The old rule of thumb is to take the player's rate of improvement from year 2 to year 3 (the first two lines that appear in his ratings history) and multiply that by 2.5. So if a player had a contact rating of 60 in spring training or his first full season, and in the second it was 68 (8 point jump) you would expect him to end up at around 80 contact when he's fully developed (8 x 2.5 = 20 points of total improvement).
Of course, in practice this is far from perfect. First, I always found 2.5 to be a very loose guideline. Some players are lucky to double their first full year's improvement, while others more than triple it. And In my (admittedly limited) experience, it worked better with skill ratings (contact, control, vL and vR, etc) than with strength ratings like power or stamina.
Now that they've made some rule changes, it's even tougher. For one thing, you can only see past numbers for your own guys, so it's a lot harder to project your opponents' players. And if I recall correctly, when they did the last update, they hinted that they would be changing development patterns. I don't think enough time has passed that anyone can really say how these have changed.