PoS Reward Standard Deviation

Does anyone have a clue as to what the variance or standard deviation looks like, besides the expected days to receive a reward?
So PoS is random, and follows some sort of statistical distribution, and yea luck is involved, so you may not receive a reward by the expected time, but I was curious as to what the standard deviation looks like?
Maybe the wallet could include that statistic as well, to give us stakers a much better idea of when we could receive a reward
I am concerned because I have an average expected time of, let's say X days, and so far it has been nearly 4X days, and I still haven't received a reward. It has been 4 times the expected time to receive a reward and I still haven't received anything. Is it just that I am extremely unlucky?
Maybe something else is going wrong?
I am becoming more open to the staking pool idea. Anyone know if this is a possibility going forward?

Using the Binomial Distribution to obtain the probability function in the specific case of receiving 0 rewards yields the following equation:
Probability of receiving 0 Qtum rewards over N trials = (1Prob of Staking)^number of trials
Prob of Staking = My Qtum Tokens / Network Weight
Say Network Weight has been fluctuating between 5,621,326 and 22,485,302.
The number of trials per day is 675.
In my case I have been staking for 14 days. So I have gone through 675*14 = 9450 trials.
I calculated the odds of me receiving 0 rewards under the above Network Weights for the last 14 days to be very very low.
I guess this could mean I am just extremely unlucky. It could also mean something else is going on in the staking reward math, that goes beyond just basic probability based on your Qtum / Network Weight.
Assuming Network Weight doesn't fluctuate any more than the above two values, I should be due for a reward very soon. Otherwise I will soon be experiencing a <.1% event. I'll give it another few weeks, hoping the Network Weight doesn't shift that much to make things easier. If I don't get a reward still, then I would conclude something has to be up, as I would have gone through way too many trials to not realistically receive a reward.

Deleted

Update:
I just received a reward.
According to the Binomial Distribution, the odds of me waiting this long without receiving a reward were about .5%  3% (Probabilities fluctuated as the Network Weight fluctuated)
I guess those weren't THAT bad of odds, and I was just unlucky.
I would have been more concerned if I reached the .1%.01% territory, but that didn't happen. To me that would signify that I would have been impractically unlucky to the point that maybe my understanding of the probability of staking is inaccurate. But that hasn't happened so everything is looking reasonable to me.