Ok, this got me thinking. Freya's Tainted Bloodline trait comes from many of her family being psykers, relatively speaking. One in ten of those with Tainted Bloodline become psykers at some point in their life. Freya's own father developed psychic powers well after the usual age they're found. What that means is Syr - as one who holds the trait - has a one in ten chance of being or becoming a psyker.
Or at least she would, if she were raised on Vanaheim. But she wasn't. She was born and raised on Avernus. Avernus, where the "one in a billion" Gamma/Delta psykers number 42 (153 if you count those still in training) on a planet with a population of 3.6 billion. That's 11.6 (42.5) times the number of Gammas/Deltas than normal! Syr is 11.6 (42.5) times as likely to develop psyker powers than anyone else in her family (barring perhaps Freya)! I...don't actually know the math to work out her chance of becoming a psyker but it's a lot higher than 10%!
So as I was falling asleep last night I figured out what we were doing wrong.
Basically your numbers are the wrong numbers to be interested in. You've confused the multiplier for the increased chance, and I was too sleepy to figure that out.
The chance of a psyker in the rest of the Imperium seems to be "one in a billion" or 0.000000001, while on Avernus that is somewhere between 0.000000011 and 0.000000042.
That means that increased chance of an individual being a psyker on Avernus is the difference.
Between 0.00000001 and 0.000000041. (For simplicity sake I'm going to round that to between 0.00000001 and 0.00000004). Or one in 100 million to 4 in 100 million. (Which is the same as saying between 10 and 40 times as often).
That means that assuming there are no synergies between tainted bloodlines and Avernite influence, (which is a risky assumption, but this should give us the lower bound of the effect on Syr), and that the psyker bloodline is base (which does make sense), the formula is this:
0.1 + 0.1 (0.00000001) = 0.1 (rounded) = 10% < Syr's chance of being a psyker < 0.1 +0.1 (0.00000004) = 0.1 (rounded) = 10%
Meaning that the increased chance of being a psyker on Avernus has essentially no measurable impact on the likelihood of a single individual becoming a psyker.
Which makes
perfect sense.
The reason the multiplier is so large is not because the effect is large but because the effect in the rest of the Imperium is so small.