I haven’t seen any stats on the issue but I have a suggestion that might help narrow things down to allow you to conduct testing:
Aggregate and prioritise game controls :
Start by aggregating controls into logical entities and prioritise them inline of how you think the game should be played.
Test and refine design and layout:
Test and refine to distil which controls will be most used and bring them closer user action points:
- Thumbs = Most frequent
- Index = Less frequent
Keep your design Finger-Friendly:
Another thing to think about is when to use a thumb-sized target over
an index finger-sized one. It’s difficult to know whether most of your
users will use their thumbs or index fingers on your application.
However, if your application is a game, it’s likely most users will
use their thumbs to play instead of their index fingers. This is why
thumb-sized targets are particularly useful for gaming applications.
source: Finger-Friendly Design

The above clearly suggests that game applications need to optimise their design for thumbs rather than indexes. The rationale being that the use of a smaller hit/touch area (index) requires more accuracy and is associated with more effort, while catering for larger hit/touch area (thumbs) requires less effort from the player.
In line with above, touch surface dedicated to game controls "especially for most frequently used ones" need to align with average width of the index finger and thumb and game controls laid-out accordingly.
An MIT Touch Lab study of Human Fingertips to investigate the
Mechanics of Tactile Sense found that the average width of the index
finger is 1.6 to 2 cm (16 – 20 mm) for most adults. This converts to
45 – 57 pixels, which is wider than what most mobile guidelines
suggest.
source: Finger-Friendly Design
