Great job on an interesting article. It was well written and well researched. More importantly, the issue offers two extremely important implications for the 2003 Reds--the Reds are either going to start losing more often, or they're going to have to improve the run differential. Something's gotta give.
I have a few areas of research for you guys to consider if you choose to continue looking into this issue further.
1.) park effects. Although the early data on the GABP has shown it to be a neutral-hitters park, I'm not convinced that that is really the case. By the time the season ends, I believe it will end up being a hitters park, which would likey skew the run-differential data. Teams that play in hitters parks score more runs and play in higher scoring games (e.g., 8-5 games, as opposed to 2-0 games). Naturally, they are going to have run differentials that are not as nice. Using the Pythagorean projections might not necessarily present an accurate picture of reality, which is certainly the case in extreme parks like Coors.
2.) home runs. HRs tend to cause teams to "bunch" their run scoring together because HRs clear the bases of all the runners. This results in scoring pattterns than are high and low from inning to inning, and by implication, scoring patterns that are highly uneven from game to game. (As an aside, the 2001 Mariners are a great example to illustrate the contrast here. That club that outperformed its projections by scoring in smaller bunches across many more innings, whereas the Rockies score in bunches every year and never can perform up to their Pythagorean expectations.) Similarly, the 2003 Reds have hit the most taters in the NL this year (78), but the pitching staff has also given up the most homers in the NL (73). This means that the team is scoring more and getting scored against in bunches, relative to other teams. This penchant to hit (and give up) HRs suggests that the runs scored differential might be a little uneven, relatively speaking, at this point in the season.
The HRs and park effects go a long way to describing why the Colorado Rockies underperform their Pythagorean projections every year--they hit a ton of taters and play in an extreme hitters park, which combine to make the run differential more "lumpy." Similarly, the Pythagorean projections might not be presenting an accurate picture of the who these 2003 Reds actually are. At this point I am a bit ambivalent as to how the homers and park effects will affect the run scoring differential for the Reds, but my intuition leads me to believe that they will split the difference--they will improve their run scoring differential somewhat and also come closer to their Pythagorean projections. Let's face it, a team can't continue to win 90% of its extra-inning games. This is really a .500 ballclub (good hitting, atrocious pitching), which is about where the club's current record stands right now.
Finally, I'm not convinced that two months of runs differential data is sufficient to consider it a trend. The 1999 Reds were way outperforming their Pythagorean projections (+5 games, or something like that) through the end of August, 1999. At the time, analysts (Neyer included) were saying how the Reds were not going to be serious playoff contenders because of this key data point. Not sure if everyone remembers, but Sept-Oct 1999 was one of the best stretch runs ever seen, when Greg Vaughn led the club by hitting something like 16 homers in September and October. In the end, the Reds actually ended up *underperforming* the Pythagorean projections by one game, indicating that some teams might need a little more time for these data to correct themselves, either by the club losing more games or scoring more runs.
There are other issues to consider, like offensive and defensive efficiency (e.g., the value of a good bullpen, bullpen usage patterns by a manager, timely/untimely hitting, etc.). For more in-depth discussion on these points, people might want to check out this Diamond Mind article:
I think the run differential can help us provide insight into *why* the Reds have been winning (i.e., close games, HRs, etc.) more than it can offer definitive evidence that the Reds have been "monumentally lucky." Again, well done, and I hope to see more insight like this in the future.