1071巨量期末專案
# 載入所需的套件(Loading package)
library(dplyr)
library(plyr)
library(ggplot2)
library(readr)
library(reshape)
library(ROCR)
library(caret)
library(randomForest)
library(pROC)
# 更改R的預設語系
Sys.setlocale("LC_ALL",'C') [1] "C"
資料前處理
將角色名還有各個角色的類型(例如support等)放入資料集當中，但沒有保留原有數字的部分，以避免資料集過於混亂。
將gameDuration(遊戲進行時間的部分)換算成以「分鐘」為單位。
刪除不合理的值，例如首殺為0(代表該場遊戲無人拿到首殺),第一座塔為0(代表該場遊戲無人拿到第一座塔)以及遊戲時間少於15分鐘的資料。
由於本資料集無任何空值，所以沒做空值相關處理。
(處理後)資料集資訊
剩下49,856筆(原先有51,490筆) 。
- 新增10個欄位，總計共71個欄位(t1:藍方、t2:紅方，雙方各隊分別5位玩家，總計共10位玩家，變數說明在此處不贅述)：
- gameId:遊戲編號
- creationTime:遊戲創立時間
- gameDuration:遊戲時間
- seasonId:第幾季
- winner:哪一隊贏
- firstBlood:哪一隊拿到首殺
- firstTower:哪一隊拿到首塔
- firstInhibitor:哪一隊拿到首兵營
- firstBaron:哪一隊拿到首巴龍
- firstDragon:哪一隊拿到首小龍
- firstRiftHearld:哪一隊拿到首預示者
- t1_champ1id:藍方第一個角色名稱
- t1_champ1id_tags:藍方第一個角色種類
- t1_champ1_sum1、sum2:藍方第一個角色召喚師技能1、2
- …
- t1_towerKills:藍方拆了幾個塔
- t1_inhibitorKills:藍方拆了幾個兵營
- t1_baronKills:藍方拿了幾隻巴龍
- t1_dragonKills:藍方拿了幾隻小龍
- t1_riftHeraldKills:藍方拿了幾隻預示者
- t1_ban1:藍方第一ban
- …
- t2同上
載入資料集(Loading dataset)：[LOLgamedata.csv]
我們透過組員自身的遊戲經驗，挑出我們認為較顯著之資料欄位進行變數型態轉換
lol <- read.csv("LOLgamedata.csv",header = T)
# View(lol)
# 將欄位進行型態轉換(transfer our data as factor)
lol$winner <- as.factor(lol$winner)
lol$firstBlood <- as.factor(lol$firstBlood)
lol$firstTower <- as.factor(lol$firstTower)
lol$firstInhibitor <- as.factor(lol$firstInhibitor)
lol$firstBaron <- as.factor(lol$firstBaron)
lol$firstDragon <- as.factor(lol$firstDragon)
lol$firstRiftHerald <- as.factor(lol$firstRiftHerald)
新增變數
lol$tower_gap <- (lol$t1_towerKills - lol$t2_towerKills) # 勝負隊伍塔差
# lol_train$tower_gap <- (lol_train$t1_towerKills - lol_train$t2_towerKills)
# summary(glm(winner ~ lol_train$tower_gap, data= lol_train, family = "binomial"))
lol$dragon_gap <- (lol$t1_dragonKills - lol$t2_dragonKills) # 勝負隊伍殺小龍數量差異
lol$baron_gap <- (lol$t1_baronKills - lol$t2_baronKills) # 勝負隊伍殺巴隆數量差異
lol$inhibitorKills_gap <- (lol$t1_inhibitorKills - lol$t2_inhibitorKills) # 勝負隊伍水晶兵營數量差異
邏輯式迴歸(glm)
# 將資料切割成Training Set(lol_train), Testing Set(lol_test)
set.seed(2018)
train_idx <- sample(1:nrow(lol), size = 0.8 * nrow(lol), replace = F)
lol_train <- lol[train_idx,]
lol_test <- lol[-train_idx,]
summary(glm(winner ~ firstBlood + firstTower + firstInhibitor + firstBaron + firstDragon + firstRiftHerald, data = lol_train, family = "binomial"))
Call:
glm(formula = winner ~ firstBlood + firstTower + firstInhibitor +
firstBaron + firstDragon + firstRiftHerald, family = "binomial",
data = lol_train)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.9057 -0.3409 -0.1809 0.3495 2.8710
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.72064 0.11624 -6.199 5.67e-10 ***
firstBlood2 0.28354 0.03497 8.108 5.14e-16 ***
firstTower2 0.82213 0.03631 22.644 < 2e-16 ***
firstInhibitor1 -2.02436 0.05042 -40.153 < 2e-16 ***
