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So..

A char is RE ([a-zA-Z][\^\$\~])

A fill is RE [\.,]

Freq = fills / (chars + fills)

Input:
F1 F2 F3 F4 Aa$.c$A..,.$,.,$.^~.
F1 F2 F3 F4 one^~.two.a$threeA$four.five$six
F1 F2 F3 F4...

There are some issues with the match strings you supplied. For one some match strings are substrings of others. If you wanted to know occurrences of ".$" and "." you'd have to look at the count of...

Always post some sample data. A couple of input lines and then the desired output. So here's a guess....

{
count = split($9, a, "[.,~^]");
printf ("%s %.3f\n", $0, (count - 1) / $8);
...