Yes, there is a tradeoff between payout and confidence. You want to submit the lowest C possible to maximize your payout, but at the same time if the staking pool is exhausted before your stake gets considered then you can’t win anything, so you want to maximize your C to ensure you get considered for payout. If payout wasn’t inversely proportional to C, then there wouldn’t be a compelling reason for participants to be realistic about their estimates of confidence, instead they would just submit higher and higher confidences to ensure they would be considered for payout.
The paper claims “The higher p, the higher c a data scientist will submit, and the more dollars the data scientist can win from the auction.” Then why didn’t XIRAX stake more numeriare than PHIL_CULLITON?
The amount of NMR that anyone is staking is obviously going to depend on how much they have, and their risk tolerance. If everyone had an unlimited amount of NMR, then of course, everyone is going to stake increasingly massive amounts, but that’s not the reality.
Lastly, why are payouts not simply inversely proportional to the logloss? Is this just a convenience?
This question is essentially asking “why isn’t the staking competition more like the main competition?” and the answer is because it’s a different competition. Log loss doesn’t matter for staking except in whether it’s better than chance or not. Log loss matters for the main competition, and in that case accounts are ranked by log loss with the top 100 getting payouts that decrease by rank. There are two different goals at work in these competitions. The main competition is about how much you can beat chance by. Unfortunately, the winners of this fluctuate massively from week to week because this isn’t an easy task with so much noise in the data. The staking competition favors consistency in performance, because the more often you beat chance, the higher your confidence will be and the more you can stake. There is more regularity in the winning accounts here as people are training models for consistency rather than low log loss.