Heh, if I can't convince you with "any possible math and logic", let me try with this great video (also that one) that shows the consequences of "reasoning via outrage".

That shows one aspect of the consequences of reasoning via outrage. It doesn't indicate that the strategy itself is bad. In a similar way the consequences of randomizing and defending Podunk 1/11 times is that 1/11 times (against a good player) you will end up on youtube losing Metropolis.