A Grading Thought Experiment

This is one of the times of year when those of my ilk turn from teachers into graders. A colleague of mine proposed an experiment the other day and I'm interested to see if your intuitions are the same as mine.

Take a stack of papers, grade just the first sentence, then go through them again and grade just the first paragraph, finally grade the whole paper. Will there be a difference in the grades?

I bet the first sentence grade would be irrelevant since it takes students a while to learn not to begin papers with annoying, banal, and completely meaningless or utterly false first sentences like, "Since the beginning of time, people have argued about (insert philosophical problem student had never heard of before)." No, they haven't -- people weren't around at the beginning of time and even after homo sapiens arrived, it took them quite a while to formulate this little intellectual nugget.

Although I would bet that there would be little difference between the paragraph and paper grades. If the person thought about the topic before writing, there would be a thesis sentence and something resembling a claim in the opening paragraph. Generally, this means there's actually a coherent argument in the paper. If they are handing me a discovery draft -- a piece where they think through their keyboard, the first paragraph will contain only vacuous claims like "Rene Descartes was one of the most important thinkers in history." Blah, blah, frickin' blah... Maybe at the very end, they'll find something that would have made a nice paper, but that would mean starting over and actually writing a good paper, but since it was written the night before, that's all she wrote -- or he wrote, depending upon the writer, of course.

So, any relation between these three hypothetical grades?