Question: Who is a former professional American football quarterback who broke his left hand and had a professional American football halfback replace him however he was relieved by Tittle in the fourth quarter of the game?  

Context paragraphs:
1963 Rose Bowl: The 1963 Rose Bowl was a college football bowl game played on January 1, 1963, at the end of the 1962 college football season.  It was the 49th Rose Bowl Game.  The USC Trojans defeated the Wisconsin Badgers, 42–37.  This is the first #1 versus #2 match-up to occur in a bowl game, although #1 versus #2 match-ups had occurred previously as regular season games (typically referred to as "Games of the Century").  Ron Vander Kelen, the Wisconsin quarterback and Pete Beathard, the USC quarterback, were both named the Rose Bowl Player of the Game.  Down 42–14 in the fourth quarter, Vander Kelen put together a number of drives to score 23 unanswered points and put the Badgers in position to win the game.  Due to the historic #1 versus #2 bowl match-up, the number of Rose Bowl records set, and the furious fourth quarter rally by Wisconsin, this game frequently appears on lists of "greatest bowl games of all time."

Pat Coffee: James Lilburn "Pat" Coffee (August 3, 1915 – January 25, 1986) was a professional American football halfback and quarterback in the National Football League (NFL).  He played for the Chicago Cardinals in 1937 and 1938.  He set an NFL record in 1937 with the Cardinals with a 97-yard touchdown pass to receiver Gaynell Tinsley.

Buddy Allen: Elihu "Buddy" Allen, Jr. (born July 11, 1937 in St. Louis, Missouri) is a former professional American football halfback in the American Football League.  He played college football at Utah State University, and played professionally for the Denver Broncos in 1961.

Billy Martin (halfback): William Vance Martin (June 6, 1938 – November 8, 1976) is a former professional American football halfback in the National Football League.

Doc Baker: Charles "Doc" Baker was an early professional American football halfback for the Akron Indians of the "Ohio League" from 1906-1908.  He returned to the team for one last season in 1911.  He was the second-ever African American to play professional football, the first being Charles Follis.  Baker, earned his nickname, "Doc", while serving as an aide to a physician in Akron, Ohio.  He also a target of opponents trying to injure him.  Although Baker was never implicated, his football experience was marred by several gambling scandals.  According to a 1911 article the "Canton Repository", Baker was involved in just about every offensive and defensive play during a game between the Akron Indians and the Canton Professionals (who were later renamed the Canton Bulldogs in 1915) According to the "Repository" write-up; “Halfback Baker, from appearances a second Jack Johnson, was Akron’s best man.  He was in every play both on offense and defense and seemed impervious to injury.  On several occasions he was thrown hard, with several others on top of him.  But he always came up smiling.  His plunges through and outside of tackle were the best ground-gainers for the Akron team,”

Y. A. Tittle: Yelberton Abraham Tittle Jr. (born October 24, 1926), better known as Y. A. Tittle, is a former professional American football quarterback.  He played in the National Football League (NFL) for the San Francisco 49ers, New York Giants, and Baltimore Colts, after spending two seasons with the Colts in the All-America Football Conference (AAFC).  Known for his competitiveness, leadership, and striking profile, Tittle was the centerpiece of several prolific offenses throughout his seventeen-year professional career from 1948 to 1964.

Bob Paffrath: Robert William Paffrath (July 3, 1918 – May 21, 2005) is a former professional American football halfback.  He played for the Miami Seahawks and the Brooklyn Dodgers of the All-America Football Conference, for the Ottawa Rough Riders of the Interprovincial Rugby Football Union, and for the Edmonton Eskimos of the Western Interprovincial Football Union.  Paffrath also played one year in the Ontario Rugby Football Union with the Toronto Indians, where he was MVP.

Ray Ratkowski: Raymond James Ratkowski was a former professional American football halfback.  He played football at the University of Notre Dame.  He was drafted in the last round of the 1961 NFL draft but later played for the Boston Patriots of the American Football League during the 1961 AFL season.

Jim Cason: James Allnut Cason Jr. (July 25, 1927 – November 24, 2013) was a professional American football halfback who played eight seasons in the All-America Football Conference (AAFC) and the National Football League (NFL), mainly for the San Francisco 49ers.  He was selected for two Pro Bowls.  He also started one game at quarterback in 1954 after Y. A. Tittle broke his left hand.  However, Cason was relieved by Tittle in the fourth quarter of the game.

Tony Teresa: Anthony Michael Teresa (December 8, 1933 – October 16, 1984) was a professional American football halfback in the National Football League (NFL) and the American Football League (AFL).  He played 1 game for the NFL's San Francisco 49ers in 1958 and one season for the AFL's Oakland Raiders.  He also played quarterback in the Canadian Football League for the BC Lions in 1956 and 1957.  He completed 35.8% of his 67 passes for 371 yards.  He is survived by his 4 kids and Wife Pat Teresa.

Supporting paragraphs: Jim Cason Y. A. Tittle
Answer: Yelberton Abraham Tittle Jr.