There is no one rule to determine the greatest rivalry in sports. It's a personal choice influenced by where you live, what sport you follow and what team you root for.
Duke vs. North Carolina is a contender along with Giants vs. Dodgers. Redskins vs. Cowboys. Auburn vs. Alabama. Michigan vs. Ohio State. There's no right or wrong.
But Red Sox vs. Yankees is tough to top.
Consider these crazy stats:
In the last 10 years, the teams have played 170 regular-season games. The Yankees have an 87-83 lead in terms of wins, but the Red Sox have scored 23 more runs. So for 170 games, 1,550 or so innings, the difference is 23 runs.
The average score in the last 10 years has been Red Sox 5.47-Yankees 5.33.