The best way to deal
with negative people is to use their negativity against them. If their negativity is a weakness, feed into it until they're so devastated, they would rather be silent. My favorite is to pick apart their delivery or pin carry. If their negativity is their strength, then turn it into a weakness. Feel sorry for them and make sure they believe you. Always do it with a smile and kindness, as if you really are concerned. Then rip their heart out on the lanes :-)
Of course, if by taking 'them' apart mentally takes you out of your game, then just ignore them. Usually, if you know what you're doing, it's easy to justify the means. You'll know how successful you've been by how they bowl and what they're like the next time you compete.
I applaud everyone's good shots. I'm happy when anyone, even my competitors shoot high scores. I just want them to know if they make a single mistake, it could be lights out.
One of my favorite quotes is from Marcus Aurelius and it goes like this; “If you are distressed by anything external, the pain is not due to the thing itself, but to your estimate of it; and this you have the power to revoke at any moment.”