Criminal Sentence 579: Run-on Question

From a baseball Q&A in today's paper:

"Last year you were in the All-Star Game, do you rather participate in it or relax during the break?"

I'll bet that when the reporter asked the player this question, the journalist paused for a few beats after saying, "All-Star Game." That's because this is the end of a sentence, and it needs a period; this first part is just a statement. The question actually begins with the "Do you" part. Here's the correct punctuation:

"Last year you were in the All-Star Game. Do you rather participate in it or relax during the break?"

I guess I won't comment on the oddness of "Do you rather participate." "Do you prefer participating ... relaxing ..." would be better, don't you think?