Does the 'Big Prize' Really Motivate Innovation?

Over the past few weeks there's been a lot of discussion and debate over the possible connection between "big prizes", like the Nobel prize awards, and innovation. The arguments presented by people on both sides of the debate make a lot of sense, for the most part, and a valid case could be made for whether or not there is a direct link.

At the same time, one has to wonder if the scope of the discussion is much too narrow. The focus on "big prizes" tends to restrict the debate to the exceptional cases rather than the general case, and provides very few data points to use for validation.  At the same time, we have to wonder what the underlying purpose of the debate is. Is it a plea for more "big prizes" to be created in order to spur innovation? Is there a general feeling that innovation has been stifled due to a lack of "big prizes"? Or is the debate just an academic exercise with no specific purpose or intended outcome?

Is innovation, especially technological innovation that manifests itself in science and industry, that radically different from sports like baseball?

It might be useful to compare winning the World Series with a scientist who wins the Nobel Prize. Almost every player, no matter what their age, realizes that the odds are weighted heavily against them. Realistically, they know that there is almost no chance for them to win 'the prize.' Yet a significant number of children and adults take up the sport with surprising vigor and enthusiasm, And they often stay devoted to baseball as fans for the rest of their lives.

What's going on here? Are they involved because of the 'big prize', or are there other factors motivating them? Would creating another World Series type 'big prize' have a positive impact?