Simply deleting XMLRPC file

You shouldn’t delete that file – it will be restored after update – so deleting it makes no sense (and it shouldn’t be treated as security fix).

You can disable XMLRPC using filter:

add_filter('xmlrpc_enabled', '__return_false');

And even block access to that file. Below code for Apache (sandrodz showed code for nginx):

<Files xmlrpc.php>
    Order deny,allow
    Deny from all
</Files>