Another thing I see people say a lot is "so and so started off cold last year (or two, or three years ago) and had a good finish, so it doesn't matter that he's doing bad right now". Or vice versa for somebody that starts hot. This is almost always just random variation, and has nothing whatsoever to do with particular players. Just by random fluke there will be tons of guys who start hot/cold three years in a row, or finish hot/cold three years in a row, and it almost always is absolutely meaningless. Mark Teixeira and Dan Haren have been big ones. For some reason everybody believes Teix always starts slow, and Haren always finishes slow. In 2011 Teix's highest monthly OPS was in April (907). In 2006 and 2008 his Aprils were great (845 and 886 OPS). Did he just forget to start slow those years? The Haren stuff, that he always had a terrible finish to the season, was also debunked as inaccurate. People love to find little meaningless patterns which are most of the time coincidences along a normal distribution curve.
I've even seen people - people that are far too smart to believe this garbage - contemplate whether Teix's June will be OK or if his typical slow start will be moved 2 months forward. Or they think that Matt Joyce will be amazing in May because his career splits said so (this has been talked about a lot since he did so well this year; I'm sure it will be an even hotter topic next season). Or Alex Rios' odd/even year thing where he's only good in even years. As if that's a "thing". I mean, Bret Saberhagen did it and he's only like 0.1% of the MLB pitchers since the 80's so surely it can't be a fluke.
Anyway, most reasonable people know not to put too much stock into hot/slow starts. Pretty much the only thing that matters is injuries or role changes at this point, or identifiable skill changes. Meaning things that stabilize pretty quickly like K%, as opposed to a guy hitting homeruns on 50% of his fly balls or having a .100 BABIP. I see a lot of people saying not to make major trades in April and to wait until the dust settles, but to me, it's the best time to make trades with the people that overreact to April stats.