firstInhibitor2 1.91971 0.05078 37.805 < 2e-16 ***
firstBaron1 -0.91436 0.04685 -19.518 < 2e-16 ***
firstBaron2 1.18904 0.04549 26.141 < 2e-16 ***
firstDragon1 -0.26268 0.11836 -2.219 0.0265 *
firstDragon2 0.54305 0.11849 4.583 4.58e-06 ***
firstRiftHerald1 -0.18285 0.04329 -4.224 2.40e-05 ***
firstRiftHerald2 0.16980 0.04365 3.890 0.0001 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 55288 on 39883 degrees of freedom
Residual deviance: 23077 on 39873 degrees of freedom
AIC: 23099
Number of Fisher Scoring iterations: 6# 預測(glm prediction)(common sense)
model1 <- glm(winner ~ firstBlood + firstTower + firstInhibitor + firstBaron + firstDragon + firstRiftHerald, data = lol_train ,family = "binomial")
result <- predict(model1,newdata = lol_test, type = "response")
table(lol_test$winner, result>0.5) %>% {sum(diag(.))/sum(.)} # ACC = 0.9044324[1] 0.9044324# 預測(glm prediction)(加入towel_gap)
model1 <- glm(winner ~ firstBlood + firstTower + firstInhibitor + firstBaron + firstDragon + firstRiftHerald + tower_gap, data = lol_train ,family = "binomial")
result <- predict(model1,newdata = lol_test, type = "response")
table(lol_test$winner, result>0.5) %>% {sum(diag(.))/sum(.)} # ACC = 0.9736262[1] 0.9736262# 預測(glm prediction)(加入towel_gap,並拿掉不顯著之變數)
model1 <- glm(winner ~ firstTower + firstInhibitor + firstRiftHerald + tower_gap, data = lol_train ,family = "binomial")
result <- predict(model1,newdata = lol_test, type = "response")
table(lol_test$winner, result>0.5) %>% {sum(diag(.))/sum(.)} # ACC = 0.9731247[1] 0.9731247# 預測(glm prediction)(加入towel_gap, dragon_gap, baron_gap, inhibitorKills_gap, gameDuration)
model1 <- glm(winner ~ firstBlood + firstTower + firstInhibitor + firstBaron + firstDragon + firstRiftHerald + tower_gap + dragon_gap + baron_gap + inhibitorKills_gap + gameDuration, data = lol_train ,family = "binomial")
result <- predict(model1,newdata = lol_test, type = "response")
table(lol_test$winner, result>0.5) %>% {sum(diag(.))/sum(.)} # ACC = 0.9742278[1] 0.9742278summary(model1)
Call:
glm(formula = winner ~ firstBlood + firstTower + firstInhibitor +
firstBaron + firstDragon + firstRiftHerald + tower_gap +
dragon_gap + baron_gap + inhibitorKills_gap + gameDuration,
family = "binomial", data = lol_train)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.8432 -0.0338 -0.0023 0.0325 4.7229
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.37382 0.27022 1.383 0.166540
firstBlood2 -0.12787 0.07033 -1.818 0.069042 .
firstTower2 -0.87222 0.07553 -11.548 < 2e-16 ***
firstInhibitor1 0.51610 0.13912 3.710 0.000207 ***
firstInhibitor2 -0.58941 0.14017 -4.205 2.61e-05 ***
firstBaron1 0.52945 0.13253 3.995 6.47e-05 ***
firstBaron2 -0.08496 0.13143 -0.646 0.518002
firstDragon1 0.47420 0.26300 1.803 0.071388 .
