Using that we could work out a similar formula for project or time based equity.
Lets say you agree that a developer gets say %5 (e) for building the first prototype. Assuming developer only gets the project half built he gets half of e(completion percentage) 2.5%.
The difficulty here are the same though as in normal fixed price, namely that of scope change and creep. This is in particularly a problem with startups, where you should be changing scope and direction all the time.
A possibly better way could be to work out an time based deal based on how much a founder would get.
Lets say programmer A and B are both of equal skill level:
A agrees to work fulltime as a founder receives 10% (e) complete with regular vesting over 4 years.
B can not for whatever reason offer to work fulltime but would like a similar deal only with hourly vesting. As there isn't a normal 1 year cliff we probably want to reduce e to maybe half of what A is making so lets put e to 5% as a example. This would of course all be for personal negotiation.
Lets assume 4 years is equal to 8000 hours. He is vested using a variation of pg's formula e(hours/8000). So if he only ended up doing 100 hours during the life of the project his share would be 0.0625%.
Thoughts?