Technically speaking a full PoW solution is one whose hash value is below a certain threshold value say V. It is not equivalent to saying that the hash value must begin with say X number of zeros (unless the threshold value is a power of 2).
My question is what is the usual practice in mining pools where one needs to submit partial proof of work to give a proof that he has worked on finding the block honestly? Lets say in some 'round' the miners in a pool have got their best (the least) hash values as v= v1,v2,..v_n. Is there a function that takes in v as an input and computes the reward for each of the miners ? Are there are checkpoint sort of system where say if the submitted share has hash value lying in between some range then that miner is categorised in that range. Once all the members are categorised into groups (which would reflect how powerful mining rigs they have), they can then be paid for their service proportionately. Of course there is no need to categorise, like the way I mention but is it how it works in practice ? If so, how are the level checkpoints distributed ?