The Fallacy of Forecasting in a Complex World

“Statistical prediction is only valid in sterile laboratory conditions, which suddenly isn’t as useful as it seemed before”- Gary King

I’ve noticed a rising trend in fire and EMS deployment models based on “Predictive analytics,” “Forecasting,” “Statistical analysis,” and the newest term “Near-casting.” Most recently, a “Standards of Coverage” report based on Orange County Fire Authority (OCFA) suggested a deployment model that reduced fire suppression units during the midnight hours based on a low level of fires during the night. When I read these reports I feel like standing up and yelling “that’s not how it works; that’s not how any of this works.”
First of all, the frequency of occurrence does not equal level of risk. In other words, just because an event has never happened does not mean it has a low probability of happening. Consider the case of a snake bite. I have never been bitten by a rattlesnake; therefore my frequency of occurrence is zero. But a frequency of zero when it comes to snake bites tells you nothing about the risk of being bitten. If I stick my hand under a rock with a rattlesnake, my risk of being bitten is very high, regardless of the frequency of occurrence. But this is the exact logic the authors of OCRA’s standard of coverage used when they suggested a deployment model based on the frequency of occurrence.

Studying historical statistics can be incredibly useful when trying to explain what happened. But just identifying a trend in statistical data does not automatically translate into a forecast for the future. Statistics is an explanatory tool, not a predictive tool. If you try to bridge statistical data into a predictive model, you may find yourself drowning in a lake that is on average only 4 feet deep or burning to death in a building that is on average 75 degrees.

Getting burned in building with an average temperature of 75 degrees

Imagine you arrive on the scene of a fire alarm in four story apartment building with two ride-alongs; Blaise and Pierre, both world renowned statisticians. Excitement shows on Blaise and Pierre’s faces once they recognize the address as a building they have studied for years with remote sensors installed in every room. Immediately they open an app on their phone and to access the statistical data on the building.

The fire panel shows a fire alarm on the fourth floor. Your crew grabs its gear and starts for the stairs. Suddenly Pierre protests. Based the data, Pierre claims you should leave the equipment and take the elevator instead of the stairs. “We have all of the data” Pierre yells. “The average temperature in the building is only 75 degrees. We have been monitoring this building for years and based on the statistical trends and we have a 99% confidence there is no fire. A fire in this building is a five sigma event.”

Your crew ignores Pierre and climbs the stairs. Insistent, Pierre follows, continuing to barrage you with terms such as correlation, central limit theorem, interference, and regression analysis.

On the fourth floor, as you open the stairwell door to a smoke-filled hallway, Pierre yells one last protest; “it is a near impossibility a fire will happen, and I fear you lack an understanding of Laplace’s laws.” Just before masking up, you yell back; “yes sir, but I fear you lack an understanding of Murphy’s law.”

Murphy’s Law — “Whatever can happen will happen” — Augustus De Morgan, 1866

The origin of Murphy’s law is uncertain, but its transcendence through our culture is an endorsement of its truth. Although not universally applicable (your car is not going to turn into a turkey), the philosophy of Murphy’s Law has relevance to the emergency management domain; in our ideal world we expect the best, but in the real world we plan for the worst and prepare to be surprised.

The idealist vs the realist

In an ideal world, events happen in an isolated, predictable pattern; all possible variables can be mapped out and weighed against the alternatives, producing precise forecasts.

However, in the real world, events are not isolated, patterns are erratic, and countless variables interact, creating unimaginable events, like life itself. The opposing world views of idealism vs. realism have plagued the domain of probability since it’s origin.

The origins of probability — Gambling 1653 A.D.

A Priori, knowing before the event

In 1653 and young French scholar named Blaise Pascal published “treatise on the arithmetical triangle,” now known as Pascal's triangle. Pascal invented a methodology to predict the result of games by mapping out every possible outcome and comparing it to alternative outcomes.

For example, if I asked the odds of rolling a “3” on a six-sided dice, Pascal’s theory is how we calculate the odds are 1 in 6 since “3” is one alternative to six equally likely options. And if I asked the odds of rolling a “1” or “2” on an eight sided dice, the odds are 2 in 8. The procedure gets exponentially complicated as the variables increase, but the process is still the same.

Pascal’s Triangle based on the roll of two ten sides dice

And although brilliant, Pascal methods were designed for games played in a sterile and controlled environment. Pascal never intended his work to be applied to the real word, as we will see later in his personal life Pascal used an entirely different approach I will call “risk management.”

