In "The Skein Hash Function Family" paper authors wrote:
The MIX/permute structure has been designed to provide full diffusion in 9 rounds for Threefish-256, 10 rounds for Threefish-512, and 11 rounds for Threefish-1024.
How they know it? Is there some rule of designing such structures, which can quarantee some level of diffusion and it was used there (then they could estimate the number of rounds needed directly)? Or they measure diffusion experimentally?
By the way they further write:
We designed Skein to maximize diffusion at every level, and have defined the number of rounds to be high enough to allow for many full diffusions. Each input bit position affects every output bit position in 10 rounds for Skein-512 (9 rounds for Skein-256 and 11 rounds for Skein-1024), so the algorithm is specified with 7–8 full diffusions. By comparison, AES-128 and Twofish have only 5 full diffusions.
So maybe this is how they figured it out. But without precise analysis this still not clear to me, especially because mix function in Threefish is so simple and there is not much more going on there, than that mixing.