In the case of the D-backs, many of their impact players were selected after that.
Among those selected later is right-hander Brandon Webb, who was the 249th overall pick in the 2000 Draft. Webb has had plenty of success since reaching the big leagues in 2003 and winning the National League Cy Young Award in 2006. He finished second in the Cy Young Award balloting in 2007 and 2008.
Who will be the stars to come out of Round 4 this year? Stay tuned.
After 111 picks on Day 1 -- including Round 1, Compensation Round A, Round 2, Round 3 and Compensation Round B -- and Rounds 4-30 on Day 2, the Draft will resume with exclusive coverage on MLB.com with Round 31 at 8:30 a.m. MST on Thursday.
MLB.com's coverage will include a live pick-by-pick audio stream, expert commentary and the exclusive Draft Tracker, a searchable database of every Draft-eligible player, featuring statistics, scouting reports and video highlights.
Fans will not only be able to follow along every minute of the way online, but they'll be able to interact directly with Draft-eligible players and MLB.com Draft experts, among others.
The Draft Tracker will also feature the addition of Twitter and the participation of "tweeters" such as MLB.com Draft expert @JonathanMayoB3, who will also be serving as on-air talent for all three days of the Draft, and reporter @LisaWinstonMLB, who will be writing the up-to-the-minute coverage for MLB.com.
In addition, MLB.com has created a Twitter account devoted to the Draft, where you can stay updated on every piece of info as it becomes available (@MLBDraft).
Sometimes a player selected after pick 111 moves relatively quickly like Chad Tracy, who was taken with the 218th pick in 2001 and made the big leagues for the first time in 2004.
Other times it takes a little bit of perseverance.
First baseman Josh Whitesell was picked with the 177th overall pick in the 2003 Draft and got his first seven at-bats in the big leagues last year for the D-backs.
And of course there's the ultimate story of perseverance from reliever Clay Zavada. The left-hander was selected with the 897th overall pick in the 2006 Draft. He ended up leaving baseball following the season after his father passed away.
Zavada spent the 2007 season tending to the family farm in Streator, Ill., before once again playing last year and getting his first taste of big league action last month.
Other D-backs that got picked after No. 111 include Eric Byrnes (225, 1998), Doug Davis (293, 1996), Augie Ojeda (381, 1996), Mark Reynolds (493, 2004), Chris Young (493, 2001) and Ryan Roberts (530, 2003).
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.