I am a recent Slush pool member and former BTC Guild member.  I prefer many things about how BTC Guild reports statistics, but the increased centralization of hashing on any pool seems detrimental to the long term value of my coins. 

I have what is probably a naive question that I think many new miners might share.

In a nut shell, when someone gets a shiny new ASIC, they know the coins it will produce are front loaded - the difficulty is going up, so they want low variance so they get the benefit from the maximum theoretical reward of their device with out the risk that bad luck/reward variance causes them to miss reward when network difficulty is low.

Has anyone quantified the relationship between the pool hashrate and network difficulty for an individual member's hash rate as it relates to the desire to get maximum reward as early as possible?

So far my daily payout seems comparable to BTC Guild.  I assume the higher a member's hash rate then the less they need to join a big pool to receive low variance rewards up front.  I think if this is true (and could be explained well) maybe people would spread their hashing around a bit more and not just flock to the largest pool.

My intuition tells me you can somehow compute the theoretical variance from a large pool vs. smaller pool for a particular hash contribution. 

An example (with bogus numbers) of what I'd like to see a report on might look something like this:

Small pool (Slush):

 - Expected daily reward with for 700 Gh/s member is 0.70 +/- 0.5  BTC/day (SD = 0.1) for pool with 5% of hashing power and network difficulty of 510,929,738.02.

Large pool (BTC Guild):

 - Expected daily reward with for 700 Gh/s member is 0.70 +/- 0.2 BTC/day (SD = 0.01) for pool with 35% of hashing power and network difficulty of 510,929,738.02.

Solo mining:

 - Expected daily reward with for 700 Gh/s member is 0.70 +/- 17 BTC/day (SD = 1.2) and network difficulty of 510,929,738.02.

My statistics fu is not up to the task, so hopefully someone has already figured out the equation 'f' that returns:

  (avg return, std deviation) = f(miner hash rate, pool hash rate, network difficulty)

Even better would be if you could solve to find the minimum pool hash rate that gives a miner with a fixed hash rate a minimum desired standard deviation on BTC return within some time frame (eg. 1 day).

For the smallest miners, the largest pool is best to even out average payouts and take advantage of current (lower) difficulty.  But for larger miners I suspect it is more nuanced and you only need a pool that is over some threshold to get the benefit of being in a pool.  I know pool fees and details are also important, but I am ignoring that for this analysis.