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Armstrong said that "luck" was necessary.
From the text:
Well, it had succeeded! He'd been lucky! Lucky and skillful of course. He was a good man at his job - but that wasn't enough for success. You had to have luck as well. And he'd had it! An accurate diagnosis, a couple of grateful women patients - women with money and position - and word had got about. "You ought to try Armstrong - quite a young man - but so clever - Pam had been to all sorts of people for years and he put his finger on the trouble at once!" The ball had started rolling.
And Then There Were None