This article is from 2005. Are its precepts still valid?
If you buy a domain and don't renew, theres a ~45 day "redemption period", during which you can pay a fee to get it back (GoDaddy charges $80 for this). If you don't, the domain is released back into the wild by Verisign, and all registrars get an equal crack at it. The reason Pool has such a good chance is that they own 80 registrars, so they have 80 horses in the race. That's what the original article discusses.
However, in the last few years drop-catching has become largely irrelevant. Here's why, using GoDaddy and TDNAM as an example:
During that 45 day redemption period, GoDaddy auctions off the right to buy the domain via the TDNAM. If someone pays the fee, they'll renew it themselves to sell it, it never hits the wild again, and the drop catchers never get a shot.
This is how I got GeorgeWBushLibrary.com for $15 (paid TDNAM fee), which I then sold for $35,000 less than a year later.
Network Solutions has NameJet, enom has one too (forget the name). Between those 3, most domains are covered, making drop catching a dying art.
Edit: Its important to note that each aftermarket can only sell domains currently registered at their registrar. So TDNAM only sells domains regged @ GoDaddy, NameJet only sells domains regged @ NetSol, etc.
Basically:
If the domain you want was regged with GoDaddy, Network Solutions, or eNom, buy it out of their aftermarket (much cheaper, better chance).
Otherwise hire drop catchers. You can hire several, because you only pay the winner. However, be careful what you're getting yourself into here - for that the original article is still very relevant.
For expired names that were registered at Godaddy/Wildest, the name goes into a 10 day auction around 25 days after expiration. At the end of the 10 days, it goes to the highest bidder. Then the winning bidder has to wait another 7 days before the domain is in their possession.
As far as the players, SnapNames, Godaddy, and Pool still are still around. Enom's Club Drop is now NameJet. As mentioned in the article, Network Solutions had an exclusive agreement with Snap (now they are using NameJet). In the past few years, many more registrars have adopted this strategy where they partner with an auction service and make money when the domains are sold.
Most names with these partner agreements become available around 35 days after expiration. These names do keep their original creation date so it's as if the original owner transferred it to you rather than it actually deleting and being re-registered.
If the name is with a registrar who does not have a partner agreement or a name that is not backordered during the auctions, it eventually deletes around 75 days later where the actual dropcatching referenced in the article picks up.