In open world I believe statistic leaderboards on player level are not the way to go. What I would prefer is some kind of reputation system were statistics have an effect on your reputation. For instance if you manage to regularly sink bigger ships, if your hit ratio is very high/low, if you have sailed a lot of miles, if you have traded a lot in a certain product, if you sunk a lot of ships of a specific nation. This could perhaps all translate somehow in your reputation visable to other players.
The normal stats could be private and comparable to the average of all players so you can see how you are doing in a specific category.