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From the minor league baseball website:

AAA - 46 teams
AA - 30 teams
A (high) - 30 teams
A (short season) - 22
Rookie - 82 teams

210 teams x 25 players = 5,250

There will be some overlap between short season and rookie players. Assume that to be 500 players? Making the total minor league players somewhere around 4,700 each year.
Bob,

There's a few of those AAA teams I don't recognize, but I sure like the name "Sarape Makers".

Aguascalientes Railroadmen
Angelopolis Tigers
Campeche Pirates
Cancun Lobstermen
Mexico Red Devils
Monclova Steelers
Monterrey Sultans
Oaxaca Warriors
Puebla Parrots
Saltillo Sarape Makers
San Luis Tuneros
Tabasco Cattlemen
Tijuana Bulls
Vaqueros Laguna
Veracruz Red Eagles
Yucatan Lions

I would guess most clubs have around 200 players in there system at any given time. This includes those on active rosters and others who are injured. The best guess would be 5,000 to 6,000 total players in MLB organizations.
All teams have:

1 AAA team
1 AA team
1 high A team
1 low A team
1 rookie league team

Most have either a short season low A team or another rookie league team as well, so a good estimate would be:

30 teams x 6 affiliates x 25 players = 4500 players. Add on the players that are injured, you're looking at 4500-5000 pros in the minors, not counting indy ball, of course.

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