If models with MMC>0 have Mean(CORR)=0.0318 and Mean(MMC)=0.015 and you demand models with high MMC, the multiplier of MMC should be at least twice the multiplier of CORR. That is to say:
Payout = w CORR + (2-w) MMC ; such that w<0.667
Why? Because improving CORR by +2d is easier than improving MMC by +d. This is in average terms, in marginal terms it can change a little bit.
1.- Start with this initial scheme:
Payout = w CORR + (2-w) MMC ; such that w=0.65
2.- Adjust “w” depending on the marginal improvement of the average CORR and MMC over time.
3.- In this way the payout scheme can be changed for every tour in order to give an incentive to the submission of high MMC models.
Here is an example:
Mean(CORR) = 0.0318
Mean(MMC) = 0.015
In two months:
Mean(CORR) = 0.0418
Mean(MMC) = 0.0175
Delta(CORR) = 0.0418 - 0.0318 = 0.01
Delta(MMC) = 0-0175 - 0.015 = 0.0025
w 0.01 = (2-w) 0.0025 => w = 0.4
An alternative to avoid too much fluctuations or negative marginal values would be to consider total value instead of marginal values:
w 0.0418 = (2-w) 0.0175 => w = 0.6
In general, w = 2/(1+Mean(CORR)/Mean(MMC))
with this particular cases:
Mean(MMC) = 0 => w=0 => payout = 2 MMC ; the current MMC competition
Mean(MMC)=Mean(CORR) => w=1 => payout = CORR + MMC ; the master_key proposal
Mean(CORR)=0 => w=2 => payout = 2 CORR ; all the incentive goes to CORR since mean=0