The probability of attaining good form for your team at home games are almost certain. Even players with a low 'Form' stat should get a green arrow at home most of the time.
The situation is different at away games though, and I find that, from my experience, the following factors will improve player form to some degree, however small. (I have a bad habit of reloading saves which give me bad form for the next away match, so I can tell which players occasionally gets bad form in away games, and which players might get a green arrow):
- High 'Form' Stat for the player
- Player is consistently scoring goals
- Player is consistently getting a high rating (> 7) at the end of the match
- Consistent clean sheets (goalkeeper only)
- Player scored a hat trick in the last game
- A substitute scoring a goal in the previous match (this happened a lot to my Hernandez)
- Team is on a winning streak/leading on the league table (I find that my team's away form usually improves after the January Transfer Season, after winning most games prior).
Things to avoid if you don't want players with bad form:
- Bad 'Form' Stat for the player (The stat does improve after some time though. My youth players sometimes have improved 'form' stat after a few years with the team)
- Low rating for the player in the previous game (< 6.0)
- Your Starting XI contains players who are on international duty prior to this game
I've also noticed that in away games against rival teams, you will almost be guaranteed a bad form for most of your players. Perhaps that's how Konami intended to make derbies more 'interesting'?
Hope this helps you, OP.
EDIT:
Prior match rating has nothing to do with it.
Actually, it does, from my experience. I use Ramsey as my CMF in my ManU ML save, and he's pretty good at slide tackling the opponents and get the ball back for my side and passing it around (disclaimer: I did train him up with the Sliding Tackle player card though). He usually gets something like a 6.5-7.0 rating at the end of the game most of the time. He doesn't score for my team, only provides a handful of assists, and doesn't have a great form stat, but he's usually available for my team in green arrow for most games, and only sometimes in blue arrow (but I use him in blue arrow anyway. Not much choice at the moment) and very rarely purple arrow.