I have a question that requires, I think, actual training in statistics and probabilities. (My background consists entirely of reading articles about baseball that use sabermetrics, so...)
I play in a standard 5x5 head-to-head fantasy league, and a proposal has been made to extend our playoff rounds from one week each to two. It's argued that this will substantially reduce the role that chance plays in the outcome of the playoffs - that is, it's assumed that the better team will be more likely to win ('100% better!', one of the other managers has ludicrously claimed') - but I question whether this is actually true. (I ran comparisons of HR and AVG totals - first on a week by week basis and then pairing adjacent week, so as to test the accuracy of the proposal versus what we used previously - against the mean, and the one week totals for HR showed a standard deviation that was 48% of the mean, while the two week SD was 42%; likewise, AVG improved from 12.5% to 9.8%. Pretty tiny improvements in each case, I think. But this assumes that my methodology is sound. Can anyone tell me?)
I'm sure that it will make the results slightly more reflective of each team's true talent levels, but it seems to me that a two week sample is hardly more accurate than one week. (I know, from Jonah Keri's book, that samples of either size for individual players are terrible indicators of a player's talent level. Can an entire team of terrible samples be much better?)
So the question, again - and hopefully someone can help me answer it - is what sort of effect on statistical accuracy and reliability does the switch from one to two weeks make? And is it actually a significant improvement - one that's worth creating a playoff format that will eliminate more than half the league from contention with a month to play in the actual MLB season?