To explore the 'strictly research' angle further, then: I really do recommend that you set up a box and practice with John the Ripper
. Install it, learn about it, run it against hashes, tweak it, run it against more hashes.
As a sysadmin, it is good to have an understanding about how common password cracking approaches work. The utility can additionally be used to audit for weak passwords - particularly if your predecessors have a history of not enforcing strong ones.
I'd add: I took a weekend to familiarize myself with John the Ripper, and it was time very well spent. I propped up a (free) Amazon EC2 instance, and let it bang away at various passwords that I pre-selected. Based on the results, I modified the algorithm John followed a bit, and fine-tuned it to a happy place.
You will realize very quickly that simple passwords can be cracked in seconds in most cases. You'll also see that sufficiently strong passwords will take many months or many years
unless you have the computing capacity of a large corporation or gov't.