[1] He played as a right-handed pitcher in Major League Baseball from 1964 through 1976, most notably as a member of the Oakland Athletics dynasty that won three consecutive World Series championships between 1972 and 1974.

[2] Odom led Ballard-Hudson High School in Macon, Georgia, to two consecutive state championships while amassing a 42–2 record.

He only made one appearance at the major league level all season, pitching one inning and allowing one earned run against the Washington Senators on September 22.

[5] Odom split the 1966 season between Kansas City and the double A Mobile A's, going 5–5 with a 2.49 ERA at the major league level.

[9] He was named to his second consecutive All Star team, but was tagged for five runs (four earned) in just a third of an inning as the National League cruised to a 9–3 victory.

[11] He recovered, and went 15–6 with a 2.50 ERA in a rotation that also included future Hall of Famer and Cy Young award winner Catfish Hunter, two-time no-hitter throwing Ken Holtzman, and simultaneous Cy Young and MVP-winner Vida Blue as the A's cruised to their second consecutive division title in 1972.

With one out and Odom on third base, he tried to score after Reds second baseman Joe Morgan caught a pop fly in foul territory, and was thrown out at the home plate to end the ball game.

He made just one appearance in the 1973 American League Championship Series, pitching five innings and giving up just one earned run in their 6–0 loss to the Orioles in game two.

He left the game in the fourth without giving up a run, however, Darold Knowles allowed both base runners he inherited from Odom to score.

The incident lasted less than a minute, however, Fingers required six stitches on his head, and Odom sprained his ankle and had a noticeable limp.

Joe Rudi led off the following inning with a home run to put Oakland up 3–2, and give Odom the win.

In just his second start for the ChiSox on July 28, Odom combined with reliever Francisco Barrios to pitch a no-hitter against his former team, the Oakland A's.

[28] Odom pitched six games for Oakland's triple-A affiliate, the San Jose Missions in 1977 before retiring.

He was asked to represent the Athletics at the 2008 First-Year Player Draft, June 5 in Lake Buena Vista, Florida.

Then, during the trial, he was arrested a second time on December 11, for assault with a deadly weapon as he held his wife, Gayle, at gunpoint with a shotgun, holding police at bay for six hours.