organofcorti, possibly easy question, or possibly extremely difficult to answer: Due to the random nature of block solves, is it accurate to say that on average, a pool will spend more time with negative "luck" than with positive "luck"? I want to say that's the case, and it's why miners are always pointing out how pool has consistent bad luck.
In my eyes: Bad luck is DEFINED as a long period with fewer blocks than expected, while good luck is defined as a lot of blocks in a shorter period. So you would expect that a pool would probably spend most it's time negative when viewed on a graph with time as the X-axis. However, the good luck bursts only need to last a fraction of that time to "make up" for the bad times. When viewed on a graph, that would paint the picture of consistent bad luck, but when evaluated over a long enough period, you would find it gets very close to the expected average.
I'd love some confirmation/observations from you on the matter [...]
This is a really important question, because along with interpreting moving averages as trends, reporting shares per round / difficulty wrt to time is incorrect and as you say leads to incorrect interpretations of the data. What "luck" is depends on how you define it. If you take a time average of shares per round over difficulty, it will be on average worse than expected. A moving average will appear to spend more time indicating bad "luck" than good.
I always show shares per round / difficulty "luck" measurements either wrt to number of blocks solved by the pool (for example moving average measurements) or grouped (for boxplots). Even so, in the Bitminter piece I still did boxplots wrt to a difficulty period when I really should have done it wrt to number of blocks solved - but in that case I was trying to show how variance increases when the number of solved blocks is reduced.
You could still chart a moving average of shares per round / difficulty wrt to blocks solved and just add the dates corresponding to the block number on the x axis.
Another possibility that in some circumstances would be unaffected by a daily or moving average is blocks per day. This will be a Poisson distributed random variable if the pool's hashrate never changes, and so would be possible to average over time without distorting the perception of "luck" - as long as you provide confidence intervals as well.
However, pools do not maintain a constant hashrate wrt to difficulty, so instead you'd have to calculate blocks per N shares (think PPLNS) which is only Poisson distributed wrt to the submitted shares, but not to time. So again, you can't average this type of "luck" measurement by day either.
The way I get around this in the weekly pools stats is to provide a CDF probability for the number of shares it took to solve the number of blocks during the week. Then we expect to get a bunch of random dots each week. If the dots don't look randomly distributed, then there's a problem. Unfortunately this doesn't seem intuitively understandable to most miners. I like BitMinters CDF based "luck" page, and it's easy for me to see at a glance what the pool's luck has been, but it seems most miners can't.
Maybe the easiest thing to do would be changing the charts to show luck wrt to blocks solved and add in the corresponding dates.
[maybe split to another thread, but it does fit in with this BitMinter thread as well, so it's your choice].
A new thread's a good idea - people can ask questions and I can try to answer them, or look for answers if I can't. Or maybe other people can help answer. I'll set up a thread when I get back from Mother's day dinner.