A Little Mathematics, Maestro!

(The following is a reprint of a June, 2010 blog post.  Since its arguments are still valid I thought you might enjoy reading or rereading it.) 

In my latest travel book, On The Other Guy’s Dime, I describe one of the more successful techniques I have used to locate working vacations–the cold call.  I would contact a department chair in a city or country where I want to live and say something like “I don’t know you and you don’t know me, but I would love to come to your institution to work for a few months and contribute in any way I can.  Please let me show you why you should hire me.”  I would then attach a copy of my resume, lists of workshops and courses  I could teach, and services I could provide to the school and its faculty.

Classical Dancers in Bhutan. A Cold Call Resulted in a Spectacular Three-Month Working Vacation in Thimphu

Some skeptics will read the previous paragraph and scoff at the idea of cold calls as a way of finding working vacations.  With images of all those struggling telemarketers firmly in mind they will argue you have only a miniscule chance of success.  However, believe me when I say it is nowhere near as futile as they portray.  You are not some nobody shilling aluminum siding or stain remover; we are talking about highly trained professionals–e.g., doctors, nurses, teachers, engineers, lawyers, artists, business people–offering to share their special skills with developing nations that sorely need them.  I could argue for the efficacy of this technique by simply stating that it got my wife and me to Kenya, Turkey, Zimbabwe, Mongolia, and Bhutan.  But, instead, let me show that cold calling is a realistic technique by proving it mathematically!

A few years ago New Yorker ran a cartoon entitled “What Hell Is Really Like.”  There was Satan, with horns and pitchfork, standing over some unfortunate wretch writhing in pain and straining to read the words on a piece of paper.  It said “A train leaves Chicago going 40 miles per hour … ”  While I don’t believe Hell is a never-ending set of algebra problems, I know many of you will smile and sympathize.  Therefore, I tread carefully when presenting a mathematical argument and will try my best not to make this difficult to follow.

Let’s assume there is only 1 chance in 20 (probability p = 0.05) of success, i.e., of getting a “Yes, we would love to have you join us for a few months” response to your cold call.  That means you will get a “No thank you” 19 times out of 20 (p = 0.95).  Furthermore, let’s say you contact four institutions, A, B, C, and D, trying for that one dream offer.

The likelihood that exactly 1 of these 4 places will make an offer is equal to the chance of getting exactly 1 Yes and 3 Nos, which is (0.05) x (0.95) x (0.95) x (0.95) = 0.04287.  Now that single Yes could come from either A, B, C, or D, so the overall probability is four times that number or 4 x 0.04287 = 0.1715, or 17%.

However, the actual odds are even better.  If you are lucky you might get 2 Yeses.  Of course you cannot accept two jobs, but you are free to pick the one that best suits you. There are 6 different ways that 2 institutions could respond Yes:  (A, B), (A, C), (A, D), (B, C), (B, D), and (C, D).  The chance of any one of these events happening is the probability of getting exactly 2 Yeses and 2 Nos, which is (0.05) x (0.05) x (0.95) x (0.95) = 0.0022562.  So, the overall probability is 6 times that value, or 6 x 0.0022562 = 0.0135, or 1.3%.  I won’t go through the mathematics of 3 and 4 Yeses (rare events) but the sum of all these possibilities is the probability that you will receive at least 1 Yes in response to your 4 cold call inquiries. That total is 0.1855, or about 18.6%.

Think about what that last number means. Even if you have only 1 chance in 20 of someone hiring you, simply by contacting 4 schools (or hospitals, labs, government agencies, … ) you have improved your chances of landing a working vacation from 1 in 20 to about 18.6%, almost 1 in 5.  If I told you that spending an hour or so on your computer would result in a 1 in 5 chance of an all-expense paid trip to Turkey or a 3 month no-cost safari in Kenya would you do it?  Of course you would.  Well, why haven’t you!

And you can do even better.  The Web makes it easy to find contact names and addresses at overseas institutions, so why limit yourself to 4?  If, for example, you send out 8 emails, and the probability of a single success is still 1 in 20, your overall odds go up to 1 in 3.  That certainly isn’t the miniscule possibility that skeptics would have you believe.

And, finally, for those who scoff at my assumption of a 1 in 20 chance of success (a value based on my own cold calling experiences), let’s lower it to 1 in 50.  Even with these dismal odds (who would bet on a 50-1 shot at the racetrack?) if you were to send out 8 exploratory emails you would still have a 15% chance of landing a position; send out 15 and the odds rise to 1 in 4–a heck of a lot better than the lottery!   With the universal availability of the Web, word processors, and e-mail, sending out 15 inquiries is probably not even a single day’s labor.

So, for those who have been able to stay with my mathematical arguments this far, I hope you will be motivated to send a few unsolicited emails to those dream destinations–India, Norway, Chile, Austria–described to me in your comments.  Remember, the odds are definitely in your favor!

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One response to “A Little Mathematics, Maestro!

  1. Very smart! And, a useful set of examples – inspiring!

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