To my understanding, the round luck expresses the ratio of spent shares to solve a block. While intuitive as immediate value, it is not suitable for intuitive statistical analyses. Take e.g. the following series of luck values (real ones starting from block 338694):
- 137.70%
- 3971.90%
- 18.20%
- 393.70%
Looks not so bad at first sight - makes one think the sub 20% one is well compensated by the lucky ones. But truth is, you need to average over the reciprocal values to get the combined luck of a series, formally:
luck(n1..nk) = 1 / [(1/n1 + 1/n2 + ... + 1/nk) / k]
For the above example we get the series luck calculated as
1 / [(0.726 + 0.025 + 5.495 + 0.254)/4] = 1 / [6.5/4] = 61.54%
If my assumption is correct, then this was a quite bad luck series.
Talking variance: shouldn't the average over a longer series be close to 100%? I manually typed the round lucks for the last 100 blocks into a spreadsheet for closer inspection. The averaged luck over this series (covering last ~3 weeks of mining) is 78.74% - which I found shocking low since variance should be leveled out quite well. I disbelieve this number that much that I assume my interpretation is just wrong.
Anyone with better understanding willing to comment?
@wizkid: are those numbers at http://eligius.st/~wizkid057/newstats/blocks.php available in CSV or JSON format?
Thanks
