Suppose that you are worried that you might have a rare disease. You decide to get tested, and suppose that the testing methods for this disease are correct 90 percent of the time (in other words, if you have the disease, it shows that you do with 90 percent probability, and if you don’t have the disease, it shows that you do not with 90 percent probability). Suppose this disease is actually quite rare, occurring randomly in the general population in only 10 of every 1,000 people.

If your test results come back positive, what are your chances that you actually have the disease?

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Surprisingly, the answer is less than 9% chance that you have the disease!

The basic reason we get such a surprising result is that the disease is so rare that the number of false positives greatly outnumbers the people who truly have the disease. This can be seen by thinking about what we can expect in 1,000 cases. In those 1,000, about 10 will have the disease, and about 90 of those cases will be correctly diagnosed as having it. Otherwise, about 990 of the thousand will not have the disease, but of those cases about 100 of those will be false positives (test results that are positive because of errors) due to only 90% accuracy of the testing method. So, if you test positive, then the likelihood that you actually have the disease is about 10/(10+100), which gives the same fraction as above, approximately 9.1% or less than 10 percent!

Note that you can increase this probability by lowering the false positive rate by improving accuracy from 90% to 95% accuracy).

Now imagine that we see a bargain stock candidate. Excited that we might be on to a winner, we deploy the most rigorous stock analysis. All these efforts give usa high degree of confidence that our analysis is 90% accurate. At the same time, we also know that true bargains occur only in 10 cases out of perhaps 1,000, often even occur even less frequently.

If our 90% accurate stock analysis is showing strong bargain signal, what are the chances that we actually found a bargain?

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Unfortunately, the answer remains that we only have the same 9% likelihood that our analysis has uncovered a bargain stock.

The reason is unsurprising; the rarity of bargains coupled with “only” 90% accuracy of our stock analysis means that we’ll come to an incorrect decision in 10% of cases. Applying our rigorous analysis on 1,000 stocks will result in false bargain signal 10% of the time which is 100 cases. Using Bayesian formula, this means that out of 10 true bargains in the pile of 1,000, our analysis will mistakenly identify 100 leading to an inevitable conclusion that any given “bargain” that we think we’ve found has only 9% probability (10 / (10 + 100)) of being an actual bargain.

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Can we do better? Yes. The answer lies in improving the accuracy of your analysis, say from from 90% to 99%. That’s what Buffett means by investing in no-brainers:

“I don’t look to jump over seven-foot bars; I look around for one-foot bars that I can step over”.

99% accuracy of your analysis will increase your odds to 50% (10 / (10 + 10)). So it is by intensely focusing on few opportunities within our circle of competence, that we both understand and are capable of appraising accurately with a high degree of confidence, that we identify qualifying investing candidates.

Another good Buffett quote captured this idea well:

“We believe that a policy of portfolio concentration may well decrease risk if it raises, as it should, both the intensity with which an investor thinks about a business and the comfort-level he must feel with its economic characteristics before buying into it. In stating this opinion, we define risk, using dictionary terms, as “the possibility of loss or injury.”

How does one filter opportunities? By eliminating the difficult-to-understand ones? Buffett says that he has three boxes on his desk: “In, Out and Too hard.” So should we.