Can Murphy’s Law Be Described Mathematically?

In its simplest form, Murphy’s Law is defined as “Anything that can go wrong, will go wrong.” Even if you have not heard of this profound law, you most likely have experienced its effects. Getting a flat tire, when it is raining, while late for a party. Who else can you blame but Murphy? But then the question arises: Can Murphy’s Law be described mathematically and, therefore, predicted?

The term “Murphy’s Law” originated in 1949 at Edwards Air Force Base, California. The MX981 Project was being conducted in hopes of determining the amount of G-forces a human body could withstand. During the test, a sled traveled down a track at more than 200 miles per hour and then abruptly stopped in less than a second. Sometimes this sled would carry a test dummy, sometimes an actual person. Edward A. Murphy Jr., a captain in the Air Force, developed a set of sensors used during the testing. These sensors, when attached to the safety harness, would measure the amount of G-force applied when the sled was stopped. When a zero reading was measured after the first test, it was discovered that, although there were only two ways to connect each sensor, the technician had installed each one wrong. Frustrated, Murphy said something like, "If there are two ways to do something, and one of those ways will result in disaster, he'll do it that way." Later, the man who rode the sled during the testing, Colonel John Paul Stapp, attributed the tests good safety record to the team’s awareness of Murphy’s Law which he described as being, "Whatever can go wrong, will go wrong." From there, Murphy’s Law became a part of popular culture with books and websites dedicated to its words.

But can it be proven mathematically? A psychologist, a mathematician and an economist (sounds like the start of a bad joke) set out to do just that. Contracted by British Gas, Dr. David Lewis, Philip Obadya and Dr. Keylan Leyser studied 1000 victims of Murphy’s (or Sod’s, as it is known in England) Law and came up with this equation:

Where:

R_SL = Sod’s Law Rating

U = Urgency

C = Complexity

I = Importance

A = Aggravation

S = Skill

F = Frequency

The five main factors that make up this equation, Urgency (U), Complexity (C), Importance (I), Skill (S) and Frequency (F), are set by the individual for each task. These are assigned a number between 0 and 9 with zero being low and nine being high. The value for Aggravation (A) is set at 0.7 based on a poll given to 1000 study participants. The result is Sod’s Law Rating (R_SL ) with higher numbers indicating a greater risk of something going wrong.

What does this equation illustrate? The higher the urgency, complexity, importance, skill required and/or frequency of the task, the more likely something will go wrong. Common sense.

Another equation to predict Murphy’s Law occurrences was developed by Joel Pel, a biological engineer.

Where:

P_M = Murphy’s Probability

K_M = Murphy’s Constant

I = Importance

C = Complexity

U = Urgency

F = Frequency

F_M = Murphy’s Factor

This equation has four main factors, similar to the previous equation. These factors, Importance (I), Complexity (C), Urgency (U), and Frequency (F), are task dependent and range from 1 to 10. The value for Murphy’s Constant (K_M) is set at one. Murphy’s Factor (F_M), as described by the author, is “… a very small number that can only be calculated on a 386-computer running Windows 3.1.” He suggested using F_M~0.01 as an approximation. The result, Murphy’s Probability (P_M), will approach a value of one as the risk of a problem occurring gets higher.

As much as I enjoyed dusting off my seldom used formula writing skills in Microsoft Excel to test this equation, I was disappointed to discover that, for the given parameters, this equation returns only the value one, regardless of the values for the other factors.

Meaning? “Anything that can go wrong, will go wrong.”

References:

https://people.howstuffworks.com/murphys-law1.htm

http://illyria.proboards.com/thread/26788/mathematical-proof-murphys-law

https://www.scq.ubc.ca/the-murphys-law-equation/