First and third basemen are really made rather than drafted. The two positions, and especially first base, don't exactly excite scouts. They like athletic players and the best athletes in high school and college tend to play up the middle, even if there's no chance they'd play there as pros. As a result, many major league first and third basemen moved there from other positions.
The relatively low regard in which scouts hold amateur corner infield players is evident from the draft, in which they're seldom chosen in the top ten overall picks. In the past five years, no team has selected a first baseman* in the top ten. The earliest-chosen first baseman was Dominic Smith, whom the Mets selected with the 11th pick in 2013. Third baseman have fared a little better. Kris Bryant was the second overall pick that same year. In fact, there was a run on third baseman in 2013, as Clint Frazier (who was listed as a third baseman but has never played there as a pro) and Colin Moran both also went in the top ten. That draft, though, was an exception. The only other third baseman taken in the top ten in the last five drafts was Anthony Rendon. Of the 250 first round picks in those five drafts, including supplemental first rounders, only six were first basemen and 18 were third basemen.
The Pirates certainly follow this practice. In seven drafts, the current front office has selected and signed only one first baseman earlier than the 11th round. That was Alex Dickerson, taken in the 3rd round in 2011. In the three drafts since then, the Pirates have selected and signed only one first baseman in any round, that being Danny Collins. The Pirates did draft Pedro Alvarez with the second overall pick in 2008, which was the first draft pick made by the current regime. Since then, the highest-drafted third basemen have been Eric Wood and Dan Gamache, both selected in the 6th round. For the sake of completeness, what follows is a list of all the corner infielders drafted and signed by the Pirates since 2008.
1B: Calvin Anderson, Aaron Baker, Matt Curry, Jared Lakind, Justin Howard, Alex Dickerson, Danny Collins
3B: Pedro Alvarez, Jeremy Farrell, Matt Hague, Matt Payne, Dan Gamache, Chris Lashmet, Eric Wood, Jordan Steranka, Erich Weiss, Beau Wallace, Chase Simpson
Instead of signing corner infielders, the Pirates' tendency has been to move players there from other positions. Since the team also tries to keep the real prospects at the most defensively challenging positions for as long as possible, the end result is that first and third base prospects are few and far between. The only bona fide prospect the team has at either position right now is Josh Bell, and he's only at first base in deference to an outfield that many think could be the best in MLB. Bell is the heir apparent for the Pirates' first base job, but it's hard to say whether he'll be able to fill the role given the very limited power he's shown the last two years.
Once you get past Bell, there's not much to see besides long shots. Stetson Allie, who's moved to right from first because of Bell, has taken a step backward so far this year and wasn't enough of a prospect to get chosen in the Rule 5 draft. At third base, Eric Wood has some power potential but hasn't shown much in games. Bradenton has two first basemen in former outfielder Jose Osuna and former third baseman Edwin Espinal. Osuna is in his third year in high A, which the Pirates would have avoided had they consider him a real prospect. Espinal has shown some hitting ability in brief spurts, but hasn't put it together on any consistent basis. At third base, converted catcher Wyatt Mathisen is handling the defensive part of his move well, but he's struggling to hit.
Aside from Bell, the most interest in the infield corners in the system comes from the team's positional bingo game at West Virginia. It actually started in March, when the Pirates had many of their lower level outfielders working out at third base. The team eventually settled on Jordan Luplow, who's going to have to show a lot with the bat as a draftee from a four-year college playing in low A. The other most significant corner infielder at West Virginia will probably be Connor Joe, who has yet to play a game as a pro as he recovers from back problems. The Pirates originally announced that Joe would play right field, then that he would get a chance to catch, but the latter plan got scuttled due to the back problems. In camp he appeared to settle in at first.
Over the next five years or so, the Pirates' success with the corner positions will probably depend heavily on their ability to improvise. Well, that and Bell. Their current situation reflects that, as Pedro Alvarez moved to first from third and Josh Harrison moved to third from everywhere. The degree to which they'll have to improvise will depend, in turn, on whether Alvarez can return to his 2013 hitting form and Harrison can recover from this year's alarming trends in his BB and K percentages. The next bit of improvisation could involve Jung-Ho Kang, one of the few players on the team lately who seems to know which end of the bat to hold. The team will also probably look to add any needed depth the way they did with Corey Hart and Sean Rodriguez, rather than bringing it up from the minors. Unless something miraculous happens with Allie or Wood, there isn't likely to be any depth-type help arriving from that direction.
*I'm going by the positions that teams listed when the players were drafted.