A good way to add and average all data in multiple files using awk

I’ve read the following link but not sure if it can be expanded to what I want.

Simple way to add columns from multiple files

I want to do is to add data in 20 files to one file as an average value. But for simplicity, if I have data in three files (They are 4 x 4)

#1.
0 0 1 0
1 0 0 1
1 0 0 0
0 0 0 0

#2.
0 0 0 0
0 0 0 1
1 1 1 1
1 1 1 1

#3.
1 1 1 1
0 0 0 0
0 0 0 0
0 0 0 0

The output will be their averaged value of 4×4 (#1 + #2 + #3 / 3)
0.33 0.33 0.66 0.33
0.33 0.00 0.00 0.66
0.66 0.33 0.33 0.33
0.33 0.33 0.33 0.33