Weaver VS World

What are the odds? Seriously...

2008.10.21

What are the odds? Seriously. Nothing like lightning striking your winning PowerBALL ticket in hand while standing on an unmowed patch of four leaf clovers, but pretty cool nonetheless.

It's a regular Monday morning. I am happily hacking away at a demo of Orion NPM monitoring a fleet of Cisco Routers. Skype rings and flashes with an unknown number. I pickup and answer with my standard work greeting, "Hello, this is John." The caller responds, "This is Matt [surname removed] from OfficeDepot, can I speak with Sheila please." I inform the caller, "No Sheila here, think you have the wrong number." "Sorry about that. Well, if you see her please let her know her order has arrived for pickup and thank you for using OfficeDepot."

At this point I am confused. Sheila? Don't know her. OfficeDepot? Never set foot in one.

Not two seconds after the call ended did my eyes dart up and to the left as the visual recall systems were putting together a small puzzle triggered by the name and ineptitude of an OfficeDepot employee.

Ah-ha! I knew him. Worked with him at DataWave six years ago. He was the bumbling Sales Engin... idiot who had difficulties grasping IP addresses and their "use of dots instead of commas." Mind you this was a guy selling re-branded Internet T1's and DSL. I spent fifteen minutes helping him enter data into an Excel spreadsheet only to find out that rows and columns were the same thing "at his school." Hard to forget someone with that level of mastery.

So what are the chances of answering the phone to a legitimately dialed wrong number *and* knowing the person on the other end?

Well? I decided to find out. Make note that what follows cannot be considered accurate. Many assumptions are made. It is an order of magnitude estimate, and a poor one at that. Any correctness should be assumed coincidental and the mathematical equivalent of throwing rocks at a cliff face resulting in an exact replica of one of [King] Richard Petty's personalized belt buckles.

Physics 201 Taught Me Things

Like how many New York Sewer rats would be required to feed the rabid fans at Lambeau Field for four quarters of football. Or how much gas would have to be passed from the asses of those Packer fans and burned in the grilling equipment to prepare the rats for consumption. Needless to say, the system is not a perpetual motion machine in disguise.

How Many Names Can You Recognize?

Back to the task at hand. I'll define knowing the person on the other end to recognizing their name. According to "Contacts and influence." (Direct PDF) and other sources online this number is somewhere between 500 and 5,000 persons with the average around 3,000 depending on the individual.

Number of Calls Made Per Soul Per Time

The latest Federal Communications Commission Trends in Telephone Service from 2005 (latest), table 10.2 lists the combined number of both local and toll calls to be 505,834,870,000. The U.S. Census Bureau reports the population of the U.S. in 2005 to be 295,895,897 souls. (Say goodbye to sig figs right now) This divides to around 4.68 calls made per person per day, 32.8 calls per person per week. Bear in mind that this calculation includes all souls, of all ages. The eleven month old diaper wearing, eating, sleeping, shitting apple of somebody's eye to the eleven hundred month old diaper wearing, eating, sleeping, shitting, living holdup on a will. All chattin' away. Note: Since two parties are involved in a given call, the numbers also correspond to the average number of calls received per soul per time.

Number of Wrong Numbers Received Per Soul Per Time

Seeing as I could find absolutely no research in this field, I had to do it myself. I made calls to people I know and flat out asked them. My sample size is 32... ish. Funny enough, I even dialed a wrong number, which I later found out is in line with my results. Averaging out all of the responses I determined people to receive on average 2.1 wrong numbers per month, which divides (for the month of February anyway) to 0.53 wrong numbers per week, and 0.08 wrong numbers per day. This data sucks on the grounds of insufficient sample size, sample distribution, lack of formal questioning of samples, lack of statistical methods, and an altogether lack of effort.

Putting it all Together

Note: Percentages are used as results below, remember to shift the decimal point for non-percentage representation.

First it is necessary to calculate the chance that a given call will be a wrong number. 0.08 wrong numbers per day divided by 4.68 calls per day gives a 1.7% chance that a given call will be a wrong number.

Next, let us determine the chance that you will *recognize* the name of a person sampled at random from the United States of America. Assuming the average of 3,000 recognizable names and a population of 295,895,897 souls, this gives a 0.001% chance.

Now the chance that a given call will be a wrong number multiplied by the chance that you will recognize the name of a random person from the United States of America gives us a chance of 0.00002%.

Conclusion

• There is a 1.7% chance that your next received call will be a wrong number.
• There is a 0.001% chance that you will recognize the name of the person on the other end of your next received wrong number.
• There is a 0.00002% chance that your next received call will be a wrong number and you will recognize the person on the other end.
• There is a 0.0002% chance that you will be struck by lightning in a given year.
• One in 5,000,000 calls a person receives will result in a received wrong number where the receiving party recognizes the calling party's name.
• At a call rate of 4.68 received calls per day (and 4.68 dialed calls per day) it would take 3,000 years for this event to happen to a given person.
• However, in the grand scheme of daily call volume this happens in the United States of America around three hundred times per day. Around ten times per hour. Once every ten minutes. So it is more common across the populace than it would seem.

Final Thoughts

I am not that special. It is highly probable that I am terrible with probability. In the words of my former roommate, "I just did the math, I'm gonna fail Calc."

-John "What are the odds of Metallica's Death Magnetic rocking your socks off?" Urbanek

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