I'm curious, at what point do players get pulled do to injury. It seems like the doubtful status on half my players doesn't actually mean anything. Do players just play until they get "out"?

In the game if a player is injured they are given a "time to recovery" value and sit on the bench until that time arrives. Depending on the severity of the injury this may be a few plays to the rest of the game. The state of the injury (probable, doubtful, etc) is not actually calculated until the end of the game.

ok so what does each actually mean though
probable - they probably will play with the injury?
doubtful - they probably won't play with the injury?
out - they won't play with the injury?
any info on percentage of chance? or is it completely random?

As far as I can tell, each is based off the player's health in the injured area on the player card. Each area affects a player's game play in different ways, and the more injured the player is in an area determines how likely it is that the player will suffer another injury.

In terms of game mechanics, players with probable, questionable, or doubtful injuries will still play in a game. Although the ones with doubtful injuries probably shouldn't unless it's an important game.

What bothers me more is that you do not get an accurate idea of how longer a player will be out. If you have a player marked out for 8 weeks, that doesn't actually mean he's out for 8 weeks. It means he's out for a week or so, doubtful for 5 weeks, then questionable, then probable. I stashed my starting MLB on IR last season when he was marked out for 10 weeks, only to find that he would have been available for the playoffs.