67
## - USGP 1 806.27 870.27
## - ASTGame 1 816.91 880.91
##
## Step: AIC=859.34
## isAllStar ~ PF + PER + ThreePAr + FTr + ORBP + DRBP + TRBP +
## ASTP + BLKP + TOVP + USGP + DWS + WS + WS48 + OBPM + DBPM +
## BPM + VORP + FGP + ThreePP + TwoPP + eFGP + TOVGame + STLGame +
## PTSGame + TRBGame + ASTGame + FTGame + FTAGame + TwoPGame +
## TwoPAGame
##
## Df Deviance AIC
## - PTSGame 1 795.35 857.35
## - WS48 1 795.53 857.53
## - TwoPGame 1 795.64 857.64
## - TOVP 1 795.66 857.66
## - TwoPAGame 1 795.66 857.66
## - STLGame 1 795.74 857.74
## - DRBP 1 795.79 857.79
## - OBPM 1 795.85 857.85
## - VORP 1 795.92 857.92
## - DBPM 1 795.99 857.99
## - ThreePP 1 796.00 858.00
## - BPM 1 796.24 858.24
## - ORBP 1 796.34 858.34
## - TRBP 1 796.35 858.35
## - TwoPP 1 796.42 858.42
## - PER 1 796.51 858.51
## - WS 1 796.83 858.83
## - BLKP 1 797.14 859.14
## <none> 795.34 859.34
## - DWS 1 797.99 859.99
## - FTr 1 798.39 860.39
## - TOVGame 1 798.53 860.53
## - FGP 1 798.64 860.64
## - FTGame 1 798.73 860.73
## - FTAGame 1 798.96 860.96
## - ThreePAr 1 799.30 861.30
## - eFGP 1 800.27 862.27
## - TRBGame 1 800.64 862.64
## - PF 1 802.51 864.51
## - ASTP 1 802.85 864.85
## - USGP 1 806.73 868.73
## - ASTGame 1 817.43 879.43
##
## Step: AIC=857.35
## isAllStar ~ PF + PER + ThreePAr + FTr + ORBP + DRBP + TRBP +
## ASTP + BLKP + TOVP + USGP + DWS + WS + WS48 + OBPM + DBPM +
## BPM + VORP + FGP + ThreePP + TwoPP + eFGP + TOVGame + STLGame +
## TRBGame + ASTGame + FTGame + FTAGame + TwoPGame + TwoPAGame
##
## Df Deviance AIC
## - WS48 1 795.54 855.54
## - TwoPGame 1 795.64 855.64
## - TwoPAGame 1 795.67 855.67
## - TOVP 1 795.71 855.71
## - STLGame 1 795.75 855.75
## - DRBP 1 795.79 855.79
## - OBPM 1 795.86 855.86
## - VORP 1 795.92 855.92
## - DBPM 1 795.99 855.99
## - ThreePP 1 796.00 856.00
## - BPM 1 796.24 856.24
## - ORBP 1 796.34 856.34
## - TRBP 1 796.37 856.37
## - TwoPP 1 796.45 856.45
## - PER 1 796.54 856.54
## - WS 1 796.83 856.83
## - BLKP 1 797.23 857.23
## <none> 795.35 857.35
## - DWS 1 798.00 858.00
## - FTr 1 798.46 858.46
## - FGP 1 798.64 858.64
## - TOVGame 1 798.72 858.72
## - FTAGame 1 798.96 858.96
## - FTGame 1 799.28 859.28
## - ThreePAr 1 799.31 859.31
## - eFGP 1 800.34 860.34
## - TRBGame 1 801.02 861.02
## - PF 1 802.70 862.70
## - ASTP 1 804.42 864.42
## - USGP 1 809.42 869.42
## - ASTGame 1 821.51 881.51
##
## Step: AIC=855.54
## isAllStar ~ PF + PER + ThreePAr + FTr + ORBP + DRBP + TRBP +
## ASTP + BLKP + TOVP + USGP + DWS + WS + OBPM + DBPM + BPM +
## VORP + FGP + ThreePP + TwoPP + eFGP + TOVGame + STLGame +
## TRBGame + ASTGame + FTGame + FTAGame + TwoPGame + TwoPAGame
##
## Df Deviance AIC
## - TwoPGame 1 795.87 853.87
## - TwoPAGame 1 795.87 853.87
## - VORP 1 795.92 853.92
## - TOVP 1 795.96 853.96
## - OBPM 1 796.06 854.06
## - DRBP 1 796.10 854.10
## - STLGame 1 796.20 854.20
## - ThreePP 1 796.20 854.20
## - DBPM 1 796.22 854.22
## - BPM 1 796.39 854.39
## - TwoPP 1 796.63 854.63
## - ORBP 1 796.66 854.66
## - TRBP 1 796.72 854.72
## - WS 1 796.85 854.85
## <none> 795.54 855.54
## - PER 1 797.72 855.72
## - DWS 1 798.00 856.00
## - BLKP 1 798.10 856.10
## - FTr 1 798.56 856.56
## - FGP 1 798.81 856.81
## - TOVGame 1 798.93 856.93
## - FTAGame 1 799.02 857.02
## - FTGame 1 799.30 857.30
## - ThreePAr 1 799.49 857.49
## - eFGP 1 800.49 858.49
## - TRBGame 1 801.60 859.60
## - PF 1 802.79 860.79
## - ASTP 1 804.43 862.43
## - USGP 1 811.23 869.23
## - ASTGame 1 821.52 879.52
##
## Step: AIC=853.87
## isAllStar ~ PF + PER + ThreePAr + FTr + ORBP + DRBP + TRBP +
## ASTP + BLKP + TOVP + USGP + DWS + WS + OBPM + DBPM + BPM +
## VORP + FGP + ThreePP + TwoPP + eFGP + TOVGame + STLGame +
## TRBGame + ASTGame + FTGame + FTAGame + TwoPAGame
##
## Df Deviance AIC
## - TwoPAGame 1 795.88 851.88
## - VORP 1 796.22 852.22
## - STLGame 1 796.27 852.27
## - TOVP 1 796.29 852.29
## - DRBP 1 796.35 852.35
## - OBPM 1 796.46 852.46
## - ThreePP 1 796.54 852.54
## - DBPM 1 796.57 852.57
## - BPM 1 796.76 852.76
## - ORBP 1 796.86 852.86
## - TRBP 1 797.01 853.01
## - TwoPP 1 797.04 853.04
## - WS 1 797.11 853.11
## - PER 1 797.76 853.76
## <none> 795.87 853.87
## - BLKP 1 798.10 854.10
## - DWS 1 798.18 854.18
## - FTr 1 798.56 854.56
## - FGP 1 798.96 854.96
## - FTAGame 1 799.03 855.03
## - TOVGame 1 799.05 855.05
## - FTGame 1 799.31 855.31
## - ThreePAr 1 799.64 855.64
## - eFGP 1 800.87 856.87
## - TRBGame 1 802.25 858.25
## - PF 1 802.82 858.82
## - ASTP 1 805.30 861.30
## - USGP 1 811.40 867.40
## - ASTGame 1 821.57 877.57
##
## Step: AIC=851.88
## isAllStar ~ PF + PER + ThreePAr + FTr + ORBP + DRBP + TRBP +
## ASTP + BLKP + TOVP + USGP + DWS + WS + OBPM + DBPM + BPM +
## VORP + FGP + ThreePP + TwoPP + eFGP + TOVGame + STLGame +
## TRBGame + ASTGame + FTGame + FTAGame
##
## Df Deviance AIC
## - VORP 1 796.24 850.24
## - STLGame 1 796.28 850.28
## - DRBP 1 796.36 850.36
## - TOVP 1 796.38 850.38
## - OBPM 1 796.48 850.48
## - ThreePP 