Candy Crush
Joel Jr Rudinas
October 28, 2018
- 1 Loading the Dataset
- 2 Getting the data
- 3 Examining the data
- 4 Having a visual look at the data
- 5 Analysis with respect to difficulty
- 6 Analysis with respect for losses
- 7 Applying concepts of Machine Learning onto the data
- 8 Note
Greetings!. Today i will have a look at the Candy Crush dataset that i found online. While part of the code involves something from the Datacamp project, i do would like to take a further look into the dataset
Let us load the library first. I would go for tidyverse since it’s the mother of all packages because once you load it, you’ll also get to load other necessary packages:
1 Loading the Dataset
library(tidyverse)## -- Attaching packages ----------------------------------------------------------------------------------- tidyverse 1.2.1 --## v ggplot2 3.0.0 v purrr 0.2.5
## v tibble 1.4.2 v dplyr 0.7.6
## v tidyr 0.8.1 v stringr 1.3.1
## v readr 1.1.1 v forcats 0.3.0## -- Conflicts -------------------------------------------------------------------------------------- tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()2 Getting the data
library(readxl)
candy_crush <- read_excel("D:/Working Directory/candy_crush.xlsx")
View(candy_crush)3 Examining the data
head(candy_crush)## # A tibble: 6 x 5
## player_id dt level num_attempts num_success
## <chr> <dttm> <dbl> <dbl> <dbl>
## 1 6dd5af4c7228fa353d50~ 2014-01-04 00:00:00 4 3 1
## 2 c7ec97c39349ab7e4d39~ 2014-01-01 00:00:00 8 4 1
## 3 c7ec97c39349ab7e4d39~ 2014-01-05 00:00:00 12 6 0
## 4 a32c5e9700ed356dc8dd~ 2014-01-03 00:00:00 11 1 1
## 5 a32c5e9700ed356dc8dd~ 2014-01-07 00:00:00 15 6 0
## 6 b94d403ac4edf639442f~ 2014-01-01 00:00:00 8 8 1str(candy_crush)## Classes 'tbl_df', 'tbl' and 'data.frame': 16865 obs. of 5 variables:
## $ player_id : chr "6dd5af4c7228fa353d505767143f5815" "c7ec97c39349ab7e4d39b4f74062ec13" "c7ec97c39349ab7e4d39b4f74062ec13" "a32c5e9700ed356dc8dd5bb3230c5227" ...
## $ dt : POSIXct, format: "2014-01-04" "2014-01-01" ...
## $ level : num 4 8 12 11 15 8 12 12 4 15 ...
## $ num_attempts: num 3 4 6 1 6 8 15 18 1 27 ...
## $ num_success : num 1 1 0 1 0 1 1 0 1 0 ...summary(candy_crush)## player_id dt level
## Length:16865 Min. :2014-01-01 00:00:00 Min. : 1.000
## Class :character 1st Qu.:2014-01-02 00:00:00 1st Qu.: 6.000
## Mode :character Median :2014-01-04 00:00:00 Median : 9.000
## Mean :2014-01-04 01:06:15 Mean : 9.287
## 3rd Qu.:2014-01-06 00:00:00 3rd Qu.:14.000
## Max. :2014-01-07 00:00:00 Max. :15.000
## num_attempts num_success
## Min. : 0.000 Min. : 0.0000
## 1st Qu.: 1.000 1st Qu.: 0.0000
## Median : 3.000 Median : 1.0000
## Mean : 5.535 Mean : 0.6272
## 3rd Qu.: 7.000 3rd Qu.: 1.0000
## Max. :258.000 Max. :55.0000names(candy_crush)## [1] "player_id" "dt" "level" "num_attempts"
## [5] "num_success"4 Having a visual look at the data
candy_crush %>%
ggplot(aes(level, num_attempts, col = num_success)) +
geom_point() +
labs(x = "\n Candy Crush levels \n") +
labs(y = "\n Number of attempts per player \n") +
labs(title = "\n Scatterpoint Distribution of Attempts per level \n")
