Here’s a possibly useful chart that may answer whether it matters in baseball whether a team gets the first pick in the draft, or falls to a later pick. Our initial thought may be that it matters more in other sports, but it still clearly matters in baseball. These numbers are muddled a bit by the fact that some teams purposely draft a player with less potential who demands a lower signing bonus early in the draft. Even with that in mind, it does seem that the first pick is significantly better than later picks.
The blue line is the average career WAR (from baseball-reference.com) of players drafted in that round, going back to 1990. The red line is the number of players drafted before 2009 (6 years ago) who have a WAR of less than 0.1. So the red line is the number of players drafted in that round who never contributed significantly at the major league level.
What we see is that player quality drops off significantly after the first rounds, and your chance of drafting a bust rises dramatically after round 4. That being said, I think there’s a kind of downward spiral that may happen if a team loses too much. Chemistry and culture probably make a big difference, and so the Braves may be better off winning as much as they can the last few weeks of the season, grabbing a pick between 2 and 4, and trying to build that culture into something that wins in 2017 when they move into their new stadium. What do you think?