I am very interested in this topic and hope more people can chime in,
My leagues for years have just used a randomized seed given right before the draft so i never really thought to heavily on the strategy, just did enough mocks to get a feel, This year instead of just randomizing the draft order we are selecting teams out of a hat and you get to pick your draft spot, (i'm sure there is a name for that

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In the first league i have picked the 2 spot, because i am a hanley homer, and if he goes one oh darn you get pujols,
In my other league i have gotten the 3rd pick on draft spots, 1st guy selected #2 draft spot, 2nd guy hasn't selected yet, so i virtually can pick from anywhere. If he passes on the 1st i will most likely grab it but if not i am really not that sure. I have liked picking from the 12 spot before, i think the back to back picks become a slight advantage in the mid to end game. But I am beginning to get wary of that spot now from all the responses though.
A previous poster said they would be fine with the first 11, but not 12, who are you avoiding D.Wright?