The group, announced Monday on ESPN, includes the preseason favorite -- Stanford quarterback Luck -- and at least one player, Mathieu, who was low profile when the season began.
Luck is a finalist for the second straight season, while the other QB on the list, Griffin, is the first Baylor player to get an invitation to the Heisman dinner in New York. The school has never had a player finish better than fourth in the Heisman voting.
Richardson is the second Alabama running back to be a finalist in the last three years. Former teammate Mark Ingram won the Heisman in 2009.
Mathieu, the LSU defensive back nicknamed Honey Badger, has made numerous game-changing plays for the top-ranked Tigers.
The Heisman Trophy will be presented Saturday night.
Luck was the Heisman runner-up to Auburn's Cam Newton last year and passed up a chance to be the No. 1 pick in the NFL draft to return to Stanford for his junior season. From the moment he made the decision to stay in school in January, he became the odds-on favorite to win the Heisman this season.
Luck had another stellar season, passing for 3,170 yards with 35 touchdowns while leading the Cardinal to an 11-1 record and a second straight BCS bid. But the competition has been so fierce that it's been tough for Luck to hold onto his front-runner status.
In fact, Griffin seemed to take the lead in the race over the last month of the season.
The quarterback called RG3 by Baylor fans leads the nation in passer rating (192.3), with 3,998 yards and 36 touchdowns. He has also run for 644 yards and nine touchdowns. And much like Luck, Griffin has led a long-struggling program to its greatest success in decades. Baylor is 9-3 this season, its first nine-win season since 1986.
The best showing a Baylor player has ever had in the Heisman voting was quarterback Don Trull's fourth-place finish in 1963.
Richardson has been the unquestioned offensive engine for No. 2 Alabama. He's fifth in the nation in rushing at 131.9 yards per game and tied for fifth in touchdowns with 23. Richardson and the Crimson Tide will meet Mathieu and LSU in the BCS championship game on Jan. 9 in New Orleans.
The sophomore cornerback is the second defensive player to be a Heisman finalist in the last three years. Defensive tackle Ndamukong Suh of Nebraska finished fourth in 2009.
Mathieu, though, is more like Charles Woodson, the do-it-all defensive back who won the 1997 Heisman for Michigan.
Mathieu has forced five fumbles, intercepted two passes and scored four touchdowns, including two long punt returns in LSU's last two games against Arkansas and Georgia.
He also was suspended for a game this season for violating the team's drug policy.
Ball has been a touchdown machine for Wisconsin and ranks fourth in rushing at 135.3 yards per game. He has 12 more touchdowns than the next best player in the nation and if he can tack on two more in the Rose Bowl against Oregon, he'll break Sanders' record.