See the my toy data (here)[https://github.com/ecosang/misc/blob/master/ttt.csv]

library(tidyverse)
library(magrittr)
dat <- read_csv("https://raw.githubusercontent.com/ecosang/misc/master/ttt.csv")
## Warning: Duplicated column names deduplicated: 'E' => 'E_1' [4], 'E' =>
## 'E_2' [5], 'A' => 'A_1' [6], 'A' => 'A_2' [7], 'E' => 'E_3' [8], 'E' =>
## 'E_4' [9], 'A' => 'A_3' [10], 'A' => 'A_4' [11], 'R' => 'R_1' [13], 'R' =>
## 'R_2' [14], 'A' => 'A_5' [15], 'A' => 'A_6' [16], 'R' => 'R_3' [17], 'A' =>
## 'A_7' [18], 'A' => 'A_8' [19], 'E' => 'E_5' [20], 'E' => 'E_6' [21], 'R' =>
## 'R_4' [22]
# https://raw.githubusercontent.com/ecosang/misc/master/ttt.csv
knitr::kable(dat)
stu A E E_1 E_2 A_1 A_2 E_3 E_4 A_3 A_4 R R_1 R_2 A_5 A_6 R_3 A_7 A_8 E_5 E_6 R_4
1 20.00 NA 21.25 NA 25.00 20.00 NA 20.00 NA 23.75 NA 23.75 21.25 NA NA 25.00 22.50 25.0 20.0 NA 25.00
2 20.00 NA 17.50 NA 23.75 21.25 NA 20.00 18.75 21.25 NA 22.50 NA 22.50 25.00 22.50 22.50 20.0 22.5 22.5 21.25
3 22.50 25.00 23.75 25.00 25.00 23.75 NA NA NA 25.00 NA 25.00 NA 23.75 23.75 NA 23.75 25.0 25.0 25.0 NA
4 22.50 25.00 23.75 NA 25.00 NA NA 21.25 25.00 20.00 25.0 NA NA NA NA 25.00 25.00 25.0 22.5 25.0 22.50
5 21.25 18.75 16.25 NA 22.50 21.25 NA NA 20.00 20.00 NA NA NA 25.00 25.00 16.25 21.25 NA 20.0 NA NA
6 21.25 NA 16.25 20.00 18.75 20.00 NA 21.25 20.00 NA 25.0 NA NA 23.75 NA NA 18.75 20.0 NA 20.0 20.00
7 NA 17.50 NA 21.25 20.00 20.00 NA NA 21.25 NA 22.5 NA NA 23.75 NA NA 18.75 20.0 NA 22.5 17.50
8 18.75 NA 16.25 25.00 20.00 16.25 NA NA 20.00 21.25 22.5 NA NA 22.50 22.50 22.50 20.00 20.0 22.5 22.5 18.75
9 22.50 NA 16.25 18.75 23.75 21.25 NA 23.75 NA 23.75 22.5 NA NA NA NA NA NA 22.5 NA 25.0 17.50
10 21.25 21.25 21.25 NA 22.50 21.25 NA 20.00 20.00 22.50 NA 22.50 NA NA NA 22.50 20.00 20.0 NA NA NA

The read_csv doesn’t allow duplicated col names.

# it is similar to reshape2::melt (colmun name => variable)
new_dat <- dat %>% gather(2:dim(dat)[2], key = "subject", value = "score")
knitr::kable(new_dat %>% head())
stu subject score
1 A 20
2 A 20
3 A 22.5
4 A 22.5
5 A 21.25
6 A 21.25 
# change subject as factor (e.g., A, A, A, E, E, E,... since read_csv
# doesn't allow duplicated colnames)
new_dat <- new_dat %>% mutate(subject = sapply(1:length(new_dat$subject), function(x) strsplit(new_dat$subject, 
    "_")[[x]][1]) %>% as.factor())
# change score as numeric
new_dat %<>% mutate(score = as.numeric(score))
knitr::kable(new_dat %>% head())
stu subject score
1 A 20.00
2 A 20.00
3 A 22.50
4 A 22.50
5 A 21.25
6 A 21.25 
# sort data by score
sort_dat <- new_dat %>% arrange(subject, stu, desc(score))
# remove NA ?  # it is not desired. I am not sure.
sort_dat <- sort_dat[sort_dat$score %>% is.na() %>% not(), ]
knitr::kable(sort_dat %>% head())
stu subject score
1 A 25.00
1 A 25.00
1 A 23.75
1 A 22.50
1 A 20.00
1 A 20.00 
final_dat <- sort_dat %>% group_by(stu, subject) %>% mutate(idx = row_number())
knitr::kable(final_dat %>% head())
stu subject score idx
1 A 25.00 1
1 A 25.00 2
1 A 23.75 3
1 A 22.50 4
1 A 20.00 5
1 A 20.00 6 
# filter top 3
output <- final_dat %>% filter(idx <= 3) %>% group_by(stu, subject) %>% summarize(top3_mean_score = mean(score))

knitr::kable(output)
stu subject top3_mean_score
1 A 24.58333
1 E 20.41667
1 R 24.58333
2 A 23.75000
2 E 21.66667
2 R 22.08333
3 A 25.00000
3 E 25.00000
3 R 25.00000
4 A 25.00000
4 E 24.58333
4 R 24.16667
5 A 24.16667
5 E 18.33333
5 R 16.25000
6 A 21.66667
6 E 20.41667
6 R 22.50000
7 A 21.66667
7 E 20.41667
7 R 20.00000
8 A 22.08333
8 E 23.33333
8 R 21.25000
9 A 23.33333
9 E 22.50000
9 R 20.00000
10 A 22.08333
10 E 20.83333
10 R 22.50000