All the variables are declared using my at the beginning of the sub

FWIW, you're supposed to aim for smallest scope necessary, you'll develop this skill with practice :)(Tutorials: Variables and Scoping)

Compare Silenced, Loudmouth, and Smooth (always strive for Smooth)

#!/usr/bin/perl --

use strict;
use warnings;
use diagnostics;

use Data::Dumper();

Main( @ARGV );
exit( 0 );

sub Main {
    warn Dumper( Silenced('hello') ), ' ';
    warn '------' x 6;
    warn Dumper( Loudmouth('loud') ), ' ';
    warn '------' x 6;
    warn Dumper( Smooth('cop') ), ' ';
} ## end sub Main

sub Dumper { Data::Dumper->new( \@_ )->Indent(0)->Useqq(1)->Dump; }

sub Silenced {
    no warnings 'uninitialized';
    my @string_array = @_;
    my @string;
    my $basecount;
    my $pos;
    my $pos_score;
    my @temp_array;
    my %base_stat;

    foreach (@string_array) {
        @string = split( //, $_ );
        $basecount = 0;
        foreach $pos (@string) {
            $basecount++;
            $pos_score  = ord($pos) - 33;
            @temp_array = $base_stat{$basecount};    # line 124
            push( @temp_array, $pos_score );
            $base_stat{$basecount} = "@temp_array";
        } ## end foreach $pos (@string)
    } ## end foreach (@string_array)
    return \%base_stat;

} ## end sub Silenced

sub Loudmouth {
    my @string_array = @_;
    my @string;
    my $basecount;
    my $pos;
    my $pos_score;
    my @temp_array;
    my %base_stat;
    foreach (@string_array) {
        @string = split( //, $_ );
        $basecount = 0;
        foreach $pos (@string) {
            $basecount++;
            $pos_score = ord($pos) - 33;

            warn Dumper( \%base_stat ), ' ';

            @temp_array = $base_stat{$basecount};    # line 124
            push( @temp_array, $pos_score );
            $base_stat{$basecount} = "@temp_array";
        } ## end foreach $pos (@string)
    } ## end foreach (@string_array)
    return \%base_stat;
} ## end sub Loudmouth

sub Smooth {
    my %base_stat;
    for my $str (@_) {
        my $basecount = 0;
        for my $pos ( split( //, $str ) ) {
            $basecount++;
            my $pos_score = ord($pos) - 33;

#~ $base_stat{$basecount} = $base_stat{$basecount} ." ". $pos_score; #
+ loud
            $base_stat{$basecount} .= " ". $pos_score;    # smooth
        } ## end for my $pos ( split( //...))
    } ## end for my $str (@_)
    return \%base_stat;
} ## end sub Smooth
__END__
$ perl pm.897159.pl
$VAR1 = {4 => " 75",1 => " 71",3 => " 75",2 => " 68",5 => " 78"};  at 
+pm.897159.pl line 13.
------------------------------------ at pm.897159.pl line 14.
$VAR1 = {};  at pm.897159.pl line 62.
Use of uninitialized value $temp_array[0] in join or string at pm.8971
+59.pl
        line 66 (#1)
    (W uninitialized) An undefined value was used as if it were alread
+y
    defined.  It was interpreted as a "" or a 0, but maybe it was a mi
+stake.
    To suppress this warning assign a defined value to your variables.

    To help you figure out what was undefined, perl will try to tell y
+ou the
    name of the variable (if any) that was undefined. In some cases it
+ cannot
    do this, so it also tells you what operation you used the undefine
+d value
    in.  Note, however, that perl optimizes your program and the opera
+tion
    displayed in the warning may not necessarily appear literally in y
+our
    program.  For example, "that $foo" is usually optimized into "that
+ "
    . $foo, and the warning will refer to the concatenation (.) operat
+or,
    even though there is no . in your program.

$VAR1 = {1 => " 75"};  at pm.897159.pl line 62.
$VAR1 = {1 => " 75",2 => " 78"};  at pm.897159.pl line 62.
$VAR1 = {1 => " 75",3 => " 84",2 => " 78"};  at pm.897159.pl line 62.
$VAR1 = {4 => " 67",1 => " 75",3 => " 84",2 => " 78"};  at pm.897159.p
+l line 15.
------------------------------------ at pm.897159.pl line 16.
$VAR1 = {1 => " 66",3 => " 79",2 => " 78"};  at pm.897159.pl line 17.
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Questions?