How good does original research look on an application?

I'm currently in Year 11, and I'm looking to apply to Cambridge for Natsci/physics. In my free time i've been working on a research paper about a new method of mathematical optimisation I came up with that uses quantum hydrodynamics to essentially evolve a probability distribution over the function (quite frankly i have no expectations for this to be published, i'd be thrilled if this made it to arxiv). Just out of curiosity, how good does something like this look on an application relative to other stuff like running clubs or doing well on BPhO (which i'm also doing this year)? Thanks a lot in advance!