Those players change after their timers expire. If I had to guess Carpenter will change to Marte or Braun. Both NL Central players who are 86 OVR.
You also need to look at tickets as a substitute for stubs. Everybody doesn't enjoy the hassle of flipping cards so this allows them to get a chance to buy those expensive players.
To the OP....I'm almost Level 36. Each Captain goes to Level 42. I'm sittinh on about 2700 tickets hoping somebody good pops up. I suggest saving your tickets.