How do I use hook_form_alter() to add CSS classes to a custom input field in user_register_form?
Looks like you're trying to use the HTML ID of the element you're interested in as the identifier in PHP - not quite how it works.

For a field API field, that will look more like:

$form['field_personal_best'][LANGUAGE_NONE][0]['value']['#attributes']['class'][] = 'foo';


Your mileage will probably vary there, have a read of Why is hook_form_alter() so messy? for some relevant information, and make sure you have the Devel module installed to help with debugging (dpm($form) will tell you pretty much everything you need to know).