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When you talk about a hitter "legitimizing" a lineup in the same breath as hitting is contagious, it gives me a sense that some hitters can be a carrier for the hitting virus, but others only contract it.  What would be the difference between these two types of hitters.  Certainly no one on the M's last year was a carrier.  For example in the early part of 2010 the M's were hovering around .500 with pretty much only Guti providing anything near a MOTO bat.  His hitting was NOT contagious though.  In fact the others' malaise and swoons was contagious to him.  
I definitely do not reject the idea of contagious hitting, but it would be invaluable to know what makes one hitters hot streaks contagious and the next hitters not.  
If there is such a hitter I think his main quality would be to be able to change his own fortunes regardless of what was going on around him (opponent pitcher, whether his mates were slumping, whether he himself was slumping, whether the hotels bed last night was lumpy, etc.).  There are some of these types of hitters of course.  The Pujols of this world.  Although Ichiro is a guy I would put in this category, but he of course didn't infect the M's last year at least.
Or is it more of a pushing water over a hill problem, once you have enough hitters to tilt the balance then the "contagion" flows freely.  So now we are talking about a team having enough good hitters going good at the same time to get to the breaking point to bring the strugglers with them.  And in that case the contagiousness of the player doesn't so much matter as how many of them there are.  I think I am more inclined to buy this theory.
Of course as is usual i am sure it is a combination of all the above and 20 or 30 other factors not listed ;)