I was looking over the Original Research section of True Lineages and had a question on page 27. My maga has a Magic Theory of 7, with a specialty in experimentation. She also has Puissant Magic Theory, bringing the total to 10. This means she can modify her roll by anything from -2 to +2. This is all clear as can be.
What is unclear is when she may choose how much to modify the roll by. It says:
This seems to imply to me that the modifier is chosen AFTER the die roll. Is this supposition correct? Does this mean that by being able to add or subtract up to 2 from the roll that I would theoretically have a 5 in 10 chance of rolling the Discovery result?
Based on my reading of the rules, I believe it is as you say. You can modify your result by as much as +2 or -2 after you roll. In the next step, when you try to stablize your discovery, you will have to add or subtract the same amount, though. This isn't too onerous, and it means that characters with high Magic Theory tend to be better at getting the results they want.
As for your specific question, I believe the errata slightly affect the premise upon which your statistics are based. As far as I can tell, the gist of the errata is: "Roll on the Extraordinary Results table. Add your risk modifier (+2 in your case). Apply the indicated result. Then (as long as you don't botch or get a complete failure) add or subtract up to your risk modifier to see if you can get a discovery result in addition to your first result."
That interpretation gives a slightly greater than 50% chance of a discovery on a risk modifier of +3. With a risk modifier of +2, I believe you have a 31.1% chance of a discovery. That is, you get a discovery on an unmodified roll of 7, 8, 9, 1-4, or 1-1-2 on the Extraordinary Results table. Add your risk modifier of +2, and these generate 9 (special/story), 10 (discovery), and 11 (modified effect). All of these are within +/-2 of 10, granting a discovery in addition to your first result.
(Rolling a six would result in an 8. While this is within +/-2 of 10, it's a complete failure and unfortunately doesn't count. I take it that if you rolled an unmodified 10 you wouldn't actually get a discovery, you'd merely get more rerolls, but that's open to dispute.)