When you declare a variable with my, you initialise it. If you do this inside a loop, the variable is re-initialised on each loop iteration. But if you want the variable to grow as the loop iterates, you need to declare it once only, before the loop:

my @initials;
my @scores;

while (...)    # The major loop
{
    ...
    push @initials, $initial_add;
    push @scores,   $score_total;
    ...
}

# access @initials and @scores here
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Hope that helps,