ELO VS CENTIPAWN LOSS. Make a ranking of player taking into account their centipawn loss

For example: My centipawn loss is 67.9 in blitz, that should more of less make me better than the 80% of the players and rank me about 30000th in the site. On the other side, It would be interesting if you guys make a correlation between centipawn loss and elo. For example: put in the x axis centipawn loss and in the y axis elo so you can get the function or the plot that relates elo to centipawn

I attach an example of what I mean:

average centipawn loss doesnt necessarily correlate to elo. your average centipawn loss depends on how likely your opponents are to put you in a complex position and how much you prefer or not prefer complex positions yourself. personally i have an average centipawn loss that is lower than some of the higher ranked players on this site, where is my extra 300-400 boost in elo lmao

I does not matter if centipawn loss do not correlates to elo. That is indeed my question. Lets analize the data for this site and see what is the result. Is definitly true my that my best games are where I played with the less centipawn loss that would of course be equivalent as If I had played with a higher elo perfomance.

@Assios. I dont even have a way to annalize all that data. My topíc was more on the side of: it is possible for LICHESS.ORG to do that automatically?

I even have an idea, if we call

centipawn loss: cpl
number of moves in the game by each side: nom
elo of the player at the moment the game started: elo

I think the ratio cpl/nom would give a even better correlation to elo

So at the end we should be looking at something like: cpl/nom vs elo

For each player that my not work, but working with GB of data and thousands of players, this I think should give interesting results.

according this study on online games correlation seems weak
but this study show correlation. Please note that pure centipawn loss per move is domes to fail. It player is upd down say a 300cp whats the point of making accurate moves? for winner simplifying is more importanta than accuracy and the other way round for loser. So this sort of considerations have to be addressed

obviously one needst do more complex descriptor as in link above to get anything out. And those results are impressive

But still not to be included into rating. Rating is supposed predict probablility of win and I dont think anything but whom you won and to whom you lost woudl a good predictor