1. Since drafting Joe Mauer 1st overall in 2001 the Minnesota Twins have had 16 1st round selections thanks to Type A and B compensation, and have whiffed on all but two of those: Only Denard Span (2002), Matt Garza (2005) and Glen Perkins (2004) have seen serious time in the Majors. Perkins turned out rather ordinary while Garza didn't hit his stride until he was traded to Tampa Bay and only now is Span paying dividends after a ton of time in the minors.
Even the woebegone Pirates, notorious for whiffing on high picks, managed to get six of their picks in the 2000's to the bigs, and once Brad Lincoln gets an expected callup sometime this year that will make it seven.
2. In back to back years, the Yankees drafted players in the 2nd round who didn't sign and went on to prominent football careers. In 1981 they burned their 2nd rounder on an OF named John Elway, and in 1982 they spent a 2nd round pick on a high school SS named Bo Jackson. The latter of course comes with an obvious caveat: Bo Jackson would become a two sport star at Auburn University and eventually get drafted in the 4th round of the 1986 draft by the Kansas City Royals, going on to a famous dual career with the Royals and football's Los Angeles Raiders.
3. You'd be hard pressed to find a team that drafted more MLB value in the 3rd round than the Texas Rangers, but sadly most of that value paid off for other teams.
Dean Palmer (1986) would go on to a solid career with the Detroit Tigers. Scott Podsednik (1994) would eventually break in with the Mariners, see his first regular action with the Brewers and go on to win a World Series with the White Sox. Ryan Dempster (1995) broke in with the Marlins and has since gone on to a productive career with the Cubs. And their biggest 3rd round prize, Barry Zito (1998), did most of his damage as a star for the rival Oakland Athletics.
The only 3rd rounder the Rangers picked who became a solid player under their watch? Darren Oliver (1988) became a productive pitcher for them during the 1990's, and at age 39 is coincidentally with them today as their top lefthanded reliever.
4. The 4th round is where the percentage of eventual MLBers really drops. But the Angels had the most prolific stretch of 4th rounders prior to 1996, producing 16 players that would eventually reach the bigs out of 30 4th round selections. Key regulars from this stretch included catcher Brian Harper, pitchers Mike Witt and Kirk McCaskill, and LF Garret Anderson. But since 1995, only one of their 4th round picks has reached the bigs, and the one that did got away: Brian Matusz passed on the Angels offer, went to college and eventually got drafted by the Baltimore Orioles in 2008.
Prolifically barren histories include the aforementioned Pirates, who of their 45 selections only produced 8 players who eventually saw MLB time, and of those eight only Jeff Keppinger (2001), Wes Chamberlain (1987) and pitcher Stew Cliburn (1977) would become MLB regulars for any real length of time. The Brewers only produced 7 major leaguers from 43 picks, and none of those picks produced more than 0.5 WAR over their careers. Granted, one of those MLBers was the late Josh Hancock, who died in a car wreck very early in his career with the Cardinals, and the jury's out on 2005 pick Mat Gamel.
The greatest 4th round pick of all time had to come from the Oakland A's in 1976, when they burned the 96th overall pick on a local outfielder from Technical HS named Rickey Henderson.
The Dodgers had the most interesting stretch of 4th rounders. After drafting eventual catcher Steve Yeager in 1967, the Dodgers had 19 consecutive 4th round picks between 1970-1989 that never played a game in the big leagues. Following that, 9 of their next 13 4th round selections would go on to play in the Majors, though none ever became a productive regular. Since 2003 none of their 4th rounders have reached the Majors.
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