The Correlation of Men Left on Base with Offensive Success

My dad suggested that I investigate the link between the number of men left on base (per game) and offensive performance in baseball. Conventional wisdom suggests that this should be a negative correlation: the more men a team leaves on base, the lower their offense's output should be. Thus, we hypothesized that more men left on base --> less offensive output --> lower winning percentage. 

I checked the correlation between men left on base (per game) and win percentage for the past 7 years (as far back as the data went from Teamrankings). It turns out this correlation is slightly positive: 0.181, meaning that the more men were left on base, the better the team performed (slightly). I then took this a step further and checked the correlation between men left on base in scoring position (per game) and win percentage. It also was slightly positive: 0.127. This contradicts my dad and I's hypothesis: but it also logically makes sense. The more men are left on base, the more men are getting on base: and thus the more runs are being scored by the team. In fact, the 2007 World Series champion Red Sox, 2008 ALCS Red Sox, 2009 World Series champion Yankees, 2010 ALCS Yankees, 2012 NLCS Cardinals, and 2013 ALCS Tigers all led the league in men left on base per game.

It turns out this study was already done in greater detail by Baseball Prospectus. They used a much larger sample size (1971 to 2007) and found the same thing: runners left on base correlates strongly with times on base (0.72), and times on base correlates very strongly with runs scored (0.91), which leads runners left on base to positively correlate with runs scored (0.52).