5 Analysis with respect to difficulty
5.1 Let us check the number of players.
print("Number of players")## [1] "Number of players"length(unique(candy_crush$player_id))## [1] 68145.2 Computing level difficulty
difficulty <- candy_crush %>%
group_by(level) %>%
summarise(wins = sum(num_success), attempts = sum(num_attempts)) %>%
mutate(p_win = wins/attempts) %>%
mutate(p_loss = (attempts-wins)/attempts)
print(difficulty)## # A tibble: 15 x 5
## level wins attempts p_win p_loss
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 818 1322 0.619 0.381
## 2 2 666 1285 0.518 0.482
## 3 3 662 1546 0.428 0.572
## 4 4 705 1893 0.372 0.628
## 5 5 634 6937 0.0914 0.909
## 6 6 668 1591 0.420 0.580
## 7 7 614 4526 0.136 0.864
## 8 8 641 15816 0.0405 0.959
## 9 9 670 8241 0.0813 0.919
## 10 10 617 3282 0.188 0.812
## 11 11 603 5575 0.108 0.892
## 12 12 659 6868 0.0960 0.904
## 13 13 686 1327 0.517 0.483
## 14 14 777 2772 0.280 0.720
## 15 15 1157 30374 0.0381 0.9625.2.1 Plotting difficulty profile
Given that we now have information for all 15 levels, as we try to measure difficulty as the probability of success at a difficulty level in a single attempt, a lower value implies a higher level of difficulity.
Let us try to plot the level of difficulity with respect to the level.
p <- ggplot(difficulty, aes(x = level, y = p_win)) + geom_line()
p <- p + labs(x = "\n Level in Candy Crush \n")
p <- p + labs(y = "\n Percentage Win \n")
print(p)
5.2.2 Standard error for p_win for each level
difficulty <- difficulty %>%
mutate(error = sqrt(p_win * (1 - p_win)/attempts))
print(difficulty)## # A tibble: 15 x 6
## level wins attempts p_win p_loss error
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 818 1322 0.619 0.381 0.0134
## 2 2 666 1285 0.518 0.482 0.0139
## 3 3 662 1546 0.428 0.572 0.0126
## 4 4 705 1893 0.372 0.628 0.0111
## 5 5 634 6937 0.0914 0.909 0.00346
## 6 6 668 1591 0.420 0.580 0.0124
## 7 7 614 4526 0.136 0.864 0.00509
## 8 8 641 15816 0.0405 0.959 0.00157
## 9 9 670 8241 0.0813 0.919 0.00301
## 10 10 617 3282 0.188 0.812 0.00682
## 11 11 603 5575 0.108 0.892 0.00416
## 12 12 659 6868 0.0960 0.904 0.00355
## 13 13 686 1327 0.517 0.483 0.0137
## 14 14 777 2772 0.280 0.720 0.00853
## 15 15 1157 30374 0.0381 0.962 0.001105.2.3 Plotting uncertainty
Let us try to use error barplot to show the uncertainty in the plot. We’ll try to set the length of the error bars to one standard error. Upper and lower limit ought to be p_win + error and p_win - error respectively.
p <- ggplot(difficulty, aes(x = level, y = p_win)) + geom_line() + geom_point() + geom_hline(yintercept = 1)
p <- p + geom_errorbar(aes(ymin = p_win - error, ymax = p_win + error))
p <- p + labs(x = "\n Level in Candy Crush \n")
p <- p + labs(y = "\n Percentage of win \n")
print(p)
5.2.4 Final metric
What is the probability of completing the episode without any major hitch i.e. losing a single time
a <- prod(difficulty$p_win)
print(a)## [1] 9.447141e-126 Analysis with respect for losses
This wasn’t part of the Datacamp project but i will expand it anyway
6.1 Plotting loss profile
Inversely, let us plot the loss profile as the probability of loss at a difficulty level in a single attempt.
q <- ggplot(difficulty, aes(x = level, y = p_loss)) + geom_line()
q <- q + labs(x = "\n Level in Candy Crush \n")
q <- q + labs(y = "\n Percentage of Loss \n")
print(q)
6.2 Determining standard error for losses
difficulty <- difficulty %>%
mutate(error_loss = sqrt(p_loss * (1 - p_loss)/attempts))
print(difficulty)## # A tibble: 15 x 7
## level wins attempts p_win p_loss error error_loss
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 818 1322 0.619 0.381 0.0134 0.0134
## 2 2 666 1285 0.518 0.482 0.0139 0.0139
## 3 3 662 1546 0.428 0.572 0.0126 0.0126
## 4 4 705 1893 0.372 0.628 0.0111 0.0111
## 5 5 634 6937 0.0914 0.909 0.00346 0.00346
## 6 6 668 1591 0.420 0.580 0.0124 0.0124
## 7 7 614 4526 0.136 0.864 0.00509 0.00509
## 8 8 641 15816 0.0405 0.959 0.00157 0.00157
## 9 9 670 8241 0.0813 0.919 0.00301 0.00301
## 10 10 617 3282 0.188 0.812 0.00682 0.00682
## 11 11 603 5575 0.108 0.892 0.00416 0.00416
## 12 12 659 6868 0.0960 0.904 0.00355 0.00355
## 13 13 686 1327 0.517 0.483 0.0137 0.0137
## 14 14 777 2772 0.280 0.720 0.00853 0.00853
## 15 15 1157 30374 0.0381 0.962 0.00110 0.001106.3 Plotting uncertainty
q <- ggplot(difficulty, aes(x = level, y = p_loss)) + geom_line() + geom_point() + geom_hline(yintercept = 1)
q <- q + geom_errorbar(aes(ymin = p_loss - error_loss, ymax = p_loss + error_loss))
q <- q + labs(x = "\n Level in Candy Crush \n")
q <- q + labs(y = "\n Percentage of Loss \n")
print(q)
6.4 Probability of defeat
q <- prod(difficulty$p_loss)
print(q)## [1] 0.0057942697 Applying concepts of Machine Learning onto the data
7.0.1 Filtering the data
I’m going to try to deselect player ID and dt in an attempt to apply the principles of machine learning on this.
