Keyword Competition: What do you do?

I was just doing some quick keyword research and finding out which keywords I should use and I came across a new method of measuring keyword competition......

My Original Method:
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Searched with quotes "phrase here" and I got a lot of pages that I thought were actually competing for the keyword. They have the keyword on the page, sure....but they're not really targeting it as I would be. This is what I've been doing for awhile, until about 10 minutes ago...

pitbull dog training without quotes..... 1,100,000
pitbull dog training with quotes.... 6,320

New Method:
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I tried this approach in google -- allintitle:"phrase here" -- and I get my actual competition, the guys who are trying to get the top ranking for the keyword.

pitbull dog training with quotes... 6,320
allintitle:"pitbull dog training" .... 857

From what I can see, the new method is FAR more accurate in terms of measuring actual competition.

The problem though is that people don't search with quotes nor do they search with the "allintitle" method.... This then raises the question: what should I base my "keyword" decisions on.... the "quotes" method? or the allintitle:"keyword" method?

I'm not looking for anyone to "tell me what to do", per say, I'd just like to know how you experts measure the competition of keywords.

Thanks,

-Sean

P.S. I hate when I try to do something simple, like keyword competition research, and it turns into something complicated.