Introduction

This is a reddit community survey for Fate Grand/Order (FGO) players taken in the June - July 2018 period. The survey focused on the Super Super Rare (SSR) heroic spirits. A total of 4930 submissions were collected.

Data processing/cleaning was conducted before analysis of the data. These included:

  1. Removal of blank and NA rows
  2. Removal of F2P user with 420 total SSRs with less than 1 month played
  3. Merging of the multiple columns for easier data analysis e.g. grouping Sabers together etc.
  4. Assuming that blank sex indicated “Prefer not to say”

After data processing, a total sample size of n=4794 was available (approximately 4% reduction in data). Submissions with missing data were removed for faster analysis though it is not the most efficient use of the data. A possible improvement would be to use data imputation to fill in missing data instead of discarding the whole submission.

It is important to consider the bias in the data set. Since it was taken from 3 sources (one of which was reddit), it may not be representative of the whole player base of FGO.

Spending Demographics

Table 1: Spending of Players
Spending Frequency Percent of Total
F2P 1341 27.97
Paid Gacha Only 1451 30.27
1-100 USD monthly 1238 25.82
100-500 USD monthly 690 14.39
500+ USD monthly 74 1.54

From Table 1, 72.03% of players have spent at least $1 in the game so far. Of the players who have spent money on the game, 42.03% were from paid gacha only, 35.85% spent $1 to $100, 19.98% spent between $100 and $500 per month, and 2.14% spent more than $500.

Sex

Table 2 to 4 summarises Spending and Sex.
Table 2: Spending vs Sex
Female Male Prefer not to say
F2P 148 1094 99
Paid Gacha Only 125 1232 94
1-100 USD monthly 118 1069 51
100-500 USD monthly 58 592 40
500+ USD monthly 7 64 3

Table 2 contains the frequency for each of the categories of left blank, Female, Male and “Prefer not to say”.

Table 3: Spending vs Sex Conditioning on Spending
Female Male Prefer not to say
F2P 0.11 0.82 0.07
Paid Gacha Only 0.09 0.85 0.06
1-100 USD monthly 0.10 0.86 0.04
100-500 USD monthly 0.08 0.86 0.06
500+ USD monthly 0.09 0.86 0.04

Table 3 displays the proportions of each Sex given they are a certain spender e.g. in F2P, females make up 11% of the total. This means that summing up each row will result in 100%.

Table 4: Spending vs Sex Conditioning on Sex
Female Male Prefer not to say
F2P 0.32 0.27 0.34
Paid Gacha Only 0.27 0.30 0.33
1-100 USD monthly 0.26 0.26 0.18
100-500 USD monthly 0.13 0.15 0.14
500+ USD monthly 0.02 0.02 0.01

Similarly, Table 4 conditions on the Sex variable e.g. given someone is Male, 27% of them are classified as F2P. In other words, summing up the columns will add up to 100%.

Playtime

The variable playtime was divided into five categories:

  • Less than 1 month
  • 1-3 months
  • 3-6 months
  • 6-12 months
  • 12+ months (more than a year)
Table 5 below displays the frequencies of playtime summarised by spending type.
Table 5: Spending vs Playtime
Less than 1 month 1-3 months 3-6 months 6-12 months 12+ months
F2P 39 132 207 389 574
Paid Gacha Only 18 116 183 386 748
1-100 USD monthly 6 53 148 373 658
100-500 USD monthly 6 33 61 192 398
500+ USD monthly 0 1 5 25 43
Table 6 represents the frequencies as proportions, conditioning on the rows e.g. spending category.
Table 6: Spending vs Playtime Conditioning on Spending
Less than 1 month 1-3 months 3-6 months 6-12 months 12+ months
F2P 0.03 0.10 0.15 0.29 0.43
Paid Gacha Only 0.01 0.08 0.13 0.27 0.52
1-100 USD monthly 0.00 0.04 0.12 0.30 0.53
100-500 USD monthly 0.01 0.05 0.09 0.28 0.58
500+ USD monthly 0.00 0.01 0.07 0.34 0.58
Table 7 shows the proportions of the frequencies conditioning on the columns e.g. by playtime.
Table 7: Spending vs Playtime Conditioning on Playtime
Less than 1 month 1-3 months 3-6 months 6-12 months 12+ months
F2P 0.57 0.39 0.34 0.28 0.24
Paid Gacha Only 0.26 0.35 0.30 0.28 0.31
1-100 USD monthly 0.09 0.16 0.25 0.27 0.27
100-500 USD monthly 0.09 0.10 0.10 0.14 0.16
500+ USD monthly 0.00 0.00 0.01 0.02 0.02

It is interesting to see the proportion of F2P decrease over playtime.