1 796.56 850.56
## - DBPM 1 796.58 850.58
## - BPM 1 796.78 850.78
## - ORBP 1 796.87 850.87
## - TRBP 1 797.01 851.01
## - TwoPP 1 797.06 851.06
## - WS 1 797.13 851.13
## - PER 1 797.76 851.76
## <none> 795.88 851.88
## - BLKP 1 798.11 852.11
## - DWS 1 798.23 852.23
## - FGP 1 798.96 852.96
## - TOVGame 1 799.09 853.09
## - FTAGame 1 799.22 853.22
## - FTGame 1 799.31 853.31
## - FTr 1 799.53 853.53
## - ThreePAr 1 799.99 853.99
## - eFGP 1 800.88 854.88
## - PF 1 802.83 856.83
## - TRBGame 1 805.05 859.05
## - ASTP 1 805.75 859.75
## - USGP 1 817.62 871.62
## - ASTGame 1 824.23 878.23
##
## Step: AIC=850.24
## isAllStar ~ PF + PER + ThreePAr + FTr + ORBP + DRBP + TRBP +
## ASTP + BLKP + TOVP + USGP + DWS + WS + OBPM + DBPM + BPM +
## FGP + ThreePP + TwoPP + eFGP + TOVGame + STLGame + TRBGame +
## ASTGame + FTGame + FTAGame
##
## Df Deviance AIC
## - STLGame 1 796.48 848.48
## - DRBP 1 796.64 848.64
## - TOVP 1 796.69 848.69
## - OBPM 1 796.84 848.84
## - ThreePP 1 796.90 848.90
## - DBPM 1 796.93 848.93
## - BPM 1 797.05 849.05
## - ORBP 1 797.13 849.13
## - WS 1 797.18 849.18
## - TRBP 1 797.26 849.26
## - TwoPP 1 797.41 849.41
## - PER 1 797.77 849.77
## - BLKP 1 798.15 850.15
## <none> 796.24 850.24
## - DWS 1 798.93 850.93
## - FGP 1 799.36 851.36
## - TOVGame 1 799.50 851.50
## - FTAGame 1 799.75 851.75
## - FTr 1 799.96 851.96
## - FTGame 1 800.06 852.06
## - ThreePAr 1 800.37 852.37
## - eFGP 1 801.36 853.36
## - PF 1 803.02 855.02
## - TRBGame 1 805.16 857.16
## - ASTP 1 805.86 857.86
## - USGP 1 817.82 869.82
## - ASTGame 1 824.27 876.27
##
## Step: AIC=848.48
## isAllStar ~ PF + PER + ThreePAr + FTr + ORBP + DRBP + TRBP +
## ASTP + BLKP + TOVP + USGP + DWS + WS + OBPM + DBPM + BPM +
## FGP + ThreePP + TwoPP + eFGP + TOVGame + TRBGame + ASTGame +
## FTGame + FTAGame
##
## Df Deviance AIC
## - TOVP 1 796.86 846.86
## - DRBP 1 796.98 846.98
## - OBPM 1 797.12 847.12
## - ThreePP 1 797.14 847.14
## - DBPM 1 797.16 847.16
## - WS 1 797.24 847.24
## - BPM 1 797.32 847.32
## - ORBP 1 797.51 847.51
## - TwoPP 1 797.59 847.59
## - TRBP 1 797.73 847.73
## - PER 1 797.84 847.84
## - BLKP 1 798.29 848.29
## <none> 796.48 848.48
## - DWS 1 799.20 849.20
## - FGP 1 799.45 849.45
## - TOVGame 1 799.50 849.50
## - FTAGame 1 799.78 849.78
## - FTGame 1 800.08 850.08
## - FTr 1 800.21 850.21
## - ThreePAr 1 800.39 850.39
## - eFGP 1 801.37 851.37
## - PF 1 803.15 853.15
## - TRBGame 1 805.23 855.23
## - ASTP 1 807.86 857.86
## - USGP 1 819.41 869.41
## - ASTGame 1 825.43 875.43
##
## Step: AIC=846.86
## isAllStar ~ PF + PER + ThreePAr + FTr + ORBP + DRBP + TRBP +
## ASTP + BLKP + USGP + DWS + WS + OBPM + DBPM + BPM + FGP +
## ThreePP + TwoPP + eFGP + TOVGame + TRBGame + ASTGame + FTGame +
## FTAGame
##
## Df Deviance AIC
## - DRBP 1 797.29 845.29
## - ThreePP 1 797.51 845.51
## - DBPM 1 797.54 845.54
## - OBPM 1 797.56 845.56
## - BPM 1 797.71 845.71
## - WS 1 797.72 845.72
## - ORBP 1 797.84 845.84
## - TRBP 1 797.95 845.95
## - PER 1 797.96 845.96
## - TwoPP 1 797.97 845.97
## - BLKP 1 798.39 846.39
## <none> 796.86 846.86
## - DWS 1 799.34 847.34
## - FGP 1 800.01 848.01
## - FTGame 1 800.69 848.69
## - ThreePAr 1 800.81 848.81
## - FTAGame 1 801.40 849.40
## - eFGP 1 802.09 850.09
## - TOVGame 1 802.17 850.17
## - FTr 1 802.35 850.35
## - PF 1 803.29 851.29
## - TRBGame 1 805.32 853.32
## - ASTP 1 808.72 856.72
## - USGP 1 822.91 870.91
## - ASTGame 1 827.53 875.53
##
## Step: AIC=845.29
## isAllStar ~ PF + PER + ThreePAr + FTr + ORBP + TRBP + ASTP +
## BLKP + USGP + DWS + WS + OBPM + DBPM + BPM + FGP + ThreePP +
## TwoPP + eFGP + TOVGame + TRBGame + ASTGame + FTGame + FTAGame
##
## Df Deviance AIC
## - ThreePP 1 797.92 843.92
## - DBPM 1 797.98 843.98
## - OBPM 1 798.00 844.00
## - WS 1 798.03 844.03
## - BPM 1 798.15 844.15
## - PER 1 798.24 844.24
## - TwoPP 1 798.30 844.30
## - BLKP 1 798.78 844.78
## - ORBP 1 799.25 845.25
## <none> 797.29 845.29
## - DWS 1 799.58 845.58
## - FGP 1 800.29 846.29
## - FTGame 1 800.85 846.85
## - ThreePAr 1 801.05 847.05
## - TRBP 1 801.05 847.05
## - FTAGame 1 801.52 847.52
## - eFGP 1 802.29 848.29
## - FTr 1 802.57 848.57
## - TOVGame 1 802.73 848.73
## - PF 1 803.31 849.31
## - TRBGame 1 806.23 852.23
## - ASTP 1 808.87 854.87
## - USGP 1 822.91 868.91
## - ASTGame 1 827.57 873.57
##
## Step: AIC=843.92
## isAllStar ~ PF + PER + ThreePAr + FTr + ORBP + TRBP + ASTP +
## BLKP + USGP + DWS + WS + OBPM + DBPM + BPM + FGP + TwoPP +
## eFGP + TOVGame + TRBGame + ASTGame + FTGame + FTAGame
##
## Df Deviance AIC
## - DBPM 1 798.57 842.57
## - OBPM 1 798.58 842.58
## - WS 1 798.65 842.65
## - BPM 1 798.73 842.73
## - PER 1 798.86 842.86
## - TwoPP 1 799.01 843.01
## - BLKP 1 799.29 843.29
## - ORBP 1 799.64 843.64
## <none> 797.92 843.92
## - DWS 1 800.29 844.29
## - FGP 1 801.35 845.35
## - FTGame 1 801.47 845.47
## - TRBP 1 801.71 845.71
## - FTAGame 1 802.08 846.08
## - ThreePAr 1 802.08 846.08
