Hurlers Sonny Gray and Sean Doolittle are the current exceptions, of course, and the A's hope for more next week during the annual First-Year Player Draft.
The 2014 Draft will take place on June 5-7, beginning with the Draft preview show on MLB.com and MLB Network on Thursday, June 5, at 3 p.m. PT. Live Draft coverage from MLB Network's Studio 42 begins at 4 p.m., with the top 74 picks being streamed on MLB.com and broadcast on MLB Network. MLB.com's exclusive coverage of the second and third days will begin with a live Draft show at 9:30 a.m. PT on June 6.
MLB.com's coverage includes Draft Central, the Top 100 Draft Prospects list and Draft Tracker, a live interactive application that includes a searchable database of Draft-eligible players. Every selection will be tweeted live from @MLBDraftTracker, and you can also keep up to date by following @MLBDraft. And get into the Draft conversation by tagging your tweets with #mlbdraft.
In the meantime, here are the best picks in club history for Rounds 1-15:
Round 1: Mark McGwire, 1984
McGwire was hitting tape-measure shots at the University of Southern California when the A's used their first pick of the 1984 Draft -- 10th overall -- to snatch up the slugger, who set the baseball world on fire for a young and emerging Oakland team in '87, his official rookie campaign. He hit 49 homers that season, ultimately finishing his illustrious 16-year career with 583, good for 10th on the all-time list.
McGwire was a 12-time All-Star and finished in the top 10 in Most Valuable Player balloting five times, for many years appearing to be a lock for Cooperstown immortality. But his entry into the Hall of Fame remains a steep climb following his admittance of steroid use in 2010.
Round 2: Vida Blue, 1967
Blue's 17-year big league career began in 1969, two years after the Kansas City A's reeled in the southpaw with the 27th overall Draft pick.
In 1971, a 21-year-old Blue led the franchise to its first postseason berth in 40 years, posting a 24-8 record with an American League-leading 1.82 ERA and 24 complete games. He won the Cy Young Award and was also named the AL's Most Valuable Player.
Blue gave the A's 124 wins in nine seasons, pitching for the 1972, '73 and '74 champion clubs, and finished his career in 1986 with 209 total wins and a 3.27 ERA in 502 appearances, 473 of them starts.
Jason Giambi was also drafted in this round in 1992.
Round 3: Mike Davis, 1977
Davis' time with the A's, spanning eight seasons, wasn't so extraordinary, but he did have his moments, in 1985 giving the club 24 home runs, 34 doubles and 92 RBIs while hitting .287 in 154 games.
Unfortunately for A's fans, the outfielder will best be remembered not for what he did in his Oakland tenure but for a single moment as a Dodger, drawing a walk off A's closer Dennis Eckersley ahead of Kirk Gibson's dramatic game-winning ninth-inning homer in the first game of the 1988 World Series.
Round 4: Rickey Henderson, 1976
Henderson put on nine different uniforms in his 25-year career, but he's most fondly remembered in green and gold, transforming into a record-breaking basestealer and a power-laden leadoff man who propelled the A's to a World Series championship in 1989.
The eccentric Henderson, who totaled 14 years with the A's, was the 96th overall pick in the 1976 Draft, starting out as a green prospect and quickly establishing himself as the game's elite stolen base artist. The 10-time All-Star, inducted into the Hall of Fame in 2009, finished his prolific career with 1,406 stolen bases and 3,055 hits, making him one of just 28 members of the 3,000-hit club.
Round 5: Mickey Tettleton, 1981
Tettleton served as a part-time catcher in four seasons (1984-87) with the A's before his career really took off with Baltimore. He also enjoyed tours with the Tigers and Rangers during his 14-year big league stay, earning a pair of All-Star nods and three Silver Slugger Awards along the way.
Round 6: Sal Bando, 1965
A's manager Bob Melvin wears No. 6 in honor of Bando, captain of Oakland's World Series championship teams of 1972-74. The power-hitting third baseman was named to four All-Star teams and finished second in AL MVP voting in 1971.
Bando played in more than 2,000 games during his 16-year Major League career, slugging 242 homers and compiling 1,039 RBIs.
Round 7: Matt Keough, 1973
The A's ace played with the team from 1977-83, earning an All-Star nod in '78. But his best year came in 1980, when he finished 16-13 with a 2.92 ERA in 34 games, including 20 complete games.
Keough's Major League career, which featured 58 combined wins and a 4.17 ERA in 215 career games, included stops in Yankees, Cardinals, Cubs and Astros. He also worked as a special assistant to Beane for several years.
Round 8: Eric Byrnes, 1998
Byrnes bounced off walls with reckless enthusiasm, and fans loved him for it. In six seasons with the A's, the speedy outfielder hit .270 with 45 home runs, 164 RBIs and 35 stolen bases. He would steal 50 in 2007 for the D-backs, one of five clubs he played for during an 11-year career.
Round 9: Terry Steinbach, 1983
The three-time All-Star catcher spent 11 years behind the plate in Oakland, giving the A's 132 home runs and 595 RBIs while anchoring an extremely successful pitching staff from 1986-96, a span which brought about three consecutive AL pennants (1988-90). He caught two no-hitters in his 14-year career, one in 1990 by A's ace Dave Stewart and another in '99 by Eric Milton of the Twins.
Round 10: Lance Blankenship, 1986
Blankenship played his entire career with the A's after they drafted him in 1986, making his debut at the end of the '88 season. The utility player finished with a .222 average, nine home runs, 92 RBIs and 54 stolen bases in 461 games, landing on the A's postseason roster in 1989 and 1990.
Round 11: Greg Cadaret, 1983
Working as a reliever and occasional spot starter, Cadaret enjoyed a 10-year big league career with eight teams, including three with the A's. In 451 appearances (35 starts), the southpaw compiled a 38-32 record with a 3.99 ERA and 14 saves.
Round 12: None
Of 49 all-time 12th-round Draft picks made by the A's, just five reached the Majors. Not one experienced much success at the level.
Round 13: Rod Beck, 1986
Though the All-Star reliever never pitched in a single game for the A's, it was them who originally recognized his talent and plucked him out of the Draft, trading him to the Giants two years later.
Beck played 13 years in the Majors and recorded 286 saves, including a career-best 51 for the Cubs in 1998.
Round 14: Ron Coomer, 1987
Coomer was released by the A's before he reached the big leagues with them, but he was ultimately signed by the White Sox in 1991 and endured two trades before finally making his debut in '95 with the Twins. He stayed in the Majors for nine years, playing for four clubs and finishing with a .274 average, 92 home runs and 449 RBIs in 911 games, along with one All-Star appearance ('99).
Round 15: Jose Canseco, 1982
Canseco smashed 33 homers in his first full season with the A's, winning AL Rookie of the Year honors despite a .240 average. He never wielded a great batting average, but his immense power made him a superstar. He had 462 career home runs to his name by the time he stepped off the field for the last time in 2001.