Based on previous studies of elections, it tends to be because the nonvoting population, or those who tend to come out and vote only in presidential elections/amendments of interest, tend to lean more towards the democratic side. This usually comes down to quite a few factors, one of which is demographics; the Democratic party tends to garner much more support from younger generations, who overall have been found to not be as politically active. This difference is especially significant for the midterm elections, and is a theoretical reason for why democrats have in recent history done so poorly during these elections. An especially telling aspect of this is this statistic: Nonvoters favor Barack Obama over Mitt Romney by a wide margin (59% to 24%) (while keeping in mind that voting for the president may not be indicative of voting for a Democratic congressman over a Republican congressman). What all this means is that, given all nonvoters turning up at the polls or at least in equal proportions based on the gathered data, the Democrats would benefit significantly more than the Republicans.
But to tie this into your question, there is no actual "correlation" that one can establish with any meaningful degree of accuracy, because there isn't enough meaningful data for it. The best you can do is establish conjecture through the information that is available. The claim that a greater volume of people typically identifying as nonvoters showing up would be more beneficial for the Democrats than the Republicans is accurate, if there was equal distribution, but that doesn't necessarily mean that a greater influx of voters would have turned the favor towards the Democrats.