Michael Weddell of Detroit has done some research on early season winning streaks:

Regarding the Royals winning streak, I'd like to abandon the probability formulas and look at it a bit more subjectively. If anyone looks the probabilistic approach, they might read the Tigers article in the 1985 Bill James Baseball Abstract, which was probably the genesis of Bill James' thinking on this issue, reflected in the quote in your interview that started this discussion topic.

This isn't just any win streak, but one that starts the beginning of the season. If we restrict our inquiry to instances where teams began their seasons with long winning streaks, not just a winning streak beginning at any point in the season, then this is a rare event. The attachment lists teams since WWII that began the season winning 7 or more games -- the Royals are just the 15th team to do so. (I picked 7 as the cut off so that the median was a beginning of the season winning streak of 9, the same as the Royals just did.

Some observations from the data:

The Royals preceding year record of 62-100 (a winning percentage of .383) was by far the worst of any of the streaking teams. While all of the teams finished at .500 or better for the season that began with their winning streaks, the data doesn't really support that rosy a prediction considering where the Royals are starting from.

Of the prior 14 teams, 64% of the teams improved their winning percentage, 21% declined, and 14% remained essentially unchanged when comparing their winning percentage for the year to the prior year's winning percentage.

If we restrict our review to just teams that were coming off of a sub-.500 record and started the next season with a 7-game or longer winning streak, all 5 out of 5 teams improved. Furthermore, the average improvement was quite substantial, 12 additional games won over the course of a 162 game schedule. Note that these teams all have the Plexiglas principle (that teams' records tend to head toward .500, the mid-point) working in their favor.

Obviously the small sample size should make us wary of drawing firm conclusions. Nonetheless, I believe that the Royals win streak does hold signature significance, to borrow a Bill James phrase. While to predict a finish of .500 or better (81 wins) still seems unlikely, I'd predict that they'll do better than the 66-96 record that James insisted on. I'd guess that the Royals will avoid losing 90 games, which would be an improvement of at least 11 wins over their 2002 record.

If you like, feel free to reprint all or any edited portion of this e-mail and/or the spreadsheet in your blog, with or without accreditation. You should though credit www.baseball-reference.com for invaluable assistance in locating this data.

Here's the spreadsheet.

A nice bit of research, Michael. I'm also going to try a simulation to see if I can get a handle on the difference between my independence assumption and the real p-value.