An interesting note, through around pick 500, the Red Sox have the 4th highest amount of BA top 200 picks, and when you weigh the picks (1 point for #200, and 200 points for #1) the Red Sox are also 4th. Similarly, the Yankees appear to be dead last in weighted points and 2nd to last in number of top 200 players.
The Rays have 12 top 200 players (1478 total points) the Padres and Blue Jays both have 11 players (1293 and 1158 points respectively) and the Red Sox have 9 players (1117 points) while the Yankees are in a 4 way tie for 2nd to last with only 3 top 200 players, tied with the Astros, Angels, and the Dodgers. For the record, the Astros have 305 points, the Angels have 291 points, the Dodgers have 231 points, and the Yankees have 131 points.
The Cubs only have 2 players, but they have more points than the 4 teams with 338 points.