Tolstoy's view of history as propounded in his book "War and Peace" is that the forces that shape historical events are infinitely many and unknowable. He posits that a leader is in no ways more special then any other person in having a role in shaping history, and hence the correct historical method is not to focus on leaders, which is usually done. What evidence is there of this theory besides the evidence given by Tolstoy himself in his analysis of the French invasion?
As this question's tag implies, this is more of a philosophy than a theory. Evidence is not always something you can apply to a philosophy. That doesn't make it any less valuable though.
I understand that it was part of Communist (and thus Soviet) dogma that history is a large process that individual people cannot control any more than individual snowflakes can control an avalanche. This can be taken to extremes though. I'll go back to the same country and say that trying to claim Stalin had no real personal effect on history is patently ridiculous.
However, the typical traditional Western view of Big Men can be (and in fact has been) taken to extremes too. We miss a lot of valuable perspective when we just focus on wars and rulers. For example, you can't really understand 19th and early 20th century US history without studying the slavery culture, the Great Awakening, the rise of the union movement, and the spread of populism and socialism. However, USA history textbooks try to avoid all those subjects like The Plague.