The table below summarizes the historical 30d changes in USD/BTC. There has been 1341 datapoints.
Change is given in log (log10) base units and also percentages.
The variance in 30 day change is quite extreme, you could have made more than 8 times your money, or lost 60%.
The 10% upper tail is +157% or better, 10% lower tail is -27% or worse.
The long-term amusement that bitcoin rises 60% of the 30d sequences and goes down only 40% still holds
I read the proposals with enthusiasm and thought, which one would be easier for the forecasters - producing a continuous probability distribution, or producing a discrete distribution like the one below. The ones who can handle continuous distributions, can easily process them to give piecewise results, but not necessarily the other way round.
I would propose that the ones who want to participate, need to produce a table that gives the probabilities (adding to 100.00%) for each log slot. The slots would be with 0.05 intervals like below. Eg. 3.00-3.05 == $1,000-$1,122. Once the correct result is known, we take a geometric mean of the probabilities given to that slot in the predictions. Then you get + or - points depending if your prob was higher or lower than the average. Eg. if your prob was 8% and average was 4%, you get 8/4-1 = 1 point. If your prob was 1% and average was 3%, you get -3/1+1 = -2 points.
(in the table comma = point (US))
LOG MIN CHANGE MAX CHANGE PROBABILITY
0,90 0,95 694 % 791 % 0,15 %
0,85 0,90 608 % 694 % 0,15 %
0,80 0,85 531 % 608 % 0,37 %
0,75 0,80 462 % 531 % 0,30 %
0,70 0,75 401 % 462 % 0,97 %
0,65 0,70 347 % 401 % 1,34 %
0,60 0,65 298 % 347 % 0,82 %
0,55 0,60 255 % 298 % 0,67 %
0,50 0,55 216 % 255 % 1,19 %
0,45 0,50 182 % 216 % 2,09 %
0,40 0,45 151 % 182 % 2,46 %
0,35 0,40 124 % 151 % 2,09 %
0,30 0,35 100 % 124 % 2,68 %
0,25 0,30 78 % 100 % 2,91 %
0,20 0,25 58 % 78 % 5,74 %
0,15 0,20 41 % 58 % 5,15 %
0,10 0,15 26 % 41 % 6,86 %
0,05 0,10 12 % 26 % 10,37 %
0,00 0,05 0 % 12 % 14,09 %
-0,05 0,00 -11 % 0 % 12,98 %
-0,10 -0,05 -21 % -11 % 12,08 %
-0,15 -0,10 -29 % -21 % 6,04 %
-0,20 -0,15 -37 % -29 % 4,33 %
-0,25 -0,20 -44 % -37 % 1,79 %
-0,30 -0,25 -50 % -44 % 1,64 %
-0,35 -0,30 -55 % -50 % 0,45 %
-0,40 -0,35 -60 % -55 % 0,22 %
-0,45 -0,40 -65 % -60 % 0,07 %