candy_crush_vars <- candy_crush %>%
select(-player_id, -dt)
print(candy_crush_vars)## # A tibble: 16,865 x 3
## level num_attempts num_success
## <dbl> <dbl> <dbl>
## 1 4 3 1
## 2 8 4 1
## 3 12 6 0
## 4 11 1 1
## 5 15 6 0
## 6 8 8 1
## 7 12 15 1
## 8 12 18 0
## 9 4 1 1
## 10 15 27 0
## # ... with 16,855 more rows7.0.2 Fitting in a linear model
fit <- lm(num_attempts ~ level + num_success, data = candy_crush_vars)
summary(fit)##
## Call:
## lm(formula = num_attempts ~ level + num_success, data = candy_crush_vars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.647 -3.647 -1.665 1.263 251.801
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.10007 0.14361 14.624 <2e-16 ***
## level 0.36205 0.01287 28.125 <2e-16 ***
## num_success 0.11628 0.06466 1.798 0.0721 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.155 on 16862 degrees of freedom
## Multiple R-squared: 0.04531, Adjusted R-squared: 0.04519
## F-statistic: 400.1 on 2 and 16862 DF, p-value: < 2.2e-167.1 Loading an important library for Machine Learning
library(caret)## Loading required package: lattice##
## Attaching package: 'caret'## The following object is masked from 'package:purrr':
##
## lift7.2 Creating test and train sets
We will have to split the dataset into two. One as a training dataset and the other as a testing dataset in order to estimate how well it’s going to perform with new data. Caret’s pretty good with it. I’ll try to split it to a 80-20 ratio.
set.seed(6969) #I just love the number hahahahahahahaa.
in_train <- createDataPartition(candy_crush_vars$level, p = 0.8, list = FALSE)
training <- candy_crush_vars[in_train, ]
testing <- candy_crush_vars[-in_train, ]Just out of curiosity, i will have a little look at the training and testing data
