What is it you want to do? You want to calculate the average score of every bowler.

That means you need to loop for every bowler:

for my $bowler (0..3) {
   ...
}
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Better yet, let's not assume we know how many games there are:

for my $bowler (0..$#scores) {
   ...
}
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We will be working with the scores of a specific bowler, so let's create a shortcut:

for my $bowler (0..$#scores) {
   my $bscores = $scores[$bowler];
   ...
}
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Now, we need to calculate the average score of a bowler:

$averages[$bowler] = int(($bscores->[0] +
                          $bscores->[1] +
                          $bscores->[2])/3);
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That's ok, but it could be better. We could use a loop to remove the redundancy and to avoid assuming we know how many games there are:

my $sum = 0;
for my $game (0..$#$bscores}) {
   $sum += $bscores->[$game];
}
$averages[$bowler] = int($sum/@$bscores);
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We can clean it up a bit by using a foreach loop (since $game is only used as an index into @$bscores):

my $sum = 0;
$sum += $_ foreach @$bscores;
$averages[$bowler] = int($sum/@$bscores);
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All together now:

for my $bowler (0..$#scores) {
   my $bscores = $scores[$bowler];
   my $sum = 0;
   $sum += $_ foreach @$bscores;
   $averages[$bowler] = int($sum/@$bscores);
}
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You could even use List::Util to do the sum:

use List::Util qw( sum );

for my $bowler (0..$#scores) {
   my $bscores = $scores[$bowler];
   $averages[$bowler] = int(sum(@$bscores)/@$bscores);
}
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(Why isn't that module part of core?)