Just a few points to clear up here.
1. The rollover = 110 days. So, you'll need to take the amount of days that the player is injured and subtract the amount of game cycles left in the season and the playoffs (full playoffs is about 40 game cycles) and the 110 days of rollover. If the player is on the DL at the end of the World Series, he has a chance to recover some ratings during the World rollover. If he is still injured next season, he can be placed on the DL again with the hope that he gets additional recovery bumps next season.
2. While injured players may, over a long period of time, gain back some of the ratings they lost due to the injury, if they are not placed on the DL during the injury, they do not recover from their injury during any cycles while they are injured. If they are placed on the DL, then they have a chance to recover during cycles when they are injured.
3. When a player is placed on the DL, he typically obtains an injury recovery cycle 1 day before he comes back from injury. However, if he is still injured for more than one day when your World reaches the second to the last day of the regular season, the player might receive his injury recovery bump, assuming he is on the DL, on the second to the last day of the season. With very rare exceptions, once the World is past the second to the last day of the season, there are no more injury recovery bumps for the rest of the season. The only injury recovery bumps after the second to the last day of the season are the ones that the player MIGHT get during rollover and the ones he gets the next season if he is still injured.
4. Injury recovery depends on the team's medical budget and the player's makeup rating. I almost always run a $20 million medical budget and there have been plenty of times where my player gets injured and he doesn't get any injury recovery bump because he has a terrible makeup rating.