Stories from 'How Not to be Wrong' by Jordan Ellenberg

    
Borrowed from 'How Not to be Wrong: The Hidden Maths of Everyday Life' by Jordan Ellenberg.

Importance of data versus intelligent analysis

During World War II, numerous fighter planes were getting hit by anti-aircraft guns. Air Force officers wanted to add some protective armor/shield to the planes. The question was "where"? The planes could only support few more kilos of weight. A group of mathematicians and engineers were called for a short consulting project. Fighter planes returning from missions were analyzed for bullet holes per square foot. They found 1.93 bullet holes/sq. foot near the tail of the planes whereas only 1.11 bullet holes/sq. foot close to the engine. The Air Force officers thought that since the tail portion had the greatest density of bullets, that would be the logical location for putting an anti-bullet shield. A mathematician named Abraham Wald said exactly the opposite; more protection is needed where the bullet holes aren't - that is - around the engines. His judgement surprised everyone. He said "We are counting the planes that returned from a mission. Planes with lots of bullet holes in the engine did not return at all."

Debrief

If you go to the recovery room at the hospital, you'll see a lot more people with bullet holes in their legs than people with bullet holes in their chests. That's not because people don't get shot in the chest; it's because the people who get shot in the chest don't recover.

Remember the words of Einstein: "Not everything that counts can be counted, and not everything that can be counted, counts."

The Parable of the Baltimore Stockbroker

Imagine getting a mail from a little known stockbroking firm. The mail predicts that a certain stock will rise this week. You leave the mail aside, as you have seen enough such mails. But the prediction turns out to be right.

Next week

The Baltimore Stockbroker mails again, with another tip-this time, of a stock going south. The message turns out right too and you decide to mark the Baltimore Stockbroker as 'not spam'.

Week Three

Another hit. And your interest is piqued.
This goes on for ten weeks. Ten accurate predictions from the Baltimore Stockbroker.
You, the guy who recently retired with a substantial gratuity in the bank, are hooked.

Week eleven

The Baltimore Stockbroker sends you an offer to invest money with him, for a substantial fee of course. There is the usual caveat of past performances not guaranteeing future success, but the Baltimore Stockbroker nudges you to consider his ten week streak.
You do the math. Every week, the Stockbroker had a 50% chance with his prediction. Either he would be right, or wrong.
Combining the probabilities for ten weeks, the chances of the Baltimore Stockbroker to be right ten weeks in a row work out to... 1/2 x 1/2 x 1/2... ten times... = 1/1024

You consider. The Baltimore Stockbroker must be onto something. And it would be worthwhile to invest your nest egg with him.
You go in for the offer.

Things, from the view of the Baltimore Stockbroker, are a bit different.

What he did, was start out with sending 10,240 newsletters!
Of these, 5120 said a stock would go up, and 5120 said otherwise.
The 5120 who got a dud prediction never heard from the Baltimore Stockbroker again.
Week Two, the Baltimore Stockbroker sent 2560 newsletters, and the following week he again halved the number, based on who got his correct prediction.
This way, at the end of week 10, he had ten people, convinced he was a financial genius.
That's... The power of probabilities, cons, and the impact of mathematics on daily life... Just one aspect!

This is how the Tip Providers work.

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