Many people claim to have the best player collection in the world but what verifies it?

the word "best" is inherently subjective. if your criteria is the opinions of several seasoned collectors that have information about your collection and everyone elses, thats one thing. if your criteria is the number of cards, or number of 1/1s, or number of multi-color patches, or anything else.. its going to be based on your subjective opinion, and nothing more. perhaps someone sees single-color patches as better than multi-colored.. or having thousands of commons is better than a few rare cards.. who is to say?

so, theres nothing wrong with you calling your collection the "best". Theres also nothing wrong with someone (or anyone) else calling theirs the "best" based on their own subjective opinion.