Default statistics module. Count views of only published nodes when administration users see it
The Statistics module doesn't use any hook because generally works when Drupal has not completed its bootstrap phase. (That is if caching pages is enabled.)

What you can do is creating a custom module that runs right after the Statistics module, and execute code similar to the following one.

function mymodule_exit() {
  global $user;

  drupal_bootstrap(DRUPAL_BOOTSTRAP_VARIABLES);
  $is_node = (arg(0) == 'node' &amp;&amp; is_numeric(arg(1)) &amp;&amp; arg(2) == NULL);

  if (variable_get('statistics_count_content_views', 0) &amp;&amp; $is_node) {
    drupal_bootstrap(DRUPAL_BOOTSTRAP_FULL);
    $node = node_load(arg(1));
    if (!$node-&gt;status) {
      db_merge('node_counter')
        -&gt;key(array('nid' =&gt; $node-&gt;nid))
        -&gt;fields(array(
          'daycount' =&gt; 1, 
          'totalcount' =&gt; 1, 
          'timestamp' =&gt; REQUEST_TIME,
        ))
        -&gt;expression('daycount', 'daycount - 1')
        -&gt;expression('totalcount', 'totalcount - 1')
        -&gt;execute();
    }
  }
  if (variable_get('statistics_enable_access_log', 0) &amp;&amp; $is_node) {
    drupal_bootstrap(DRUPAL_BOOTSTRAP_FULL);
    $node = node_load(arg(1));    
    if (!$node-&gt;status) {
      db_delete('accesslog')
        -&gt;condition('title' =&gt; truncate_utf8(strip_tags(drupal_get_title()), 255))
        -&gt;condition('path' =&gt; truncate_utf8($_GET['q'], 255))
        -&gt;condition('url' =&gt; isset($_SERVER['HTTP_REFERER']) ? $_SERVER['HTTP_REFERER'] : '')
        -&gt;condition('hostname' =&gt; ip_address())
        -&gt;condition('uid' =&gt; $user-&gt;uid)
        -&gt;condition('sid' =&gt; session_id()) 
        -&gt;condition('timestamp' =&gt; REQUEST_TIME)
        -&gt;execute();
    }
  }
}