Each user is incentivized to to maximize their individual correlation score. But Numerai wants to maximize the metamodel's correlation score, where the metamodel is the stake weighted ensemble of all submissions.

Metamodel contribution `mmc`

is designed to bridge this gap. Whereas `correlation`

rewards individual performance, `mmc`

rewards contribution to the metamodel's `correlation`

or group performance.

If you are a manager of a basketball team, and you already have 4 Shaq O'Neals on your team, would you draft another Shaq as your 5th? Or would rather take a guard like Kobe?

In 2019, tree based models like integration_test have done well become very popular. Knowing this, how would you design a model that would ensemble well with this group of models?

To calculate a user's (U) `mmc`

for a given round we

select a random 67% of all staking users (with replacement)

calculate the stake weighted predictions of these users

transform both the stake weighted predictions, and U's model to be uniformly distributed

neutralize U's model with respect to the uniform stake weighted predictions

calculate the covariance between U's model and the kazutsugi targets

divide this value by 0.0841 (this step is to bring the expected score up to the same magnitude as correlation)

the resultant value is an MMC score

repeat this whole process 20 times and keep the average MMC score

Stake weight is necessary to make the system unattackable

Sampling a random 67% each time is important to incentivize some redundancy.

A very large staker submitting similar predictions to yours would penalize you too much if we didn't do this.

Read more about the MMC calculation here.

Read more about MMC and profitability here.