firstDragon2 0.59231 0.26366 2.246 0.024673 *
firstRiftHerald1 0.22080 0.08751 2.523 0.011634 *
firstRiftHerald2 -0.59453 0.08857 -6.713 1.91e-11 ***
tower_gap -1.28958 0.02374 -54.313 < 2e-16 ***
dragon_gap 0.04511 0.02163 2.086 0.037020 *
baron_gap -0.62911 0.05491 -11.456 < 2e-16 ***
inhibitorKills_gap 0.10260 0.03776 2.717 0.006591 **
gameDuration -0.01023 0.00544 -1.880 0.060134 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 55287.7 on 39883 degrees of freedom
Residual deviance: 5838.7 on 39868 degrees of freedom
AIC: 5870.7
Number of Fisher Scoring iterations: 9
邏輯式迴歸ROC(ROC curve of Logistic Regression)
pred <- prediction(result, lol_test$winner)
perf <- performance(pred, measure = "tpr", x.measure = "fpr")
auc <- performance(pred, "auc")
# 繪製ROC curve之圖形，並算出AUC
plot(perf, main = "ROC curve(Logistic Regression)", xlab = "Specificity(FPR)", ylab = "Sensitivity(TPR)")
abline(0, 1)text(0.5, 0.5, as.character(auc@y.values[[1]])) # AUC = 0.9966
邏輯式迴歸交叉驗證(Cross-Validation(CV) of Logistic Regession)
# Get k-fold CV confusion matrix for Logistic Regression model
# f: formula, d: data, k: number of folds, cutoff: cutoff point 0-1
k_fold_CV_logit = function(f, d, k, cutoff){
numOfRec = nrow(d) # number of observations
reponse_var = all.vars(f)[1] # name of the response variable
# k indices used to split data into k parts
sample_idx_k = rep(sample(1:k),round(numOfRec / k) + 1)[1:numOfRec]
# k models for k subsets of data
k_fits = Map( function(x) glm(f, d[sample_idx_k != x, ],
family = "binomial"), 1:k)
# Predicted & actual classes for each hold-out subset
predActualClass = Map(function(x){
predictedProb = predict(k_fits[[x]], d[sample_idx_k == x,],
type = "response")
predictedClass = ifelse(predictedProb > cutoff, 1, 0)
return(data.frame("predictedClass" = predictedClass,
"actualClass" = d[sample_idx_k == x, reponse_var] ) )
}, 1:k)
# A data frame with all predicted & actual classes
output_DF = Reduce(function(x, y) rbind(x, y), predActualClass)
output_DF$predictedClass = factor(output_DF$predictedClass,
levels=c(0,1),labels = c("No", "Yes"))
return( table(output_DF$predictedClass, output_DF$actualClass))
}
Map(function(cutoff) k_fold_CV_logit(winner ~ firstBlood+firstTower+firstInhibitor+firstBaron+firstDragon+firstRiftHerald,
lol[train_idx,], 10, cutoff), list(0.9, 0.8, 0.7, 0.6, 0.5, 0.45, 0.4, 0.3, 0.2, 0.1)) # 0.5[[1]]
1 2
No 19504 7456
Yes 618 12306
[[2]]
1 2
No 19129 4829
Yes 993 14933
[[3]]
1 2
No 18822 3285
Yes 1300 16477
[[4]]
1 2
No 18674 2637
Yes 1448 17125
[[5]]
1 2
No 18233 1978
Yes 1889 17784
[[6]]
1 2
No 17860 1664
Yes 2262 18098
[[7]]
1 2
No 17692 1587
Yes 2430 18175
[[8]]
1 2
No 16964 1335
Yes 3158 18427
[[9]]
1 2
No 15230 975
Yes 4892 18787
[[10]]
1 2
No 12439 526
Yes 7683 19236
隨機森林(randomForest)
試藉由組員自身遊戲經驗所找出之變數跑randomForest
變數：firstBlood, firstTower, firstInhibitor, firstBaron, firstDragon, firstRiftHerald, lol_train
ntree = 500
透過importance()來找出較重要之變數
發現firstRiftHerald變數重要度最低，故嘗試移除firstRiftHerald變數，再次進行建模
重新建模後，發現透過impotance()所挑出的變數所計算出的結果並沒有比較好
確定模型建置
# 試藉由組員自身遊戲經驗所找出之變數跑randomForest
set.seed(2018)
lol_tree <- randomForest(winner ~ firstBlood + firstTower + firstInhibitor + firstBaron + firstDragon + firstRiftHerald, lol_train, ntree = 500)
result_tree <- predict(lol_tree,newdata = lol_test)
lol_tree
Call:
randomForest(formula = winner ~ firstBlood + firstTower + firstInhibitor + firstBaron + firstDragon + firstRiftHerald, data = lol_train, ntree = 500)
Type of random forest: classification
Number of trees: 500
No. of variables tried at each split: 2
OOB estimate of error rate: 9.36%
Confusion matrix:
1 2 class.error
1 18342 1780 0.08846039
