The Red Advantage thread in 2005 referred to the fact that the Red Alliance was always the higher seeded teams in the elimination rounds. Assuming the qualification rounds are 100% random*, then the average score for both alliances should be the same. But as experience tells us, they are usually not.
Due to this fact, one team may be on a certain side of the field more often than if they were completely random. Because of the way the scores work in the game, the better you are (ringer-scoring wise) the exponentially higher your scores become. Going from 1 to 2 tubes is not nearly as much as an increase as going from 5 to 6 tubes, or from 7 to 8. So it is in these phenomenal tube scoring robots that "outlier" scores happen.
Because these outlier scores can drastically alter the average, and because of the fact that due to the altered randomosity of the match generation that teams may play on one alliance more than the other, these outlier scores will often end up on one alliance more than the other.
Using data from the first 51 matches at the NJ Regional, the average score the the red alliance was just north of 33 points, while the blue alliance lagged at about 14 points. In the data used, there are several outlier scores from the red alliance (260, 98, 128 and 236 pts). If we exclude these from the average, then the average drops to only 20 and change, which is much closer to the blue alliance's average score.
But also to note is the standard deviation of the scores. Because of the outliers in the red alliance, the standard deviation for scores in the red alliance was 51.7195 points, whereas the blue alliance was only 18.676, meaning that red has a much higher spread of data. But if we again exclude the outliers, then the standard deviation of the red alliance drops to 21.087 pts, which is much closer to the blue alliance.**
* The reason matches are not completely random is because of the algorithms used to "randomize" the matches. Although it may seem like random, adding little things like a minimum time span between a single team's consecutive matches alters the randomness of the results. Now the results are no longer 100% random, but rather the sort of "equally-spaced-out-data" random that people generally associate with randomness.
** These results of course only count for the blue alliance and not The Blue Alliance, as that always tops the lists. 