I am guessing that the formula would relate some standard optical density (minus the film base density, usually very small) to the exposure.
So, suppose that you have a known light intensity on a standard grey card. We would stipulate that a standard exposure will yield x% of the maximum optical density on the film under standard development. That will determine the nominal box speed. (astute analogue photographers will of course note that this point actually moves around a bit depending on how you develop)
In other words, you'd simply look at the log density / log exposure chart, pick the special point that you want to correlate to standard grey under standard (say, sunny 16) light and exposure, and off you go. There will be a log relationship.
Of course, every standard has its limits, and in this case the standard grey point would say nothing about what happens to the higher and lower tones. But still I suppose it'd be reasonable to subtract the high density from the low density, say grey corresponds to x% of that range, etc.