What we know is that around 2 Rank, an increase of 1 Rank is significant, around 5.5 an increase of 0.5 is equally significant, and around 9 an increase of 0.25 is also equally significant.
That tells us that, if we put power on a scale of Levels where a fixed win rate corresponds to a fixed Level difference at all levels, the derivative of Level with respect to Rank is a linear function. That means the Rank to Level conversion must be quadratic and, if Levels themselves correspond to exponential amounts of actual energy output, we get Energy = e^(a*Rank^2 + b*Rank + c)
Of course, all of this can only be accurate from Rank 1 to Rank 10, what growth looks like after that is unclear.
Also unclear is why anyone would use this weird-ass scale, unless power increments naturally come in fixed units of Rank. If so, we should definitely go for Rank increases wherever possible, because they will compound on themselves and give us ever more returns for a given level of challenge. Rank+0.25 is nothing to sniff at now, but it'll be worth much more once we're in the higher levels, even allowing for our much greater power at that point.