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I hear ya! I have a bit of a belief that players I add will do badly the first month they play, so a lot of times I will add a new player on Friday or Saturday so they can finish out the season and then get a "clean start" the next year. That's my superstition!
I'll fully admit this is not based on any real data, but it's often what I do.
That said, one of my teams added Cecil Cooper this year and after 23 games played he had an achievement for a 20 game hitting streak - so he obviously came in and did well. That same team added Billy William and he's been hitting the cover off the ball. So all players don't start out badly for sure!
I think a lot of this is related to human nature and how we remember things - you notice it when a player starts out doing badly and the times it happen stick in your mind. Other times when it doesn't occur you don't think about it so much, so when you think back in your mind all you recall is "players do badly when I first add them to the team" - even though it's not universally true.
This happens a lot when people think about coincidences - they tend to remember the things that confirm their biases and don't recall the contradictions.
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