When's the last time you've won a game?

what AFnord said, lvl does not affect your chance to win, but affects number of entries in a GA - lvl 0 GA for a brand new title will have few thousands entries - meaning you have only 0.02% to win. Same GA with lvl 1 requirements will only have 2000 entries, meaning your chances are 0,05%. Lvl 4-5 will have let's say 500 Entries, meaning you have 0.2% to win, while lvl 9 GA for the same game will only have 25 entries, because there are much less lvl 9 users. it means lvl 9 will have 4% chance to win this GA, which is 200 times more than chances in GA avaiable to lvl 0 user.

In addition there is also very important aspect of Group GAs and Whitelist GAs. Big contributor will have much better chances of being invited to both purely GA groups and social groups as well. People recognize him and wil invite him to their groups, events, ppl will put him on their whitelists - all these means access to GAs with much lesser audience than any public GA, meaning he will win more often in those as well.

EDIT: Even moar numbers to prove my point :D:
My wins consist of: 538 group GAs, 42 public GAs and 82 private/whitelist GAs. What it shows is that main gain of games are private groups - groups you cannot join if you're not active member of SG and/or you don't contribute yourself. Private GAs are hard to judge, because some of them are puzzle GAs, meaning they are accessible to anyone, and some of them were just shared with friends ones, so something like new whitelist GAs. But nonetheless they still are a big portion of my wins. And public GAs are "only" 42. But considering the fact that 2 year old account with lvl 0 will just have 3-5 public wins it still shows that lvl adds to actual chances of winning, because of avaiability of GAs with bigger win chance. Also keep in mind that with many private/group/whitelist GAs avaiable for user to enter he will prioritize those, as they give him better chance to win, so he will enter much less public GAs compared to lvl 0 user ;p