Grandpa_01 wrote:Hey MtM / K1wi I just got done reading the last 3 pages for the 3rd time trying to figure out where you guys are at in this discussion. It appears you have found some common ground in areas but quite frankly I am a bit lost as to where you guys are as far as to what your actual proposals are. It is quit obvious to this old fella that the 2 of you have allot more brain power than I. So could the 2 of you condense your thoughts and theories into individual post so I can catch up. I see quite a bit of discussion between the 2 of you on what the other is saying and I am having to jump back and forth between post to try and figure things out. (and I am failing at that task) So without discussion of what the other has said can you guys post your ideas.
I'm going to repeat the formula from a previous post and precede it with an attempt at describing the idea
Theory & Concept
In a nutshell, I am proposing to remove technological improvement as a source of point inflation over time. My reasoning behind that is that as it stands, the point system rewards technological improvement over time - you can get more points in the future simply because in the future someone will have made computers more advanced. Inflation due to technological improvement also causes issues where PPD (and therefore total points) increase exponentially over time. PG can measure the level of advancement in computer performance/technology/power, relative to a single point in time, and we can represent this as Y. That is, 3 years after the starting point, computers have gotten 400% faster, therefore Y should equal 400% (or 4). It has the added benefit that a user can compare their relative performance in one time period with another, based on their PPDs in each time period - if your ppd dropped from time period a to time period c, it was because your collection of computers/computer became relatively less powerful compared to others.
This eliminates PPD growth over time that is attributed to technological improvement but what I am proposing has the benefit in that if it is done properly, it will not influence the points curve at any one point in time, which is the graph:
Of importance is the shape of the curve, which is retained, not the TPF along the bottom (because these numbers will decrease as we account for technological improvement. What we end up is as follows:
Here the red line shows the current growth in PPD over time, the curve is not horizontal because over time computer power improves. (I think going from right to left each x step is equal to the halving of TPF - under the current system the current points curve is the same as the over time curve...)
The green line is what I aim to achieve (for a minute ignore the legend) - over time there is no point inflation due to technological improvement. But what is also important is the black lines. They represent the 'point in time' curves, which my best attempt at replicating the curve of the graph of 8004, in paint
. The black lines show that at a given time period, there will still be incentive to fold faster, because the curve retains the same incentive curve as we have today.
So, if you were to look at the current time period, the current point structure still applies and a computer that is 4x more powerful than another computer, it will earn the same proportion more points as it does now. My reasoning being that if we need to discuss this later, my model preserves the ability to do so (and if people can have the mindshift to accept this proposal, maybe it will make having a mindshift to find an equatible solution to that the next question easier). The more I look at it, the more I realise that it will solve a problem where the QRB compounds point inflation due to technological improvement because this inflation is being applied twice (once to the base model, and again to the speed ratio).
Therefore, the revision will be 'appropriate' if the growth in PPD over time remains constant, because this means we are theoretically accounting completely for the effects of technological improvement. That horizontal line would basically be the overall average for the whole of FAH. It would be possible to have a different horizontal line for each platform. I.e. if PG determines that BA should have a 20% premium over SMP then the horizontal line for BA should be 20% higher than the SMP line. But over time, it should remain horizontal. This premium would also be present for the "point in time" point curve - the curves would be the same, but the BA curve would be shifted UP by 20% across TPS where computers can complete both SMP and BA within deadlines.
It also preserves the ability for PG to shift both these lines over time if they see fit - perhaps there is a major advancement in the GPU core which increases their relative power to CPUs, but the absolute increase in 'scientific value' to PG is smaller - they can shift the GPU curve down so that it remains in line with their idea of relative scientific value. Again, this is just conjecture and could just as likely happen under the current system.
That sums up the justification and explanation for the ideas behind my proposal (hopefully), I now look at the process I use to get to a formula that I think fufils this:
Working, towards an applicable formula:
Revised PPDn = PPDn / Yn (also written as "Revised PPD = PPD / Y")
where Y is determined by PG based on whatever methodology that they think suits, and n is the time period. Changes in Y can be publicised (depending on what PG decides) - so that from time n to time n+1 etc people can understand why their current PPD has been normalised to the level it has.
This then makes:
Total Points = sum(PPD1/Y1 + PPD2/Y2 + ... +PPDn/Yn).
However, I don't think that PG can use PPDn/Yn on it's own. There needs to be a way of incorportating PPDn / Yn into the following formula:
ppd = base_ppd * speed_ratio * max(1,sqrt(x*speed_ratio))
However the following:
ppd = base_ppd * speed_ratio * max(1,sqrt(x*speed_ratio)) / Yn
does not solve the effect and this can be seen on the following graph, where over time the purple line is still increasing:
I put this down to the fact that what I said earlier and that it is because 'technological improvement' is having a compounding effect. Once in increasing the baseline PPD and then again in increasing the speed ratio.
Alternatively, and now I think about it, perhaps the following formula needs to be adjusted so that the concept of PPDn / Yn remains constant over time:
final_points = base_points * max(1,sqrt(k*deadline_length/elapsed_time))
Over time the value 'final points' for a given WU should actually decrease, because every 18 months the rate at which a given WU is completed doubles and this should cancel it out if we account for technological improvement.
I wonder, therefore, whether the following holds that true?
final_points = base_points * max(1,sqrt(k*deadline_length/elapsed_time
/ Yn)) /
Yn
Conclusion:
This is attempting to change as little of the formula as possible. It still allows PG to set relative importance on different platforms (by adjusting either the base points or the k value I think), but it simply removes the effect of technological improvement.