## - FTr 1 803.05 847.05
## - TOVGame 1 803.21 847.21
## - eFGP 1 803.65 847.65
## - PF 1 804.18 848.18
## - TRBGame 1 807.02 851.02
## - ASTP 1 809.50 853.50
## - USGP 1 823.45 867.45
## - ASTGame 1 828.01 872.01
##
## Step: AIC=842.57
## isAllStar ~ PF + PER + ThreePAr + FTr + ORBP + TRBP + ASTP +
## BLKP + USGP + DWS + WS + OBPM + BPM + FGP + TwoPP + eFGP +
## TOVGame + TRBGame + ASTGame + FTGame + FTAGame
##
## Df Deviance AIC
## - OBPM 1 798.58 840.58
## - WS 1 799.32 841.32
## - PER 1 799.49 841.49
## - TwoPP 1 799.75 841.75
## - BLKP 1 799.75 841.75
## - BPM 1 799.80 841.80
## - ORBP 1 800.43 842.43
## <none> 798.57 842.57
## - DWS 1 800.80 842.80
## - FGP 1 802.18 844.18
## - FTGame 1 802.22 844.22
## - TRBP 1 802.50 844.50
## - FTAGame 1 802.73 844.73
## - ThreePAr 1 802.90 844.90
## - FTr 1 803.57 845.57
## - TOVGame 1 803.97 845.97
## - eFGP 1 804.57 846.57
## - PF 1 804.71 846.71
## - TRBGame 1 807.59 849.59
## - ASTP 1 810.13 852.13
## - USGP 1 824.46 866.46
## - ASTGame 1 828.65 870.65
##
## Step: AIC=840.58
## isAllStar ~ PF + PER + ThreePAr + FTr + ORBP + TRBP + ASTP +
## BLKP + USGP + DWS + WS + BPM + FGP + TwoPP + eFGP + TOVGame +
## TRBGame + ASTGame + FTGame + FTAGame
##
## Df Deviance AIC
## - WS 1 799.41 839.41
## - PER 1 799.75 839.75
## - TwoPP 1 799.79 839.79
## <none> 798.58 840.58
## - BLKP 1 800.79 840.79
## - ORBP 1 800.83 840.83
## - BPM 1 801.61 841.61
## - FTGame 1 802.22 842.22
## - FGP 1 802.25 842.25
## - FTAGame 1 802.74 842.74
## - ThreePAr 1 803.20 843.20
## - FTr 1 803.58 843.58
## - TRBP 1 803.61 843.61
## - DWS 1 803.89 843.89
## - TOVGame 1 804.04 844.04
## - eFGP 1 804.61 844.61
## - PF 1 805.10 845.10
## - TRBGame 1 808.04 848.04
## - ASTP 1 810.82 850.82
## - USGP 1 825.14 865.14
## - ASTGame 1 829.07 869.07
##
## Step: AIC=839.41
## isAllStar ~ PF + PER + ThreePAr + FTr + ORBP + TRBP + ASTP +
## BLKP + USGP + DWS + BPM + FGP + TwoPP + eFGP + TOVGame +
## TRBGame + ASTGame + FTGame + FTAGame
##
## Df Deviance AIC
## - PER 1 800.04 838.04
## - TwoPP 1 800.64 838.64
## - BLKP 1 801.08 839.08
## <none> 799.41 839.41
## - ORBP 1 802.01 840.01
## - BPM 1 802.43 840.43
## - FGP 1 803.28 841.28
## - FTAGame 1 804.03 842.03
## - FTr 1 804.22 842.22
## - ThreePAr 1 804.28 842.28
## - FTGame 1 804.66 842.66
## - PF 1 805.67 843.67
## - TRBP 1 805.76 843.76
## - eFGP 1 805.97 843.97
## - TOVGame 1 807.34 845.34
## - TRBGame 1 809.69 847.69
## - ASTP 1 812.66 850.66
## - DWS 1 815.92 853.92
## - USGP 1 825.14 863.14
## - ASTGame 1 833.45 871.45
##
## Step: AIC=838.04
## isAllStar ~ PF + ThreePAr + FTr + ORBP + TRBP + ASTP + BLKP +
## USGP + DWS + BPM + FGP + TwoPP + eFGP + TOVGame + TRBGame +
## ASTGame + FTGame + FTAGame
##
## Df Deviance AIC
## - TwoPP 1 801.05 837.05
## - BLKP 1 801.17 837.17
## - ORBP 1 802.03 838.03
## <none> 800.04 838.04
## - BPM 1 802.43 838.43
## - FGP 1 803.54 839.54
## - FTAGame 1 804.14 840.14
## - ThreePAr 1 804.44 840.44
## - FTr 1 804.84 840.84
## - FTGame 1 804.89 840.89
## - PF 1 805.89 841.89
## - eFGP 1 805.99 841.99
## - TRBP 1 806.53 842.53
## - TOVGame 1 809.63 845.63
## - TRBGame 1 809.90 845.90
## - ASTP 1 814.07 850.07
## - DWS 1 816.94 852.94
## - ASTGame 1 834.50 870.50
## - USGP 1 836.40 872.40
##
## Step: AIC=837.05
## isAllStar ~ PF + ThreePAr + FTr + ORBP + TRBP + ASTP + BLKP +
## USGP + DWS + BPM + FGP + eFGP + TOVGame + TRBGame + ASTGame +
## FTGame + FTAGame
##
## Df Deviance AIC
## - BLKP 1 802.08 836.08
## - ORBP 1 802.72 836.72
## <none> 801.05 837.05
## - BPM 1 803.97 837.97
## - FGP 1 805.14 839.14
## - FTAGame 1 805.27 839.27
## - FTr 1 805.67 839.67
## - ThreePAr 1 805.96 839.96
## - FTGame 1 806.10 840.10
## - PF 1 806.72 840.72
## - TRBP 1 807.46 841.46
## - eFGP 1 808.08 842.08
## - TOVGame 1 810.37 844.37
## - TRBGame 1 810.89 844.89
## - ASTP 1 815.11 849.11
## - DWS 1 817.34 851.34
## - ASTGame 1 835.15 869.15
## - USGP 1 837.30 871.30
##
## Step: AIC=836.08
## isAllStar ~ PF + ThreePAr + FTr + ORBP + TRBP + ASTP + USGP +
## DWS + BPM + FGP + eFGP + TOVGame + TRBGame + ASTGame + FTGame +
## FTAGame
##
## Df Deviance AIC
## - ORBP 1 803.65 835.65
## <none> 802.08 836.08
## - FTAGame 1 806.07 838.07
## - FGP 1 806.28 838.28
## - FTGame 1 806.43 838.43
## - BPM 1 806.48 838.48
## - FTr 1 807.05 839.05
## - ThreePAr 1 807.35 839.35
## - TRBP 1 807.75 839.75
## - PF 1 808.00 840.00
## - eFGP 1 809.16 841.16
## - TOVGame 1 810.76 842.76
## - TRBGame 1 811.19 843.19
## - ASTP 1 817.48 849.48
## - DWS 1 818.59 850.59
## - ASTGame 1 836.45 868.45
## - USGP 1 838.81 870.81
##
## Step: AIC=835.65
## isAllStar ~ PF + ThreePAr + FTr + TRBP + ASTP + USGP + DWS +
## BPM + FGP + eFGP + TOVGame + TRBGame + ASTGame + FTGame +
## FTAGame
##
## Df Deviance AIC
## <none> 803.65 835.65
## - FTGame 1 807.10 837.10
## - FTAGame 1 807.19 837.19
## - TRBP 1 807.93 837.93
## - FGP 1 808.00 838.00
## - PF 1 808.72 838.72
## - FTr 1 808.85 838.85
## - ThreePAr 1 809.60 839.60
## - BPM 1 810.17 840.17
## - eFGP 1 810.79 840.79
## - TOVGame 1 811.85 841.85
## - TRBGame 1 812.22 842.22
## - DWS 1 818.69 848.69
## - ASTP 1 820.38 850.38
## - ASTGame 1 838.26 868.26
## - USGP 1 839.89 869.89summary(seasonstatsmodel.glm.back)##
## Call:
## glm(formula = isAllStar ~ PF + ThreePAr + FTr + TRBP + ASTP +
## USGP + DWS + BPM + FGP + eFGP + TOVGame + TRBGame + ASTGame +
## FTGame + FTAGame, family = "binomial", data = seasonstatsmodel.train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.10181 -0.23629 -0.09109 -0.03610 2.90272
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -17.813014 2.348417 -7.585 3.32e-14 ***
