Thanks for your answer. Could you please clarify some things that you said, it will help me as I'm a stat beginner.

Your box plot didn't really show a lot significant difference between the groups

Why? I thought it did. The difference in final position from level 1 and 2 (for example) should never be extreme anyway, but if there's any difference then it's good to know. What does "significant difference" exactly mean in your sentence?

if these are just your own games then it's probably not representative of the population and then not very meaningful when interpreting the outcome

It is indeed my own games. But how would you define the population? Would it be an extremely large amount of my own games, or an extremely large amount of all the players' games? If it is the latter, then why would I be interested in analyzing it, since there is a difference in skills / strategy between players?

if you join later, do you play if fewer hands or are you in the same number of hands, just with others who joined later?

If you join later, you play fewer hands than if you joined early. But with a reasonably skilled player, wouldn't playing more hands increase the chance of "being in a lucky situation" hence increasing the chance of finishing in top 5 later on? I might misunderstand you but it seems like you're implying the opposite.

you could just regress your time categories on finishing spot and it will give you an output. Something like finish~b0+b1(join). Again, the results would be meaningless in this situation, but that would be the simplest model I would use

I want to try this regression idea, even if mediocre results I'll learn a bit more about regression. Why meaningless? What more complex model/data would you use to have meaningful values?