2 1954 17808 0.09887663 # Confusion matrix:
# 1 2 class.error
# 1 18345 1777 0.08831130
# 2 1973 17789 0.09983807
# 透過importance()來找出較重要之變數
importance(lol_tree) MeanDecreaseGini
firstBlood 49.4587
firstTower 1481.5744
firstInhibitor 8485.8823
firstBaron 2454.6815
firstDragon 718.0792
firstRiftHerald 210.8131 # MeanDecreaseGini
# firstTower 1059.24050
# firstInhibitor 9253.06155
# firstBaron 2451.38878
# firstDragon 745.84541
# firstRiftHerald 91.45326 (最低)
# 移除firstRiftHerald變數，再次進行建模
lol_tree <- randomForest(winner ~ firstTower+firstInhibitor+firstBaron+firstDragon+firstRiftHerald,lol_train, ntree=500)
result_tree <- predict(lol_tree,newdata = lol_test)
lol_tree
Call:
randomForest(formula = winner ~ firstTower + firstInhibitor + firstBaron + firstDragon + firstRiftHerald, data = lol_train, ntree = 500)
Type of random forest: classification
Number of trees: 500
No. of variables tried at each split: 2
OOB estimate of error rate: 9.42%
Confusion matrix:
1 2 class.error
1 18316 1806 0.08975251
2 1953 17809 0.09882603 # Confusion matrix:
# 1 2 class.error
# 1 18322 1800 0.08945433
# 2 1966 17796 0.09948386
# 預測(randomForest prediction)(加入towel_gap, dragon_gap, baron_gap, inhibitorKills_gap, gameDuration)
lol_tree <- randomForest(winner ~ firstBlood + firstTower + firstInhibitor + firstBaron + firstDragon + firstRiftHerald + tower_gap + dragon_gap + baron_gap + inhibitorKills_gap + gameDuration,lol_train, ntree = 500)
result_tree <- predict(lol_tree,newdata = lol_test)
lol_tree
Call:
randomForest(formula = winner ~ firstBlood + firstTower + firstInhibitor + firstBaron + firstDragon + firstRiftHerald + tower_gap + dragon_gap + baron_gap + inhibitorKills_gap + gameDuration, data = lol_train, ntree = 500)
Type of random forest: classification
Number of trees: 500
No. of variables tried at each split: 3
OOB estimate of error rate: 2.4%
Confusion matrix:
1 2 class.error
1 19649 473 0.02350661
2 484 19278 0.02449145summary(lol_tree) Length Class Mode
call 4 -none- call
type 1 -none- character
predicted 39884 factor numeric
err.rate 1500 -none- numeric
confusion 6 -none- numeric
votes 79768 matrix numeric
oob.times 39884 -none- numeric
classes 2 -none- character
importance 11 -none- numeric
importanceSD 0 -none- NULL
localImportance 0 -none- NULL
proximity 0 -none- NULL
ntree 1 -none- numeric
mtry 1 -none- numeric
forest 14 -none- list
y 39884 factor numeric
test 0 -none- NULL
inbag 0 -none- NULL
terms 3 terms call
隨機森林ROC(ROC curve of Random Forest)
# 繪製隨機森林的ROC曲線，繪製ROC curve之圖形，並算出AUC
rf.pred <- predict(lol_tree, lol_test, type = "prob")
rf.roc <- prediction(rf.pred[,2], lol_test$winner)
rf.auc <- performance(rf.roc, 'tpr', 'fpr')
# rf.auc
plot(rf.auc)
abline(0, 1)
# text(0.5, 0.5, as.character(rf.auc@y.values[[1]]))
邏輯式迴歸與隨機森林在ROC曲線與AUC之比較
# 將邏輯式迴歸跟隨機森林所繪製出之ROC曲線進行比較
layout(matrix(c(1,2),1,2,byrow = F))
# 邏輯式迴歸
plot(perf, main = "ROC curve", xlab = "False positive rate", ylab = "True positive rate")
abline(0, 1)text(0.5, 0.5, as.character(auc@y.values[[1]])) # AUC = 0.9408
# 隨機森林
plot(rf.auc)abline(0, 1)
計算平均平方誤差MSE(Mean Square Error)
# mean((result-lol_test$winner)^2)
dim(lol_test) # 9972 71[1] 9972 75dim(lol_train) # 39884 71[1] 39884 75summary(model1)
Call:
glm(formula = winner ~ firstBlood + firstTower + firstInhibitor +
firstBaron + firstDragon + firstRiftHerald + tower_gap +
dragon_gap + baron_gap + inhibitorKills_gap + gameDuration,
family = "binomial", data = lol_train)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.8432 -0.0338 -0.0023 0.0325 4.7229
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.37382 0.27022 1.383 0.166540
firstBlood2 -0.12787 0.07033 -1.818 0.069042 .
