While the DNC's TV ratings might not correlate to more votes for Obama, high viewership of either convention may correlate to higher voter turnout, according to this chart by Jordan Ragusa on the blog Rule 22.

 

Ragusa, an assistant professor of political science at College of Charleston, used Nielsen data to add up ratings of both the Democratic and Republican conventions to populate the x-axis. The y-axis is the voter turnout for each year, collected from the American Presidency Project. As you can see, Ragusa found a statistically significant pattern: More viewers corresponds to higher turnout. 

"So in this context, convention ratings might give us a window into an important element of presidential elections," Ragusa writes. "Notably, turnout matters in this election because higher turnout probably favors Obama."

The dot for 2012 represents Ragusa's prediction based on the trend and lands at 53 percent. Obviously, convention ratings are not the only indicator for turnout. But if you want to make a bet off of the convention ratings, you're probably better off predicting voter turnout than who will be president.

Go to Rule 22 for more analysis.