I revised the code slightly:

use Benchmark 'cmpthese';

sub get_value {
        my $self = shift;
        return $self->[0];
}

sub get_value2 {
        $_[0]->[0];
}

my $self = bless [123], '::main';

cmpthese( 16000000, {
        normal    => sub { $self->get_value() },
        optimized => sub { $self->get_value2() },
        direct    => sub { $self->[0] },
});

exit(0);

$ perl oo_benchmark.pl 
                Rate    normal optimized    direct
normal     1462523/s        --      -21%      -90%
optimized  1858304/s       27%        --      -88%
direct    15238095/s      942%      720%        --
[download]

Yes, it took 16 million iterations to get an accurate reading on the direct attribute access. With a variant of your original benchmark modified to avoid the double-dispatch penalty, I get:

use Benchmark 'cmpthese';

my $self = bless [123], '::main';

cmpthese( 16000000, {
        normal    => sub { $self->get_value() },
        optimized => sub { $self->get_value2() },
        direct    => sub { $self->[0] },
});

exit(0);

sub get_value {
        my $self = shift;
        return $self->[0];
}

sub get_value2 {
        $_[0]->[0];
}

$ perl oo_benchmark.pl 
                Rate    normal optimized    direct
normal     1725998/s        --      -14%      -94%
optimized  2007528/s       16%        --      -93%
direct    29629630/s     1617%     1376%        --
[download]

That represents speedups of around 20%, 11%, and 100%, respectively. I can make the case for a 10% speedup perhaps, but the others are way outside anything I can explain. Thus I'm not sure this benchmark is useful.