firstTower2 -0.87222 0.07553 -11.548 < 2e-16 ***
firstInhibitor1 0.51610 0.13912 3.710 0.000207 ***
firstInhibitor2 -0.58941 0.14017 -4.205 2.61e-05 ***
firstBaron1 0.52945 0.13253 3.995 6.47e-05 ***
firstBaron2 -0.08496 0.13143 -0.646 0.518002
firstDragon1 0.47420 0.26300 1.803 0.071388 .
firstDragon2 0.59231 0.26366 2.246 0.024673 *
firstRiftHerald1 0.22080 0.08751 2.523 0.011634 *
firstRiftHerald2 -0.59453 0.08857 -6.713 1.91e-11 ***
tower_gap -1.28958 0.02374 -54.313 < 2e-16 ***
dragon_gap 0.04511 0.02163 2.086 0.037020 *
baron_gap -0.62911 0.05491 -11.456 < 2e-16 ***
inhibitorKills_gap 0.10260 0.03776 2.717 0.006591 **
gameDuration -0.01023 0.00544 -1.880 0.060134 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 55287.7 on 39883 degrees of freedom
Residual deviance: 5838.7 on 39868 degrees of freedom
AIC: 5870.7
Number of Fisher Scoring iterations: 9
【敘述統計】 欲瞭解當獲勝方為藍方時，閃現(flash)放在D鍵與F鍵的比例
summary(glm(winner ~ firstDragon, data= lol_train, family = "binomial"))
Call:
glm(formula = winner ~ firstDragon, family = "binomial", data = lol_train)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.4984 -0.8730 -0.8730 0.8873 1.5161
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.27006 0.08775 -3.078 0.00209 **
firstDragon1 -0.49825 0.08908 -5.593 2.23e-08 ***
firstDragon2 0.99897 0.08906 11.217 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 55288 on 39883 degrees of freedom
Residual deviance: 50130 on 39881 degrees of freedom
AIC: 50136
Number of Fisher Scoring iterations: 4test1 <- subset(lol_train,lol_train$firstDragon!=0)
summary(glm(test1$winner ~ as.factor(test1$firstDragon),family = "binomial"))
Call:
glm(formula = test1$winner ~ as.factor(test1$firstDragon), family = "binomial")
Deviance Residuals:
Min 1Q Median 3Q Max
-1.4984 -0.8730 -0.8730 0.8873 1.5161
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.76831 0.01535 -50.05 <2e-16 ***
as.factor(test1$firstDragon)2 1.49723 0.02159 69.34 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 54555 on 39354 degrees of freedom
Residual deviance: 49406 on 39353 degrees of freedom
AIC: 49410
Number of Fisher Scoring iterations: 4summary(glm(lol_train$winner ~ lol_train$t1_champ1_sum1,family = "binomial"))
Call:
glm(formula = lol_train$winner ~ lol_train$t1_champ1_sum1, family = "binomial")
Deviance Residuals:
Min 1Q Median 3Q Max
-1.202 -1.170 -1.150 1.185 1.247
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.06454 0.08717 -0.740 0.459
lol_train$t1_champ1_sum1Cleanse -0.09710 0.20017 -0.485 0.628
lol_train$t1_champ1_sum1Exhaust 0.01274 0.09496 0.134 0.893
lol_train$t1_champ1_sum1Flash 0.04615 0.08821 0.523 0.601
lol_train$t1_champ1_sum1Ghost 0.12308 0.12037 1.022 0.307
lol_train$t1_champ1_sum1Heal 0.06510 0.09337 0.697 0.486
lol_train$t1_champ1_sum1Ignite 0.04496 0.09459 0.475 0.635
lol_train$t1_champ1_sum1Smite 0.04236 0.09317 0.455 0.649
lol_train$t1_champ1_sum1Teleport 0.06080 0.09310 0.653 0.514