Rerolls

The rerolls is a question asking whether someone rerolled during account creation. The results are shown in Tables 8 to 10.
Table 8: Spending vs Reroll
No Yes, I rerolled
F2P 941 400
Paid Gacha Only 900 551
1-100 USD monthly 823 415
100-500 USD monthly 426 264
500+ USD monthly 47 27
Table 9: Spending vs Reroll Conditioning on Spending
No Yes, I rerolled
F2P 0.70 0.30
Paid Gacha Only 0.62 0.38
1-100 USD monthly 0.66 0.34
100-500 USD monthly 0.62 0.38
500+ USD monthly 0.64 0.36
Table 10: Spending vs Reroll Conditioning on Reroll
No Yes, I rerolled
F2P 0.30 0.24
Paid Gacha Only 0.29 0.33
1-100 USD monthly 0.26 0.25
100-500 USD monthly 0.14 0.16
500+ USD monthly 0.01 0.02

Total SSRs

The mean and median of each spending categroy was found. These are shown in Table 11 below:
Table 11: Means and Medians of Spending Categories
Mean Median
F2P 4.69 4
Paid Gacha Only 6.61 6
1-100 USD monthly 9.93 9
100-500 USD monthly 17.62 16
500+ USD monthly 45.43 35

At a glance, the mean and medians are similar for F2P, Paid Gacha Only and spending of $1-100 monthly. This suggests the means of those groups are not as skewed by outliers.

A probability density function (PDF) was also constructed based on the observations for each spending category. These plots visually support the means and medians calculated previously.

From the boxplot, there appear to be potential outliers represented as the black dots. These could be lucky players or in the case of players in the 500+ USD monthly spending category, big spenders.

Analysis of Variance

An analysis of variance (ANOVA) can be conducted to investigate spending category and total number of SSRs.

##                 Df Sum Sq Mean Sq F value Pr(>F)    
## data$Spending    4 183639   45910   909.4 <2e-16 ***
## Residuals     4789 241769      50                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

After running a one-way ANOVA using spending category as the explanatory variable, we get very strong evidence that the means of each spending category are different.

The assumptions of the ANOVA are checked via the plots below.

Diagnostics of the ANOVA assumptions indicate that:

  • the residuals of the data may not be normally distributed via the qq-plot
  • variance may not be constant by the Residuals vs Fitted plot as the group on the far right appears to have a higher variance than the other groups.

A Kruskal-Wallis test can be used instead as it makes no assumptions about the distribution (nonparametric).

## 
##  Kruskal-Wallis rank sum test
## 
## data:  SSR.Total by Spending
## Kruskal-Wallis chi-squared = 1727.3, df = 4, p-value < 2.2e-16

The test also indicates there is strong evidence that the means of total SSRs of the spending categories are different. To identify which spending categories are statistically different, the Games-Howell post-hoc test was used. The Games-Howell test was used instead of Tukey because it does not assume equal variences and sample size.

##                        n means variances
## F2P                 1341   4.7        12
## Paid Gacha Only     1451   6.6        14
## 1-100 USD monthly   1238   9.9        32
## 100-500 USD monthly  690  17.6       116
## 500+ USD monthly      74  45.4      1152
## 
##                                       diff ci.lo ci.hi    t   df    p
## Paid Gacha Only-F2P                    1.9   1.5   2.3 13.9 2790 <.01
## 1-100 USD monthly-F2P                  5.2   4.7   5.7 27.8 2023 <.01
## 100-500 USD monthly-F2P               12.9  11.8  14.1 30.7  765 <.01
## 500+ USD monthly-F2P                  40.7  29.7  51.8 10.3   73 <.01
## 1-100 USD monthly-Paid Gacha Only      3.3   2.8   3.8 17.4 2095 <.01
## 100-500 USD monthly-Paid Gacha Only   11.0   9.9  12.2 26.0  771 <.01
## 500+ USD monthly-Paid Gacha Only      38.8  27.8  49.9  9.8   73 <.01
## 100-500 USD monthly-1-100 USD monthly  7.7   6.5   8.9 17.4  908 <.01
## 500+ USD monthly-1-100 USD monthly    35.5  24.5  46.5  9.0   73 <.01
## 500+ USD monthly-100-500 USD monthly  27.8  16.7  38.9  7.0   75 <.01

From the outputs, all pairwise comparisons are statistically different with p-values < 0.01. Thus, all spending groups have different means in SSR total.

Unique SSRs

Unique SSRs are measured by having at least one of a SSR servant. Consequently, any additional copies of those servants are not counted e.g. NP2 Artoria will only count once for that person. This was measured by extracting and counting the relevant servants.

