What really matters is the type of research you are engaged in. Some interesting findings that have great potential for further investigation can fetch you more funds irrespective of the researcher. Teaming up with some good collaborators may increase your chance of getting substantial amounts in funds.
So, some good research findings that is promising and likely to have an impact on science and technology will definitely bring in large amounts in funding.
Yes, influence does matter! But I purposely didn't mention it in my first answer. I did not want to discourage you. Come up with novel ideas and write some good research projects, and I am sure you will get a substantial amount in funding.