head(training)## # A tibble: 6 x 3
## level num_attempts num_success
## <dbl> <dbl> <dbl>
## 1 4 3 1
## 2 12 6 0
## 3 11 1 1
## 4 15 6 0
## 5 8 8 1
## 6 4 1 1str(training)## Classes 'tbl_df', 'tbl' and 'data.frame': 13494 obs. of 3 variables:
## $ level : num 4 12 11 15 8 4 15 15 8 15 ...
## $ num_attempts: num 3 6 1 6 8 1 27 15 8 3 ...
## $ num_success : num 1 0 1 0 1 1 0 0 0 0 ...summary(training)## level num_attempts num_success
## Min. : 1.000 Min. : 0.000 Min. : 0.0000
## 1st Qu.: 6.000 1st Qu.: 1.000 1st Qu.: 0.0000
## Median : 9.000 Median : 3.000 Median : 1.0000
## Mean : 9.294 Mean : 5.548 Mean : 0.6257
## 3rd Qu.:14.000 3rd Qu.: 7.000 3rd Qu.: 1.0000
## Max. :15.000 Max. :258.000 Max. :55.0000nrow(training)## [1] 13494head(testing)## # A tibble: 6 x 3
## level num_attempts num_success
## <dbl> <dbl> <dbl>
## 1 8 4 1
## 2 12 15 1
## 3 12 18 0
## 4 15 5 0
## 5 14 7 1
## 6 4 3 1str(testing)## Classes 'tbl_df', 'tbl' and 'data.frame': 3371 obs. of 3 variables:
## $ level : num 8 12 12 15 14 4 5 12 13 1 ...
## $ num_attempts: num 4 15 18 5 7 3 15 5 2 1 ...
## $ num_success : num 1 1 0 0 1 1 0 1 1 0 ...summary(testing)## level num_attempts num_success
## Min. : 1.00 Min. : 0.000 Min. : 0.0000
## 1st Qu.: 6.00 1st Qu.: 1.000 1st Qu.: 0.0000
## Median : 9.00 Median : 3.000 Median : 1.0000
## Mean : 9.26 Mean : 5.486 Mean : 0.6331
## 3rd Qu.:13.00 3rd Qu.: 7.000 3rd Qu.: 1.0000
## Max. :15.00 Max. :138.000 Max. :46.0000nrow(testing)## [1] 33717.2.1 Training the model…no bootstrapping yet
fit_lm <- train(num_success ~., method = "lm", data = training, trControl = trainControl(method = "none"))
print(fit_lm)## Linear Regression
##
## 13494 samples
## 2 predictor
##
## No pre-processing
## Resampling: None7.2.2 Training a random forest model…same thing
fit_rf <- train(num_success ~., method = "rf", data = training, trControl = trainControl(method = "none"))
print(fit_rf)## Random Forest
##
## 13494 samples
## 2 predictor
##
## No pre-processing
## Resampling: None7.3 Evaluating the model
7.3.1 Let us load the library
library(yardstick)## Loading required package: broom##
## Attaching package: 'yardstick'## The following objects are masked from 'package:caret':
##
## mnLogLoss, precision, recall## The following object is masked from 'package:readr':
##
## spec7.3.2 Creating the new columns using the training data
results <- training %>%
mutate(`Linear Regression` = predict(fit_lm, training),
`Random Forest` = predict(fit_rf, training))
metrics(results, truth = level, estimate = `Linear Regression`)## # A tibble: 1 x 2
## rmse rsq
## <dbl> <dbl>
## 1 9.76 0.999metrics(results, truth = level, estimate = `Random Forest`)## # A tibble: 1 x 2
## rmse rsq
## <dbl> <dbl>
## 1 9.76 0.119print(results)## # A tibble: 13,494 x 5
## level num_attempts num_success `Linear Regression` `Random Forest`
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 4 3 1 0.799 0.983
## 2 12 6 0 0.536 0.549
## 3 11 1 1 0.567 0.674
## 4 15 6 0 0.437 0.334
## 5 8 8 1 0.670 0.401
## 6 4 1 1 0.798 0.936
## 7 15 27 0 0.448 0.337
## 8 15 15 0 0.442 0.355
## 9 8 8 0 0.670 0.401
## 10 15 3 0 0.436 0.415
## # ... with 13,484 more rows7.3.2.1 Plotting the results
results %>%
gather(Method, Result, `Linear Regression`:`Random Forest`) %>%
ggplot(aes(num_success, Result, color = Method)) +
geom_point(size = 1.5, alpha = 0.5) +
facet_wrap(~Method) +
geom_abline(lty = 2, color = "gray50") +
geom_smooth(method = "lm")
7.3.3 Same thing but with testing data
results <- testing %>%
mutate(`Linear Regression` = predict(fit_lm, testing),
`Random Forest` = predict(fit_rf, testing))
metrics(results, truth = level, estimate = `Linear Regression`)## # A tibble: 1 x 2
## rmse rsq
## <dbl> <dbl>
## 1 9.74 0.999metrics(results, truth = level, estimate = `Random Forest`)## # A tibble: 1 x 2
## rmse rsq
## <dbl> <dbl>
## 1 9.75 0.155print(results)## # A tibble: 3,371 x 5
## level num_attempts num_success `Linear Regression` `Random Forest`
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 8 4 1 0.668 0.467
## 2 12 15 1 0.541 0.618
## 3 12 18 0 0.542 0.506
## 4 15 5 0 0.437 0.330
## 5 14 7 1 0.471 0.900
## 6 4 3 1 0.799 0.983
## 7 5 15 0 0.772 0.424
## 8 12 5 1 0.536 0.438
## 9 13 2 1 0.502 0.868
## 10 1 1 0 0.898 0.995
## # ... with 3,361 more rows7.3.3.1 Plotting the results here
results %>%
gather(Method, Result, `Linear Regression`:`Random Forest`) %>%
ggplot(aes(num_success, Result, color = Method)) +
geom_point(size = 1.5, alpha = 0.5) +
facet_wrap(~Method) +
geom_abline(lty = 2, color = "gray50") +
geom_smooth(method = "lm")
8 Note
For those who want a csv copy of this dataset, i have it on github. You can get the csv raw from this link: https://raw.githubusercontent.com/joelrudinas03/Level-Difficulty-in-Candy-Crush-Saga-/master/candy_crush.csv
Grazie!