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 55288 on 39883 degrees of freedom
Residual deviance: 55285 on 39875 degrees of freedom
AIC: 55303
Number of Fisher Scoring iterations: 3a <- lol[,c(5,13,16,19,22,25)]
summary(a) winner t1_champ1_sum1 t1_champ2_sum1 t1_champ3_sum1 t1_champ4_sum1 t1_champ5_sum1
1:25211 Flash :27295 Flash :27144 Flash :27117 Flash :27104 Flash :27085
2:24645 Teleport: 4784 Heal : 4763 Heal : 4737 Heal : 4801 Teleport: 4899
Smite : 4556 Smite : 4626 Smite : 4649 Smite : 4519 Smite : 4636
Heal : 4439 Teleport: 4426 Teleport: 4529 Teleport: 4515 Heal : 4352
Ignite : 3700 Exhaust : 3770 Exhaust : 3808 Exhaust : 3863 Ignite : 3794
Exhaust : 3544 Ignite : 3697 Ignite : 3656 Ignite : 3668 Exhaust : 3634
(Other) : 1538 (Other) : 1430 (Other) : 1360 (Other) : 1386 (Other) : 1456 b <- lol[,c(5,38,41,44,47,50)]
summary(b) winner t2_champ1_sum1 t2_champ2_sum1 t2_champ3_sum1 t2_champ4_sum1 t2_champ5_sum1
1:25211 Flash :27312 Flash :27150 Flash :27280 Flash :27166 Flash :26937
2:24645 Teleport: 4790 Heal : 4704 Heal : 4687 Heal : 4757 Teleport: 4880
Smite : 4451 Smite : 4561 Teleport: 4576 Smite : 4743 Smite : 4624
Heal : 4325 Teleport: 4533 Smite : 4470 Teleport: 4456 Heal : 4428
Ignite : 3799 Exhaust : 3782 Exhaust : 3813 Exhaust : 3734 Ignite : 3840
Exhaust : 3660 Ignite : 3693 Ignite : 3642 Ignite : 3583 Exhaust : 3759
(Other) : 1519 (Other) : 1433 (Other) : 1388 (Other) : 1417 (Other) : 1388 c <- a[a$winner=="1",]
d <- b[b$winner=="1",]
summary(c) winner t1_champ1_sum1 t1_champ2_sum1 t1_champ3_sum1 t1_champ4_sum1 t1_champ5_sum1
1:25211 Flash :13819 Flash :13715 Flash :13708 Flash :13614 Flash :13681
2: 0 Teleport: 2428 Heal : 2392 Smite : 2398 Heal : 2482 Teleport: 2543
Smite : 2296 Smite : 2296 Heal : 2381 Smite : 2310 Smite : 2334
Heal : 2230 Teleport: 2215 Teleport: 2241 Teleport: 2251 Heal : 2135
Ignite : 1870 Exhaust : 1940 Exhaust : 1926 Exhaust : 1984 Ignite : 1926
Exhaust : 1792 Ignite : 1924 Ignite : 1866 Ignite : 1832 Exhaust : 1858
(Other) : 776 (Other) : 729 (Other) : 691 (Other) : 738 (Other) : 734 summary(d) winner t2_champ1_sum1 t2_champ2_sum1 t2_champ3_sum1 t2_champ4_sum1 t2_champ5_sum1
1:25211 Flash :13769 Flash :13727 Flash :13857 Flash :13659 Flash :13572
2: 0 Teleport: 2475 Heal : 2415 Teleport: 2361 Smite : 2394 Teleport: 2450
Smite : 2249 Smite : 2295 Heal : 2330 Heal : 2363 Smite : 2394
Heal : 2241 Teleport: 2240 Smite : 2181 Teleport: 2337 Heal : 2269
Ignite : 1855 Exhaust : 1926 Exhaust : 1938 Exhaust : 1954 Ignite : 1939
Exhaust : 1841 Ignite : 1875 Ignite : 1856 Ignite : 1810 Exhaust : 1882
(Other) : 781 (Other) : 733 (Other) : 688 (Other) : 694 (Other) : 705 s1 <- 13819 + 13715 + 13708 + 13614 + 13681
s2 <- 13769 + 13727 + 13857 + 13659 + 13572
s1 / (25211 * 5) # 獲勝方為藍方時，將閃現放在D鍵的比例 # 0.5437071[1] 0.5437071s2 / (25211 * 5) # 獲勝方為藍方時，將閃現放在F鍵的比例 # 0.54408[1] 0.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