I was curious, so I had a look at some random team stats at all levels, for numbers of At Bats and Innings Pitched. This table shows the level, and the number of players who got less than 10 AB, 10-30 AB, less than 5 IP, and 5-15 IP. Those seemed to be the significant numbers (and the data isn't that precise, for example, sometimes I counted a player with 31 AB or 16 IP).
Obviously it includes players who were injured. Still, each team had at least 10 players whose eligibility was used but didn't play much; divisions with larger rosters had more. 