I'm not familiar with "White Lies Admin Toolkit" but having been there at the genesis and fleshing out of S&W White Box, I can talk about the approach.
The idea was to reflect, as closely as possible, the classes of the original D&D game from 1974, using the general approach of Swords & Wizardry (1 Saving Throw, AAC, etc.). So most of the "math" is similar to what was found in OD&D. Not perfect, but a close enough analogue. For anything that I've derived from SWWB, I've kept to their example, tweaking to suite me and what I want to accomplish.
OD&D wasn't constructed in a modern thinking of algorithms, balance and budgets. It was more closely tied to what Gary & David wanted to do with their characters in their wargames and adventures. I suspect you will continue to be frustrated trying to apply a modern approach to the old school games.
Sources include the OD&D rules, the White Box rules, and various blogs from 2008-2010, including my own, and my experiences being part of the time and folks in fleshing out and blogging about S&W.