Former general manager Billy Devaney did a decent job finding talented players in the early rounds, such as Sam Bradford, James Laurinaitis, Rodger Saffold and Bradley Fletcher (but then again, it helps when you pick in the top five).
However, one reason why Devaney is currently unemployed is due to his blatant inability to strike gold in the later rounds as a direct result of him foolishly wasting picks on pet projects (Fendi Onobun) and nobodies (Hall Davis).
The current brain trust has to change the team's philosophy in the draft and realize the importance of finding quality players after the first three rounds.
If the Rams want to change their losing ways sooner rather than later, they'll have to get lucky and find some late-round stars.
So here are 10 sleepers who should be on their radar.
At 6'4" and 225 pounds, Tarheels receiver Dwight Jones possesses the incredible size that NFL scouts look for in a prospect.
Jones put together a great 2011 season with 85 receptions for 1,196 yards and 12 touchdowns.
However, Jones potentially has come character concerns stemming from the recent New Year's Eve party he planned, which attracted some heat from the NCAA.
Either way, he's worth a look.
Running back Chris Polk has been lighting it up in Washington in recent years with three consecutive 1,000-yard seasons.
He had his best season in 2011, which resulted in 1,488 yards and 12 touchdowns, as well as an additional 332 yards and four touchdowns in the receiving game.
Polk would provide the Rams with a speedy back capable of relieving Steven Jackson on third down. He would also provide Sam Bradford with a capable receiving weapon out of the backfield.
However, while Polk is agile enough to run around tacklers, he lacks the elite speed necessary to break free for a long touchdown.
The Rams are hurting on the offensive line with three underperforming busts in Jason Smith, Jason Brown and Jacob Bell.
The team can't replace all of them in one year, but they should still shoot for a late-round lineman who could potentially surprise everyone and win a starting job.
Georgia center Ben Jones is a polished four-year player capable of making most NFL rosters as at least a backup. And luckily for the Rams, he's flexible enough to play guard if needed.
Jones lacks top-notch athleticism, which is preventing him from rising up the charts.
Jayron Hosley is 5'10" and 170 pounds, which is pretty ideal for a corner, other than maybe being a bit underweight.
Hosley is a ball hawk with 12 combined interceptions in his last two seasons. He also provides added value due to his experience as a punt returner for Virginia Tech.
While Hosley is probably undersized, his instincts and athleticism still make him an appealing target for the Rams.
Oklahoma star receiver Ryan Broyles tore his ACL during the 2011 season, which makes him a question mark as far as his draft status.
His injury aside, Broyles has been one of the most dominant college receivers over his career with 4,586 total yards and 45 touchdowns.
His 2010 season was nothing short of phenomenal with 131 receptions for 1,622 yards and 14 touchdowns.
At just 5'10" and 188 pounds, Broyles lacks the prototypical size that NFL scouts desire, but he wouldn't be the first undersized receiver to light it up in the NFL.
If not for his injury, Broyles would be a second-round lock and possibly even a late first-rounder. So the Rams will need to keep an eye on him to see how far he drops, because he could be an absolute steal in the fourth round.
Outside linebacker Emmanuel Acho is the brother of Sam Acho, who was a fourth-round pick by the Arizona Cardinals a year ago.
A 4-3 defense, which the Rams run, does not truly value the outside linebackers. There are some schemes that put an emphasis on it, but it's generally not a high priority.
That is why it would be foolish for the Rams to select an outside linebacker in the first three rounds, regardless of how thin they are at the position. But if they want to grab one in the fourth round, then there will certainly be a quality player like Acho available.
Acho was a senior in 2011 and ended his career with 26 starts. He is a smart player with good instincts, but he lacks the raw athleticism required to be considered a top prospect.
Marvin Jones has not been largely productive at the college level, but he has still achieved decent numbers.
His best year came in 2011 with 62 catches for 846 yards and three touchdowns
However, at 6'3" and 202 pounds, he has the body that scouts prefer. While he was unable to use his size and athleticism to post elite numbers in college, he could potentially be coached up and groomed into a dangerous NFL receiver.
Cam Johnson supposedly played wide receiver in high school, which certainly says something about his overall athleticism.
As a defensive end for Virginia, he possessed solid skills and instincts, but his production was highly inconsistent with only 10 combined sacks in his last two seasons. The fact that defensive end was a brand new position for Johnson is probably the main reason why he wasn't able to consistently dominate, which is understandable.
He is undeniably a raw prospect who will require significant attention from the coaching staff, but it could certainly pay off in the end.
He has missed 10 total games over the last two seasons and missed the 2009 season completely.
However, at 6'3" and 300 pounds, he is a sizable tackle capable of getting after the quarterback using both speed and power. He is also an asset in the run game.
Forston will see his stock plummet due the the major questions regarding his health, but he's talented enough for the Rams to at least give him a fair look.
Tight end Michael Egnew is a local favorite in St. Louis due to the promising career he had with the Missouri Tigers.
Any St. Louis fan who took I-70 westbound on a Saturday afternoon to watch the Tigers knows Egnew has been a vital part of the team's offense, which has inevitably made people wonder if he's capable of playing a similar role with the Rams.
Egnew's most promising season came in 2010 after he caught 90 passes for 762 yards and five touchdowns.
At 6'6" and 245 pounds, Egnew would provide the offense with a suitable red-zone threat. And for only a fourth- or fifth-round pick, he's well worth the gamble.