## PF -0.004450 0.001985 -2.242 0.024954 *
## ThreePAr -11.231662 4.620505 -2.431 0.015064 *
## FTr 6.228662 2.700329 2.307 0.021075 *
## TRBP -0.248560 0.123016 -2.021 0.043326 *
## ASTP -0.233050 0.060516 -3.851 0.000118 ***
## USGP 0.405056 0.069336 5.842 5.16e-09 ***
## DWS 0.375063 0.097662 3.840 0.000123 ***
## BPM 0.192148 0.075683 2.539 0.011121 *
## FGP -49.439257 23.595669 -2.095 0.036147 *
## eFGP 59.227018 22.039166 2.687 0.007202 **
## TOVGame -0.736219 0.259649 -2.835 0.004576 **
## TRBGame 0.569243 0.200226 2.843 0.004469 **
## ASTGame 1.492532 0.274232 5.443 5.25e-08 ***
## FTGame 0.505011 0.272340 1.854 0.063690 .
## FTAGame -0.614114 0.324167 -1.894 0.058167 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1769.64 on 2498 degrees of freedom
## Residual deviance: 803.65 on 2483 degrees of freedom
## AIC: 835.65
##
## Number of Fisher Scoring iterations: 7dim(seasonstatsmodel.glm.back)## NULLsum.back <- summary(seasonstatsmodel.glm.back)
dim(sum.back$coefficients)## [1] 16 4AIC(seasonstatsmodel.glm.back)## [1] 835.654pred.glm3.train <- predict(seasonstatsmodel.glm.back, type = "response")
pred.glm3.valid <- predict(seasonstatsmodel.glm.back, newdata = seasonstatsmodel.valid, type = "response")
confusionMatrix(as.factor(ifelse(pred.glm3.train >= optimal.pcut.glm, "1", "0")), as.factor(seasonstatsmodel.train$isAllStar),
positive = "1")## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 1261 0
## 1 954 284
##
## Accuracy : 0.6182
## 95% CI : (0.5989, 0.6373)
## No Information Rate : 0.8864
## P-Value [Acc > NIR] : 1
##
## Kappa : 0.231
##
## Mcnemar's Test P-Value : <2e-16
##
## Sensitivity : 1.0000
## Specificity : 0.5693
## Pos Pred Value : 0.2294
## Neg Pred Value : 1.0000
## Prevalence : 0.1136
## Detection Rate : 0.1136
## Detection Prevalence : 0.4954
## Balanced Accuracy : 0.7847
##
## 'Positive' Class : 1
## #0.8463 accuracy
#Perform stepwise regression - 3rd best
seasonstatsmodel.glm.step <- step(seasonstatsmodel.glm.null, scope = list(seasonstatsmodel.glm.null, upper = seasonstatsmodel.glm),
direction = "both")## Start: AIC=1771.64
## isAllStar ~ 1
##
## Df Deviance AIC
## + PER 1 980.61 984.61
## + PTSGame 1 1065.55 1069.55
## + VORP 1 1138.59 1142.59
## + WS 1 1142.93 1146.93
## + FTAGame 1 1170.56 1174.56
## + FTGame 1 1173.40 1177.40
## + TwoPGame 1 1187.60 1191.60
## + BPM 1 1197.55 1201.55
## + OWS 1 1220.61 1224.61
## + TwoPAGame 1 1234.21 1238.21
## + WS48 1 1259.83 1263.83
## + USGP 1 1276.25 1280.25
## + OBPM 1 1287.65 1291.65
## + TOVGame 1 1356.88 1360.88
## + DWS 1 1470.20 1474.20
## + ASTGame 1 1557.47 1561.47
## + TRBGame 1 1579.00 1583.00
## + STLGame 1 1595.39 1599.39
## + ASTP 1 1631.79 1635.79
## + FTr 1 1637.62 1641.62
## + TSP 1 1652.17 1656.17
## + BLKGame 1 1688.22 1692.22
## + FGP 1 1692.92 1696.92
## + TwoPP 1 1704.34 1708.34
## + DRBP 1 1707.67 1711.67
## + DBPM 1 1715.46 1719.46
## + PF 1 1715.58 1719.58
## + TRBP 1 1728.75 1732.75
## + ThreePAr 1 1735.75 1739.75
## + eFGP 1 1736.56 1740.56
## + BLKP 1 1746.57 1750.57
## + PFGame 1 1746.83 1750.83
## + STLP 1 1751.43 1755.43
## + FTP 1 1752.65 1756.65
## + ThreePAGame 1 1754.87 1758.87
## + ThreePGame 1 1755.28 1759.28
## + ORBP 1 1763.93 1767.93
## + TOVP 1 1765.41 1769.41
## <none> 1769.64 1771.64
## + ThreePP 1 1768.02 1772.02
##
## Step: AIC=984.61
## isAllStar ~ PER
##
## Df Deviance AIC
## + TOVGame 1 916.99 922.99
## + PTSGame 1 921.55 927.55
## + VORP 1 937.50 943.50
## + ASTGame 1 940.73 946.73
## + FTGame 1 943.60 949.60
## + FTAGame 1 944.22 950.22
## + TwoPAGame 1 948.22 954.22
## + DWS 1 951.60 957.60
## + STLGame 1 953.69 959.69
## + WS 1 954.31 960.31
## + TwoPGame 1 959.31 965.31
## + ASTP 1 960.28 966.28
## + FGP 1 960.29 966.29
## + TwoPP 1 960.59 966.59
## + ORBP 1 960.93 966.93
## + USGP 1 960.93 966.93
## + eFGP 1 965.13 971.13
## + BPM 1 967.17 973.17
## + ThreePAGame 1 967.67 973.67
## + ThreePGame 1 970.32 976.32
## + TSP 1 971.05 977.05
## + TRBP 1 971.12 977.12
## + BLKP 1 971.21 977.21
## + ThreePP 1 971.33 977.33
## + OWS 1 973.62 979.62
## + TOVP 1 974.30 980.30
## + OBPM 1 974.35 980.35
## + DRBP 1 976.25 982.25
## + PF 1 976.79 982.79
## + ThreePAr 1 977.77 983.77
## + STLP 1 977.83 983.83
## + BLKGame 1 978.28 984.28
## <none> 980.61 984.61
## + WS48 1 978.62 