Last time the Red Sox had the No. 19 overall draft pick, they took Roger Clemens. (AP)

It was not long ago that teams signed free agents without regard for the draft pick they would have to sacrifice to do so. Clearly, that has changed.

Indeed, the pick that a team must sacrifice to sign a Type A free agent who rejects salary arbitration from his former club has become so significant that it reportedly became the subject of significant contention in the Yankees organization. Earlier this month, New York GM Brian Cashman said the Yankees — after being spurned by Cliff Lee — wouldn’t sign a Type A free agent because they were unwilling to sacrifice their first-round pick. But he was reportedly overruled at the ownership level, resulting in the decision to give up the No. 31 overall selection and sign Rafael Soriano as the most expensive setup man in history.

Just how valuable is the No. 31 overall pick? The answer varies significantly by year.

In 46 June drafts, just 15 players taken at the No. 31 spot have reached the majors. (For the complete list, click here.) Only two of them emerged as above-average players. One was Jarrod Washburn, who won 107 games after being taken by the Angels in 1995. The other? Greg Maddux, whose 355 career wins are the most by a right-hander whose career started after the World War…World War I, that is.

The Red Sox’ free-agent activity resulted in their losing their own first-round pick (No. 24 overall) while gaining two (Nos. 19 and 26). Under GM Theo Epstein, the Sox have used compensation draft picks to acquire a number of their key prospects. (For details, click here.)

But historically, what kind of players have been selected with the first-round picks gained and sacrificed by the Sox this winter? Here is a look at the history of the three first-round draft picks that were affected by the Red Sox’ free agent activity this offseason:

NO. 19 PICK

The Red Sox got the Tigers’ first-round pick in exchange when Detroit signed Victor Martinez to a four-year deal. That was the highest unprotected pick in this year’s draft, resulting in the Sox receiving the No. 19 overall pick. It will be the Sox’ highest selection since selecting David Murphy with the No. 17 pick in the 2002 draft. Here’s the full list of players taken with the 19th selection. The breakdown:

–The last time the Sox had the No. 19 pick, they selected a little known pitcher out of the University of Texas named Roger Clemens.

–Clemens is far and away the best player ever selected at this spot, but other standouts include one of the top second baseman in the history of the game (albeit an overlooked one whose Hall of Fame candidacy received far too little consideration) in Bobby Grich, All-Stars Alex Rios and Mike Scioscia as well as a fine player in Shannon Stewart. Bonus points for the fact that a guy named Drungo LaRue Hazewood was taken at this spot. Hazewood played six career games for the Orioles.

–Of the 46 selections at this spot, 32 (70 percent) reached the majors.

NO. 24 PICK

The Sox sacrificed the No. 24 overall pick in the draft to sign Carl Crawford. Here’s the overall history of that pick in the draft. The thumbnail sketch:

–Of the 46 players taken with this pick, 26 (57 percent) reached the majors.

–The Sox once gave up the No. 24 pick, in the 2004 draft, to sign free-agent Keith Foulke. The A’s drafted Landon Powell with that pick.

–Chad Billingsley, Rondell White and Terry Mulholland were All-Stars who emerged after being taken with the No. 24 pick, while Alex Fernandez once finished sixth in AL Cy Young balloting.

–A pair of managers emerged from the No. 24 pick, with Bob Geren and John Gibbons both having done the honors.

NO. 26 PICK

As a result of the Rangers signing Adrian Beltre, the Sox received Texas’ first-rounder, the No. 26 overall pick. Here’s the history of a pick with several Sox connections. The skinny:

–The Sox have had the No. 26 selection four times. None of the players they drafted has had sustained success in the majors. Craig Hansen, taken with the pick in 2005, had a tremendous arm but couldn’t translate that into results. The other Sox picks at that selection fared little better. Josh Garrett (1996) and Jeff Ledbetter (1982) never reached the majors. Reggie Harris (1987) bounced between organizations but never secured a foothold in the majors.

–In 2001, the Athletics selected high school pitcher Jeremy Bonderman with the pick, inspiring the memorable Moneyball anecdote featuring Billy Beane throwing a chair against a wall in outrage over the selection. Incredibly, that was the first of four straight years when the A’s had the No. 26 pick. Of those four, only Bonderman reached the majors.

–Current Sox outfielder Darnell McDonald was selected with the pick in 1997. So were ex-Sox players Rico Brogna (1988), Mike Stenhouse (drafted but unsigned in 1979) and Dave Henderson (1977).

–Henderson and Dan Plesac (1983) were both All-Stars selected from this pick. The best selection ever from this pick was former Tigers great Alan Trammell, who was in the majors the year after being taken out of high school.

–Of the 46 selections at this position, 21 (46 percent) have reached the majors.