Pre 1.16 Findings

North/South rule: 1.818738
East/West rule: 0.961536
Switch Z sign, then East/West rule: 0.814782
Optimal rule: (WIP, Finishing up Optimal algorithm)

1.16.1 Findings

For inter-region navigation (every 432 x 432 blocks), straight East is slightly better than every other direction. The biggest effect of direction is traveling back towards origin is bad, but even this is not hugely significant. However, in general for 1.16, the effects of which cardinal direction you run (in terms of inter-regional travel) is rather negligible. It is potentially even faster than running straight East to run diagonally in any direction than traveling straight east, but only if you're truly running diagonally and not East for a bit, North for a bit, etc..