984.62
## + FTP 1 979.26 985.26
## + DBPM 1 979.78 985.78
## + FTr 1 980.08 986.08
## + PFGame 1 980.56 986.56
## + TRBGame 1 980.61 986.61
## - PER 1 1769.64 1771.64
##
## Step: AIC=922.99
## isAllStar ~ PER + TOVGame
##
## Df Deviance AIC
## + WS 1 882.31 890.31
## + DWS 1 884.29 892.29
## + VORP 1 885.76 893.76
## + PTSGame 1 900.48 908.48
## + BPM 1 903.15 911.15
## + TOVP 1 904.89 912.89
## + OWS 1 905.87 913.87
## + WS48 1 907.76 915.76
## + TwoPAGame 1 909.40 917.40
## + DBPM 1 910.57 918.57
## + TwoPGame 1 912.03 920.03
## + FTGame 1 912.20 920.20
## + STLGame 1 912.66 920.66
## + FTAGame 1 913.00 921.00
## + ThreePP 1 913.47 921.47
## + ThreePGame 1 913.64 921.64
## + ThreePAGame 1 913.75 921.75
## + TwoPP 1 913.81 921.81
## + ASTGame 1 914.03 922.03
## + ORBP 1 914.03 922.03
## + FGP 1 914.23 922.23
## + TRBGame 1 914.88 922.88
## <none> 916.99 922.99
## + PF 1 915.58 923.58
## + eFGP 1 915.94 923.94
## + TSP 1 916.09 924.09
## + OBPM 1 916.16 924.16
## + ThreePAr 1 916.16 924.16
## + PFGame 1 916.23 924.23
## + BLKP 1 916.57 924.57
## + FTP 1 916.61 924.61
## + FTr 1 916.80 924.80
## + TRBP 1 916.82 924.82
## + USGP 1 916.88 924.88
## + BLKGame 1 916.90 924.90
## + DRBP 1 916.92 924.92
## + STLP 1 916.99 924.99
## + ASTP 1 916.99 924.99
## - TOVGame 1 980.61 984.61
## - PER 1 1356.88 1360.88
##
## Step: AIC=890.31
## isAllStar ~ PER + TOVGame + WS
##
## Df Deviance AIC
## + TOVP 1 867.57 877.57
## + PTSGame 1 867.65 877.65
## + TwoPAGame 1 868.09 878.09
## + TwoPGame 1 873.37 883.37
## + TSP 1 874.17 884.17
## + USGP 1 874.61 884.61
## + OWS 1 875.20 885.20
## + DWS 1 875.21 885.21
## + PF 1 875.47 885.47
## + TwoPP 1 876.34 886.34
## + eFGP 1 876.71 886.71
## + FGP 1 877.95 887.95
## + FTAGame 1 879.65 889.65
## + FTGame 1 879.93 889.93
## + DBPM 1 880.25 890.25
## <none> 882.31 890.31
## + VORP 1 880.34 890.34
## + TRBGame 1 880.36 890.36
## + WS48 1 880.37 890.37
## + PFGame 1 880.85 890.85
## + ThreePP 1 881.01 891.01
## + ThreePAGame 1 881.05 891.05
## + FTr 1 881.18 891.18
## + ThreePGame 1 881.32 891.32
## + STLGame 1 881.40 891.40
## + ORBP 1 881.48 891.48
## + BPM 1 881.51 891.51
## + OBPM 1 881.67 891.67
## + DRBP 1 881.74 891.74
## + ASTGame 1 881.86 891.86
## + BLKGame 1 881.91 891.91
## + STLP 1 881.99 891.99
## + ASTP 1 882.19 892.19
## + FTP 1 882.24 892.24
## + TRBP 1 882.28 892.28
## + BLKP 1 882.30 892.30
## + ThreePAr 1 882.30 892.30
## - WS 1 916.99 922.99
## - TOVGame 1 954.31 960.31
## - PER 1 968.62 974.62
##
## Step: AIC=877.57
## isAllStar ~ PER + TOVGame + WS + TOVP
##
## Df Deviance AIC
## + OWS 1 858.95 870.95
## + DWS 1 859.01 871.01
## + PF 1 859.17 871.17
## + DBPM 1 860.42 872.42
## + ASTGame 1 863.84 875.84
## + BPM 1 864.37 876.37
## + TSP 1 864.82 876.82
## + VORP 1 865.29 877.29
## + TwoPAGame 1 865.32 877.32
## + TRBGame 1 865.40 877.40
## <none> 867.57 877.57
## + PFGame 1 865.62 877.62
## + DRBP 1 865.87 877.87
## + OBPM 1 866.01 878.01
## + TwoPP 1 866.40 878.40
## + eFGP 1 866.48 878.48
## + BLKGame 1 866.48 878.48
## + ASTP 1 866.52 878.52
## + FTP 1 866.55 878.55
## + TRBP 1 866.82 878.82
## + TwoPGame 1 866.84 878.84
## + STLGame 1 866.88 878.88
## + BLKP 1 866.89 878.89
## + PTSGame 1 866.98 878.98
## + WS48 1 867.05 879.05
## + FGP 1 867.12 879.12
## + ThreePP 1 867.21 879.21
## + FTGame 1 867.36 879.36
## + ThreePAr 1 867.42 879.42
## + USGP 1 867.42 879.42
## + ThreePAGame 1 867.53 879.53
## + ThreePGame 1 867.54 879.54
## + ORBP 1 867.54 879.54
## + FTr 1 867.54 879.54
## + FTAGame 1 867.55 879.55
## + STLP 1 867.57 879.57
## - TOVP 1 882.31 890.31
## - WS 1 904.89 912.89
## - PER 1 914.87 922.87
## - TOVGame 1 947.41 955.41
##
## Step: AIC=870.95
## isAllStar ~ PER + TOVGame + WS + TOVP + OWS
##
## Df Deviance AIC
## + PF 1 845.48 859.48
## + ASTGame 1 848.58 862.58
## + ASTP 1 854.41 868.41
## + PFGame 1 854.42 868.42
## + PTSGame 1 854.69 868.69
## + ThreePP 1 856.54 870.54
## + ORBP 1 856.63 870.63
## <none> 858.95 870.95
## + BPM 1 857.75 871.75
## + ThreePGame 1 857.83 871.83
## + TwoPP 1 857.84 871.84
## + TRBP 1 857.86 871.86
## + BLKP 1 857.91 871.91
## + FGP 1 857.96 871.96
## + ThreePAGame 1 858.05 872.05
## + OBPM 1 858.10 872.10
## + BLKGame 1 858.37 872.37
## + ThreePAr 1 858.38 872.38
## + VORP 1 858.44 872.44
## + WS48 1 858.47 872.47
## + USGP 1 858.51 872.51
## + DRBP 1 858.57 872.57
## + TwoPAGame 1 858.65 872.65
## + FTP 1 858.71 872.71
## + STLGame 1 858.78 872.78
## + STLP 1 858.78 872.78
## + TSP 1 858.80 872.80
## + DBPM 1 858.82 872.82
## + eFGP 1 858.83 872.83
## + FTr 1 858.89 872.89
## + TRBGame 1 858.91 872.91
## + FTGame 1 858.92 872.92
## + DWS 1 858.93 872.93
## + FTAGame 1 858.93 872.93
## + TwoPGame 1 858.95 872.95
## - OWS 1 867.57 877.57
## - TOVP 1 875.20 885.20
## - WS 1 893.56 903.56
## - PER 1 912.04 922.04
## - TOVGame 1 940.51 950.51
##
## Step: AIC=859.48
## isAllStar ~ PER + TOVGame + WS + TOVP + OWS + PF
##
## Df Deviance AIC
## + PTSGame 