Is there a solid strategy that you can apply to increase the chances of a win?
Of course the Eldritch Horror statistics do help in working out what can go wrong/right. But they do not offer a specific strategy -- if there is one.
First and foremost, the goal is to solve mysteries. Thus, you first thought should be "How can I further that?" Otherwise, here is an ordered list of potential good moves:
This is based on a limited set of games but helped by the statistics found in the question.
I've found that certain characters do provide benefits in certain scenarios. Some of their abilties really can be game winners such as the shaman's ability to manipulate the gate stack. It's also becoming clear that different tactics are required for different Great Old Ones. We have mastered Azathoth with an all round mix of characters and tactics but we are currently battling Yog Sothoth and it seems a more Lore and magic heavy approach is required. Likewise Shub Niggurath seems to be monster heavy so some real brawlers with serious weaponry will be required for that particular black goat of the woods.
Happy Hunting and be careful out there.