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.
Sensible. I agree.
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.
Mostly sensible. Comments/Questions:
1) I don't see why the intervals would need to be of a fixed size
How would you do variable size?
2) I don't understand why you need to logarithm (I understand why it's used for modelling, that's fine, but for reporting and interpreting results I don't see the reason)
I have used it for everything in my grand excel for some time now, and don't think much in $ terms anymore. Try it, it works! (How much is bitcoin price today? - 2.70, down 0.02.)
Of course we should use dollars in reporting.
3) Furthermore, I find you choice of base 10 unnatural (base e is the natural choice!;)
Base10 is good as you instantly see the round dollar amounts:
$100 == 2.00
$200 == 2.30
$500 == 2.70
$1000 == 3.00 etc.
(doubling == 0.30. tenfolding == 1.00)
Whereas in ln (base e)
$100 == 4.61
$200 == 5.30
$500 == 6.21
$1000 == 6.91
(doubling == 0.70. tenfolding == 2.30)
4) What's the exact logic of the point system? Why is there a division and a subtraction/addition? What do the numerators and denominators represent? Why do the points seem asymmetric, i.e. lose more points on a bad guess than you gain with a good guess?
In some fields, such as art, it is important to sometimes hit big, and it does not matter so much if you sometimes produce bad works. In money management it is important to avoid mistakes. Therefore I purposely made the formula such that you are heavily penalized for not awaiting something that the others did, and what indeed happened. Millions of people in the world are forgoing the opportunity to become rich because they have decided not to believe that bitcoin can continue doubling, or even quadrupling in a month.
5) The intervals need to be in absolute terms, not relative to the price at posting time - otherwise you would also need to keep track of the price at posting time for each prediction (not difficult, just an avoidable pain in the ass)
Sure. I am proposing that the intervals are 0.05 (base10) points wide at round numbers, regardless of the price at posting.