1 841.17 857.17
## + ASTGame 1 842.33 858.33
## + TwoPAGame 1 842.52 858.52
## + PFGame 1 842.80 858.80
## <none> 845.48 859.48
## + TRBGame 1 843.80 859.80
## + TwoPGame 1 843.97 859.97
## + STLP 1 844.44 860.44
## + DRBP 1 844.82 860.82
## + WS48 1 844.96 860.96
## + DBPM 1 844.96 860.96
## + TRBP 1 845.01 861.01
## + ASTP 1 845.08 861.08
## + ThreePAr 1 845.09 861.09
## + ThreePP 1 845.16 861.16
## + BLKGame 1 845.20 861.20
## + FTAGame 1 845.21 861.21
## + OBPM 1 845.22 861.22
## + FTr 1 845.28 861.28
## + FTGame 1 845.29 861.29
## + TwoPP 1 845.30 861.30
## + FTP 1 845.30 861.30
## + ThreePAGame 1 845.35 861.35
## + USGP 1 845.36 861.36
## + BLKP 1 845.37 861.37
## + TSP 1 845.38 861.38
## + ORBP 1 845.39 861.39
## + STLGame 1 845.42 861.42
## + DWS 1 845.44 861.44
## + eFGP 1 845.44 861.44
## + ThreePGame 1 845.45 861.45
## + VORP 1 845.46 861.46
## + FGP 1 845.47 861.47
## + BPM 1 845.47 861.47
## - PF 1 858.95 870.95
## - OWS 1 859.17 871.17
## - TOVP 1 864.58 876.58
## - PER 1 880.72 892.72
## - WS 1 893.54 905.54
## - TOVGame 1 936.98 948.98
##
## Step: AIC=857.17
## isAllStar ~ PER + TOVGame + WS + TOVP + OWS + PF + PTSGame
##
## Df Deviance AIC
## + ASTGame 1 833.42 851.42
## - TOVP 1 841.24 855.24
## + ASTP 1 838.76 856.76
## - TOVGame 1 842.99 856.99
## + TwoPAGame 1 839.11 857.11
## <none> 841.17 857.17
## + PFGame 1 839.19 857.19
## + TSP 1 839.40 857.40
## + TRBGame 1 839.62 857.62
## + DBPM 1 840.00 858.00
## + eFGP 1 840.19 858.19
## + USGP 1 840.22 858.22
## + ThreePAr 1 840.34 858.34
## + TwoPP 1 840.47 858.47
## + TwoPGame 1 840.50 858.50
## + DRBP 1 840.56 858.56
## + ThreePAGame 1 840.56 858.56
## + WS48 1 840.57 858.57
## + TRBP 1 840.59 858.59
## + STLP 1 840.68 858.68
## + FTP 1 840.69 858.69
## + ThreePGame 1 840.69 858.69
## + BLKGame 1 840.76 858.76
## + ORBP 1 840.84 858.84
## + BLKP 1 840.93 858.93
## + VORP 1 840.96 858.96
## + OBPM 1 840.96 858.96
## + BPM 1 841.03 859.03
## + FGP 1 841.09 859.09
## + FTr 1 841.10 859.10
## + DWS 1 841.11 859.11
## + FTGame 1 841.12 859.12
## + ThreePP 1 841.13 859.13
## + STLGame 1 841.17 859.17
## + FTAGame 1 841.17 859.17
## - PTSGame 1 845.48 859.48
## - PF 1 854.69 868.69
## - OWS 1 858.90 872.90
## - PER 1 864.59 878.59
## - WS 1 892.73 906.73
##
## Step: AIC=851.42
## isAllStar ~ PER + TOVGame + WS + TOVP + OWS + PF + PTSGame +
## ASTGame
##
## Df Deviance AIC
## + ASTP 1 824.05 844.05
## + TRBGame 1 825.48 845.48
## + TRBP 1 825.64 845.64
## + ORBP 1 825.80 845.80
## + DRBP 1 828.39 848.39
## - TOVGame 1 833.53 849.53
## + OBPM 1 829.60 849.60
## + BLKGame 1 829.76 849.76
## + DBPM 1 829.78 849.78
## + BLKP 1 830.11 850.11
## + STLP 1 830.14 850.14
## - TOVP 1 834.18 850.18
## + ThreePAr 1 830.37 850.37
## + ThreePAGame 1 830.51 850.51
## + FTr 1 830.66 850.66
## + PFGame 1 830.98 850.98
## + ThreePGame 1 831.15 851.15
## + TwoPAGame 1 831.32 851.32
## <none> 833.42 851.42
## + STLGame 1 831.92 851.92
## + TwoPGame 1 832.03 852.03
## + FTAGame 1 832.05 852.05
## + USGP 1 832.18 852.18
## + FGP 1 832.38 852.38
## + FTP 1 832.43 852.43
## + FTGame 1 832.81 852.81
## + WS48 1 833.07 853.07
## - PF 1 837.10 853.10
## + ThreePP 1 833.32 853.32
## + BPM 1 833.37 853.37
## + eFGP 1 833.38 853.38
## + TwoPP 1 833.40 853.40
## + VORP 1 833.40 853.40
## + TSP 1 833.41 853.41
## + DWS 1 833.42 853.42
## - ASTGame 1 841.17 857.17
## - PTSGame 1 842.33 858.33
## - OWS 1 858.36 874.36
## - PER 1 859.54 875.54
## - WS 1 885.58 901.58
##
## Step: AIC=844.05
## isAllStar ~ PER + TOVGame + WS + TOVP + OWS + PF + PTSGame +
## ASTGame + ASTP
##
## Df Deviance AIC
## - TOVGame 1 824.11 842.11
## - TOVP 1 824.56 842.56
## + STLGame 1 821.15 843.15
## + STLP 1 821.24 843.24
## + FTr 1 821.63 843.63
## + ORBP 1 821.93 843.93
## + USGP 1 822.00 844.00
## + TRBP 1 822.01 844.01
## <none> 824.05 844.05
## + TRBGame 1 822.14 844.14
## + ThreePAGame 1 822.28 844.28
## + ThreePAr 1 822.32 844.32
## + TwoPAGame 1 822.68 844.68
## + FTAGame 1 822.72 844.72
## + ThreePGame 1 822.76 844.76
## + DRBP 1 822.95 844.95
## + FTGame 1 823.05 845.05
## + OBPM 1 823.09 845.09
## + PFGame 1 823.10 845.10
## + DBPM 1 823.25 845.25
## + BLKGame 1 823.27 845.27
## + BLKP 1 823.37 845.37
## + TwoPGame 1 823.54 845.54
## - PF 1 827.68 845.68
## + eFGP 1 823.70 845.70
## + WS48 1 823.85 845.85
## + TwoPP 1 823.86 845.86
## + FTP 1 823.94 845.94
## + FGP 1 823.94 845.94
## + VORP 1 823.99 845.99
## + TSP 1 824.01 846.01
## + BPM 1 824.03 846.03
## + ThreePP 1 824.04 846.04
## + DWS 1 824.04 846.04
## - PTSGame 1 831.06 849.06
## - ASTP 1 833.42 851.42
## - ASTGame 1 838.76 856.76
## - OWS 1 849.00 867.00
## - PER 1 858.66 876.66
## - WS 1 865.27 883.27
##
## Step: AIC=842.11
## isAllStar ~ PER + WS + TOVP + OWS + PF + PTSGame + ASTGame +
## ASTP
##
## Df Deviance AIC
## + STLGame 1 821.23 841.23
## + STLP 1 821.34 841.34
## - TOVP 1 825.42 841.42
## + FTr 1 821.90 841.90
## <none> 824.11 842.11
## + TRBP 1 822.28 