I used the linear log5 method outlined here, http://web.archive.org/web/20080622145043/http://www.diamond-mind.com/articles/playoff2002.htm. To estimate each teams baseline winning percentage I used BTB Power Ranking which can be found here, http://www.beyondtheboxscore.com/2010/9/4/1670477/btb-power-rankings-week-22-were#storyjump. The Win% are based on team wOBA, xFIP, baserunning and defense. Yankees have a estimated win percentage of 0.593 and the Twins are at 0.578. The historical 0.040 home field advantage was then added to the baseline win percentage. Using those numbers the Twins have a 52.5% chance of winning home games and a 44.5% chance of winning road games.
The probability of the Twins winning the series can then be figured by calculating the probability of each sequence of wins and losses that would result in a series victory and then adding those probabilities. Results and limitations are below the jump.
One limitation is that I may be underestimating home field advantage at Target Field. If the homefield advantage is 0.060 the Twins would end up as a slight favorite. Because this is the Twins first season at Target field, I thought it was best to use the historical advantage.
Another issue is that this method relies on a team's year to date statistics to calculate the estimated win percentage. The 7th reliever, 5th starter, or bench players will play a much larger role in a teams year to date statistics than they would in a playoff series. it also doesn't account of rookie callups or injured players.