Quote from: zefir on January 28, 2015, 10:09:04 PM

I need some help to correctly interpret the pool statistics.

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..n_k) = 1 / [(1/n₁ + 1/n₂ + ... + 1/n_k) / 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

After making the math for last 100 blocks :

Code:

cat Block\ List\ -\ Eligius\ Pool\ Statistics.html |egrep % | awk '{print $8}' | cut -d % -f 1 | cut -d '>' -f 2 | tr -d , | sed 1d | head -n 100 | awk '{SUM+=1/$1} END {print NR/SUM}'

78.8334% luck

For last 200 :

Code:

cat Block\ List\ -\ Eligius\ Pool\ Statistics.html |egrep % | awk '{print $8}' | cut -d % -f 1 | cut -d '>' -f 2 | tr -d , | sed 1d | head -n 200 | awk '{SUM+=1/$1} END {print NR/SUM}'

82.7441% luck

For last 500 :

Code:

cat Block\ List\ -\ Eligius\ Pool\ Statistics.html |egrep % | awk '{print $8}' | cut -d % -f 1 | cut -d '>' -f 2 | tr -d , | sed 1d | head -n 500 | awk '{SUM+=1/$1} END {print NR/SUM}'

90.384% luck

For last 1000 :

Code:

cat Block\ List\ -\ Eligius\ Pool\ Statistics.html |egrep % | awk '{print $8}' | cut -d % -f 1 | cut -d '>' -f 2 | tr -d , | sed 1d | head -n 1000 | awk '{SUM+=1/$1} END {print NR/SUM}'

93.1394% luck

For last 3000 :

Code:

cat Block\ List\ -\ Eligius\ Pool\ Statistics.html |egrep % | awk '{print $8}' | cut -d % -f 1 | cut -d '>' -f 2 | tr -d , | sed 1d | head -n 3000 | awk '{SUM+=1/$1} END {print NR/SUM}'

94.1135% luck

For everything (8870):

Code:

cat Block\ List\ -\ Eligius\ Pool\ Statistics.html |egrep % | awk '{print $8}' | cut -d % -f 1 | cut -d '>' -f 2 | tr -d , | sed 1d | awk '{SUM+=1/$1} END {print NR/SUM}'

95.989% luck (The pool is then equivalent for a loyal miner to a 4% fee PPS)

Orphan rate is 198/(8870+198) = 2.18% (Quite high if you ask me)
The total luck rate for the pool lifetime with orphan is :
95.989*(8870+198)/8870 = 98.13 %

Which leaves 1.87 % of withholding hashing power for the pool lifetime assuming it is a long enough time frame (which I think it is)