842.28
## + TRBGame 1 822.38 842.38
## + ORBP 1 822.40 842.40
## + USGP 1 822.43 842.43
## + ThreePAGame 1 822.52 842.52
## + ThreePAr 1 822.60 842.60
## + TwoPAGame 1 822.92 842.92
## + ThreePGame 1 823.01 843.01
## + FTAGame 1 823.03 843.03
## + DRBP 1 823.06 843.06
## + PFGame 1 823.14 843.14
## + OBPM 1 823.23 843.23
## + FTGame 1 823.27 843.27
## + DBPM 1 823.37 843.37
## + BLKGame 1 823.42 843.42
## + BLKP 1 823.50 843.50
## + TwoPGame 1 823.66 843.66
## + eFGP 1 823.89 843.89
## + TwoPP 1 823.96 843.96
## + WS48 1 823.98 843.98
## + FGP 1 823.99 843.99
## + FTP 1 824.03 844.03
## + VORP 1 824.04 844.04
## + TOVGame 1 824.05 844.05
## + ThreePP 1 824.09 844.09
## + BPM 1 824.10 844.10
## + TSP 1 824.10 844.10
## + DWS 1 824.10 844.10
## - PF 1 828.52 844.52
## - ASTP 1 833.53 849.53
## - ASTGame 1 838.91 854.91
## - OWS 1 854.26 870.26
## - PER 1 858.99 874.99
## - WS 1 865.28 881.28
## - PTSGame 1 870.01 886.01
##
## Step: AIC=841.23
## isAllStar ~ PER + WS + TOVP + OWS + PF + PTSGame + ASTGame +
## ASTP + STLGame
##
## Df Deviance AIC
## - TOVP 1 822.24 840.24
## + FTr 1 818.79 840.79
## <none> 821.23 841.23
## + DBPM 1 819.85 841.85
## + FTAGame 1 819.99 841.99
## + PFGame 1 820.04 842.04
## - STLGame 1 824.11 842.11
## + FTGame 1 820.18 842.18
## + USGP 1 820.25 842.25
## + ORBP 1 820.32 842.32
## + TRBGame 1 820.46 842.46
## + ThreePAr 1 820.51 842.51
## + ThreePAGame 1 820.52 842.52
## + TRBP 1 820.58 842.58
## + TwoPAGame 1 820.71 842.71
## + ThreePGame 1 820.77 842.77
## + BPM 1 820.81 842.81
## + eFGP 1 820.86 842.86
## + TwoPP 1 820.92 842.92
## + DRBP 1 820.96 842.96
## + VORP 1 820.99 842.99
## + BLKGame 1 821.06 843.06
## + WS48 1 821.09 843.09
## + ThreePP 1 821.12 843.12
## + BLKP 1 821.13 843.13
## + OBPM 1 821.14 843.14
## + FTP 1 821.15 843.15
## + TOVGame 1 821.15 843.15
## + TwoPGame 1 821.17 843.17
## + TSP 1 821.19 843.19
## + FGP 1 821.22 843.22
## + DWS 1 821.22 843.22
## + STLP 1 821.23 843.23
## - PF 1 825.46 843.46
## - ASTP 1 832.04 850.04
## - ASTGame 1 838.62 856.62
## - OWS 1 854.20 872.20
## - PER 1 856.02 874.02
## - WS 1 865.27 883.27
## - PTSGame 1 869.59 887.59
##
## Step: AIC=840.24
## isAllStar ~ PER + WS + OWS + PF + PTSGame + ASTGame + ASTP +
## STLGame
##
## Df Deviance AIC
## + FTr 1 818.81 838.81
## + FTAGame 1 820.21 840.21
## <none> 822.24 840.24
## + FTGame 1 820.46 840.46
## + DBPM 1 820.60 840.60
## + PFGame 1 820.97 840.97
## + ORBP 1 821.09 841.09
## + TOVP 1 821.23 841.23
## + TRBGame 1 821.29 841.29
## + ThreePAGame 1 821.38 841.38
## + TRBP 1 821.38 841.38
## + USGP 1 821.41 841.41
## - STLGame 1 825.42 841.42
## + ThreePAr 1 821.47 841.47
## - PF 1 825.54 841.54
## + TOVGame 1 821.60 841.60
## + ThreePGame 1 821.70 841.70
## + BPM 1 821.82 841.82
## + DRBP 1 821.90 841.90
## + VORP 1 821.97 841.97
## + TwoPAGame 1 822.03 842.03
## + BLKGame 1 822.05 842.05
## + WS48 1 822.08 842.08
## + OBPM 1 822.09 842.09
## + ThreePP 1 822.10 842.10
## + TSP 1 822.13 842.13
## + BLKP 1 822.13 842.13
## + FTP 1 822.15 842.15
## + eFGP 1 822.17 842.17
## + TwoPP 1 822.17 842.17
## + FGP 1 822.18 842.18
## + TwoPGame 1 822.23 842.23
## + DWS 1 822.24 842.24
## + STLP 1 822.24 842.24
## - ASTP 1 833.73 849.73
## - ASTGame 1 844.02 860.02
## - OWS 1 858.83 874.83
## - PER 1 861.62 877.62
## - WS 1 865.74 881.74
## - PTSGame 1 874.57 890.57
##
## Step: AIC=838.81
## isAllStar ~ PER + WS + OWS + PF + PTSGame + ASTGame + ASTP +
## STLGame + FTr
##
## Df Deviance AIC
## <none> 818.81 838.81
## + DBPM 1 817.72 839.72
## + USGP 1 817.81 839.81
## + FTAGame 1 817.86 839.86
## + ORBP 1 818.00 840.00
## - STLGame 1 822.00 840.00
## + TRBGame 1 818.04 840.04
## + PFGame 1 818.14 840.14
## + TRBP 1 818.18 840.18
## - FTr 1 822.24 840.24
## + TwoPAGame 1 818.25 840.25
## + BPM 1 818.34 840.34
## + ThreePP 1 818.42 840.42
## + VORP 1 818.43 840.43
## + WS48 1 818.43 840.43
## + FTGame 1 818.49 840.49
## + DRBP 1 818.54 840.54
## + ThreePAr 1 818.56 840.56
## + ThreePAGame 1 818.56 840.56
## + TwoPGame 1 818.67 840.67
## + TwoPP 1 818.72 840.72
## + BLKGame 1 818.72 840.72
## + ThreePGame 1 818.76 840.76
## + BLKP 1 818.77 840.77
## + TOVP 1 818.79 840.79
## + DWS 1 818.79 840.79
## + TSP 1 818.79 840.79
## + FGP 1 818.80 840.80
## + TOVGame 1 818.80 840.80
## + OBPM 1 818.80 840.80
## + FTP 1 818.81 840.81
## + STLP 1 818.81 840.81
## + eFGP 1 818.81 840.81
## - PF 1 823.24 841.24
## - ASTP 1 829.44 847.44
## - ASTGame 1 839.88 857.88
## - PER 1 848.71 866.71
## - OWS 1 855.86 873.86
## - WS 1 863.23 881.23
## - PTSGame 1 873.46 891.46summary(seasonstatsmodel.glm.step)##
## Call:
## glm(formula = isAllStar ~ PER + WS + OWS + PF + PTSGame + ASTGame +
## ASTP + STLGame + FTr, family = "binomial", data = seasonstatsmodel.train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.21064 -0.23823 -0.10314 -0.04683 3.02058
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -11.863945 0.815165 -14.554 < 2e-16 ***