Class Breakdown

Below is the class breakdown for each spending category. None represents no SSR for a given class.
Table 12: Saber Class Across Spending Category
Servants F2P Paid.Gacha.Only 1-100.USD.monthly 100-500.USD.monthly 500.USD.monthly
Artoria Pendragon 277 56 478 406 389
Altera 293 60 456 427 370
Okita Souji 158 41 302 232 254
Mordred 208 48 314 214 259
Nero Claudius [Bride] 117 46 222 148 262
Ryougi Shiki 111 45 166 108 171
None 567 482 262 83 3
Table 13: Archer Class Across Spending Category
Servants F2P Paid Gacha Only 1-100 USD monthly 100-500 USD monthly 500+ USD monthly
Gilgamesh 178 47 271 230 278
Orion 204 54 380 284 328
Nikola Tesla 68 42 178 122 159
Arjuna 96 36 148 137 162
None 881 828 529 165 3
Table 14: Lancer Class Across Spending Category
Servants F2P Paid Gacha Only 1-100 USD monthly 100-500 USD monthly 500+ USD monthly
Scathach 268 65 425 323 407
Karna 116 41 194 146 184
Brynhildr 71 40 138 91 163
Artoria Pendragon [Lancer] 15 8 49 41 30
None 908 921 574 172 6
Table 15: Rider Class Across Spending Category
Servants F2P Paid Gacha Only 1-100 USD monthly 100-500 USD monthly 500+ USD monthly
Francis Drake 201 51 425 378 337
Queen Medb 35 34 150 139 124
Iskandar 145 38 198 154 174
Ozymandias 230 54 413 334 334
None 833 657 403 124 2
Table 16: Caster Class Across Spending Category
Servants F2P Paid Gacha Only 1-100 USD monthly 100-500 USD monthly 500+ USD monthly
Zhuge Liang [El-Melloi II] 352 64 598 561 441
Tamamo-no-mae 194 58 464 361 389
Xuanzang 124 54 294 265 289
Leonardo Da Vinci 61 37 103 51 123
None 754 526 289 81 0
Table 17: Assassin Class Across Spending Category
Servants F2P Paid Gacha Only 1-100 USD monthly 100-500 USD monthly 500+ USD monthly
Jack the Ripper 193 57 423 298 343
MHX 124 44 209 132 224
Shuten Douji 162 48 280 153 268
None 916 950 546 163 5
Table 18: Berserker Class Across Spending Category
Servants F2P Paid Gacha Only 1-100 USD monthly 100-500 USD monthly 500+ USD monthly
Sakata Kintoki 105 35 148 103 150
Vlad III 241 56 465 414 374
Cu Chulainn [Alter] 97 45 258 236 235
Florence Nightingale 131 41 277 206 215
Minamoto no Raiko 245 60 373 263 387
None 701 573 301 73 2
Table 19: Ruler Class Across Spending Category
Servants F2P Paid Gacha Only 1-100 USD monthly 100-500 USD monthly 500+ USD monthly
Jeanne D’arc 344 67 561 450 396
Amakusa Shirou 55 35 97 59 94
None 958 952 621 261 6
Table 20: Avenger Class Across Spending Category
Servants F2P Paid Gacha Only 1-100 USD monthly 100-500 USD monthly 500+ USD monthly
Jeanne D’arc [Alter] 374 68 586 498 473
Edmond Dantes 98 25 128 65 98
Angra Mainyu 202 34 277 278 199
None 778 749 469 157 3

Most Common Unique SSRs

The most common SSRs are shown in descending order in Table 20. Note that this is counted in terms of unique SSR so copies above NP1 are not considered.
Servants Total
Zhuge Liang [El-Melloi II] 2016
Jeanne D’arc [Alter] 1999
Jeanne D’arc 1818
Altera 1606
Artoria Pendragon 1606
Vlad III 1550
Scathach 1488
Tamamo-no-mae 1466
Francis Drake 1392
Ozymandias 1365
Minamoto no Raiko 1328
Jack the Ripper 1314
Orion 1250
Mordred 1043
Xuanzang 1026
Gilgamesh 1004
Angra Mainyu 990
Okita Souji 987
Shuten Douji 911
Cu Chulainn [Alter] 871
Florence Nightingale 870
Nero Claudius [Bride] 795
MHX 733
Iskandar 709
Karna 681
Ryougi Shiki 601
Arjuna 579
Nikola Tesla 569
Sakata Kintoki 541
Brynhildr 503
Queen Medb 482
Edmond Dantes 414
Leonardo Da Vinci 375
Amakusa Shirou 340
Artoria Pendragon [Lancer] 143

From the table, we can see that the top five most common SSRs are:

  1. Zhung Liang [El-Melloi II]
  2. Jeanne D’arc [Alter]
  3. Jean D’arc
  4. Altera
  5. Artoria Pendragon

Conversly, the top five least common SSRs are:

  1. Artoria Pendragon [Lancer]
  2. Amakusa Shirou
  3. Leonardo Da Vinci
  4. Edmond Dantes
  5. Queen Medb