You're doing a cost-benefit analysis on a completely arbitrary guess and then using that as the basis for your conclusion? That doesn't work, sorry.

For example, what if in actuality, all other things being equal, they had a 1 in 10 chance focused vs. 1 in 300 chance sanitized, then the results would be 100% chance for the focused versus 33% chance of a response with the sanitized ones. I just used the same thing you did to make the numbers work the other direction.

For the record, based on what I've seen and read, I do think there might be a case for the shotgunned approach, and I personally have had poor luck with the focused approach. But your numbers don't help prove it, sorry.

I think it really depends. I suspect that, for a lot of people, the best strategy is to focus time and energy on companies that they're particularly interested in, have some in with, have unusual qualifications that are a particularly good match for, etc. But, perhaps in parallel, cast a wider net with a more shotgun approach that doesn't devote a lot of time to any single company pre-interview.

That's not how probability works.

10 trials with a 10% success rate yields a 65.13% chance for at least one success.

100 trials with a 0.33% success rate yields a 28.39% chance for at least one success.

You have to use the binomial probability theorem to determine any particular number of hits.

trials! / ( successes! * failures! ) * P_success ^ successes * P_failure ^ failures

I actually read an article on Medium that goes into this in-depth. It's not published anymore, but I had it in a G-Doc, which I linked here:

https://docs.google.com/a/freelanship.com/document/d/1pnuE_b...

Actually, with your numbers the chances are 65.1% and 28.3% respectively.

I appreciate the odds, but I'd hope the numbers would be better for both (we're talking chances of interview here). I usually expect candidates who are applying to jobs they are mostly or entirely qualified for will get response rates well above that (perhaps 40%), but that's only based on anecdotal evidence from my industry experience over the past ~20 years.

Too add different anecdotal evidence. Circa 2006-2007 all of my peers who were entering the job market had to send out >100 applications to get a 1-2 interviews, if they did not get referred by someone. Based on stories from younger family and friends, the situation was the same for first time jobs in 2011-2013