## PER 0.291069 0.053499 5.441 5.31e-08 ***
## WS 0.542034 0.083331 6.505 7.79e-11 ***
## OWS -0.560176 0.094186 -5.948 2.72e-09 ***
## PF -0.004377 0.002096 -2.088 0.03681 *
## PTSGame 0.202840 0.029032 6.987 2.81e-12 ***
## ASTGame 0.878998 0.199460 4.407 1.05e-05 ***
## ASTP -0.134878 0.042779 -3.153 0.00162 **
## STLGame -0.453909 0.255786 -1.775 0.07597 .
## FTr 1.630478 0.875682 1.862 0.06261 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1769.64 on 2498 degrees of freedom
## Residual deviance: 818.81 on 2489 degrees of freedom
## AIC: 838.81
##
## Number of Fisher Scoring iterations: 7sum.step <- summary(seasonstatsmodel.glm.step)
dim(sum.step$coefficients)## [1] 10 4AIC(seasonstatsmodel.glm.step)## [1] 838.8129pred.glm4.train <- predict(seasonstatsmodel.glm.step, type = "response")
pred.glm4.valid <- predict(seasonstatsmodel.glm.step, newdata = seasonstatsmodel.valid, type = "response")
confusionMatrix(as.factor(ifelse(pred.glm4.train >= optimal.pcut.glm, "1", "0")), as.factor(seasonstatsmodel.train$isAllStar),
positive = "1")## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 1221 0
## 1 994 284
##
## Accuracy : 0.6022
## 95% CI : (0.5827, 0.6215)
## No Information Rate : 0.8864
## P-Value [Acc > NIR] : 1
##
## Kappa : 0.2183
##
## Mcnemar's Test P-Value : <2e-16
##
## Sensitivity : 1.0000
## Specificity : 0.5512
## Pos Pred Value : 0.2222
## Neg Pred Value : 1.0000
## Prevalence : 0.1136
## Detection Rate : 0.1136
## Detection Prevalence : 0.5114
## Balanced Accuracy : 0.7756
##
## 'Positive' Class : 1
## #0.8436 accuracySet-up data for largetree
#Partition the data for largetree
set.seed(2016)
train.index <- sample(nrow(seasonstatsmodel), nrow(seasonstatsmodel) * 0.6)
seasonstatsmodel.train <- seasonstatsmodel[train.index, ]
seasonstatsmodel.valid <- seasonstatsmodel[-train.index, ]
#Ploting a largetree
library(rpart.plot)## Warning: package 'rpart.plot' was built under R version 3.6.3## Loading required package: rpartseasonstatsmodel.largetree <- rpart(isAllStar ~ ., data = seasonstatsmodel.train, cp = 0.0001, method = "class")
prp(seasonstatsmodel.largetree, digits = 4, type = 1, extra = 1, varlen = -10,
box.col = ifelse(seasonstatsmodel.largetree$frame$var == "<leaf>", 'gray', 'white'))
plotcp(seasonstatsmodel.largetree)
printcp(seasonstatsmodel.largetree)##
## Classification tree:
## rpart(formula = isAllStar ~ ., data = seasonstatsmodel.train,
## method = "class", cp = 1e-04)
##
## Variables actually used in tree construction:
## [1] ASTGame ASTP BLKGame DRBP DWS FTAGame FTGame
## [8] FTP FTr OBPM PER PF PTSGame ThreePAr
## [15] TOVGame TOVP TRBP TSP TwoPAGame TwoPGame VORP
## [22] WS
##
## Root node error: 284/2499 = 0.11365
##
## n= 2499
##
## CP nsplit rel error xerror xstd
## 1 0.1602113 0 1.00000 1.00000 0.055866
## 2 0.0704225 2 0.67958 0.73239 0.048623
## 3 0.0281690 3 0.60915 0.66197 0.046428
## 4 0.0158451 4 0.58099 0.65493 0.046200
## 5 0.0140845 6 0.54930 0.67606 0.046878
## 6 0.0105634 8 0.52113 0.68310 0.047102
## 7 0.0052817 16 0.42606 0.71831 0.048195
## 8 0.0035211 21 0.39437 0.72887 0.048517
## 9 0.0017606 25 0.38028 0.74648 0.049046
## 10 0.0011737 27 0.37676 0.77113 0.049772
## 11 0.0001000 30 0.37324 0.78169 0.050079#Pruning
seasonstatsmodel.pruned <- prune(seasonstatsmodel.largetree, cp = 0.0169173)
seasonstatsmodel.pruned## n= 2499
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 2499 284 0 (0.8863545 0.1136455)
## 2) PER< 19.25 2116 78 0 (0.9631380 0.0368620) *
## 3) PER>=19.25 383 177 1 (0.4621410 0.5378590)
## 6) PTSGame< 22.09166 262 100 0 (0.6183206 0.3816794)
## 12) WS< 10.85 216 67 0 (0.6898148 0.3101852)
## 24) ASTGame< 9.456535 206 58 0 (0.7184466 0.2815534) *
## 25) ASTGame>=9.456535 10 1 1 (0.1000000 0.9000000) *
## 13) WS>=10.85 46 13 1 (0.2826087 0.7173913) *
## 7) PTSGame>=22.09166 121 15 1 (0.1239669 0.8760331) *#Graphical output
prp(seasonstatsmodel.pruned, digits = 4, type = 1, extra = 1, varlen = -10,
box.col = ifelse(seasonstatsmodel.pruned$frame$var == "<leaf>", 'gray', 'white'))
#Confusion Matrix
library(caret)
library(e1071)
seasonstatsmodel.ct0 <- rpart(isAllStar ~ ., data = seasonstatsmodel.train, method = "class")
pred0 <- predict(seasonstatsmodel.ct0, type = "class")
confusionMatrix(pred0, as.factor(seasonstatsmodel.train$isAllStar), positive = "1")## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 2188 94
## 1 27 190
##
## Accuracy : 0.9516
## 95% CI : (0.9424, 0.9597)
## No Information Rate : 0.8864
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.7321
##
## Mcnemar's Test P-Value : 1.973e-09
##
## Sensitivity : 0.66901
## Specificity : 0.98781
## Pos Pred Value : 0.87558
## Neg Pred Value : 0.95881
## Prevalence : 0.11365
## Detection Rate : 0.07603
## Detection Prevalence : 0.08683
## Balanced Accuracy : 0.82841
##
## 'Positive' Class : 1
##