Bridging the gap — the ideal to the real

A Posteriori — Based on past events

Roughly one hundred years after Pascal, Pierre-Simon Laplace wanted to make predictions in the real world, specifically the movement of celestial bodies. Lacking the exact knowledge of each variable Pascal enjoyed with his games of chance, Laplace substituted historical data for the known variables of the game. In other words, Pascal knew the number of sides on each dice, whereas Laplace’s method guesses at the number of sides on the dice by observing multiple rolls, or rather the frequency of occurrence. But Laplace was not predicting the odds of rolling a “1” on a six-sided dice; he was predicting the odds of the sun rising tomorrow.
Laplace’s work evolved into a complicated domain that requires a measure of confidence in the accuracy of the result based on the quality and size of data, whereas Pascal’s predictions were precisely accurate because he knew all of the variables before the game started.
Laplace is truly a giant amongst scholars, advancing mathematics, statistics, physics, and astronomy. However, his methods can be miss applied and over-leveraged; Standing on the backs of giants comes with the risk of a tragic fall.

Murphy’s law Vs Laplace

Incidentally, Laplace calculated the odds of the sun rising tomorrow based on historical data as 99.999999…..%, which is the most confident prediction one can make based on historical data. However, the aging of the sun guarantees a day when the sun does not rise. Do to Murphy’s law, Laplace’s forecast is at best 99% accurate and one day will be 100% wrong.

The metaphor of forecasting using historical data

Imagine you are driving a car with the windshield blacked out, leaving the rear-view mirror your only means of navigation. The rear-view mirror gives clues to the environment, like the width of the road, depth of the shoulder, the slope of the terrain, and patterns in the road. With a lot of effort and a little intuition, you become an attuned to the picture behind you, allowing you to choose a comfortable speed based on the trends you notice. A simple, straight road with a forgiving shoulder allows for higher speeds, while a complex, turning road causes you to slow down. But you never go faster than your ability to recover if the road conditions change.

Along your travels, you pick up a slightly burned French statistician, Pierre. Your new passenger is surprised at the amount of effort required to keep the car on the road and offers to help. He identifies a “descriptive data sample” that “highly correlates” to the direction of the road, or in laymen’s terms, he says just simply watch the yellow line painted on the road.

Taking Pierre’s advice, you focus on the yellow line, which is much easier than surveying the entire environment. You relax and enjoy the ride, thanking your new friend.

In a hurry to get to his burns checked at a local clinic, Pierre suggests you drive faster based his 99% confidence that the current trends will continue with a small margin of error. The new speed, based solely on forecasts, is beyond your ability to recover if the road should turn dramatically. An instinctive fear creeps over you as the car accelerates and Pierre’s dazzling math surpasses your judgment.

What the finance industry learned about forecasting

A forecasting model, “Value at Risk” (VaR) is widely blamed for the extent of the financial meltdown in 2006. In a nutshell, VaR summarizes a financial firm’s cumulative risk into one metric based on probability; creating an elegant, precise measurement of risk that is deeply flawed. In the words of hedge fund manager David Einhorn, VaR is “potentially catastrophic when its use creates a false sense of security among senior executives.”

A VaR chart showing a 95% probability the portfolio will stay above 42 mil.

VaR’s potential to mislead with forecasts came under such fire that risk manager and scholar Nassim Taleb testified before Congress demanding the banning of VaR from financial institutions. In fact, in an act of intuition, Taleb predicted the damage caused by over-leveraged forecasting models publicly in 1997 claiming that VaR “Ignored 2,500 years of experience in favor of untested models built by non-traders” that “Gave false confidence” since “it is impossible to estimate the the risks of rare events.”

Despite their shortcomings, VaR type forecasting models are in the fire service. Starting with the 1972 RAND report “Deployment Research of the New York City Fire Project,” an impressive display of predictive analytics suggesting the closure of fire stations. “Convinced that their statistical training trumped the experience of veteran fire officers,” RAND spent years building computer models to predict fires and implemented station closures based the analytics. The result was numerous uncontrolled fires and over 600,000 people displaced from burnt homes. FDNY let dazzling math surpasses their judgment.

A scientific study showing the result of cutting the NY fire department, including the spread of tuberculosis and HIV

Forecasting is like a chainsaw, it’s easy to use, hard to use well, and always dangerous.

As cities such as Atlanta and Cincinnati dive into predictive analytics, New York is taking another swing at it with FireCast, “an algorithm that organizes data from five city agencies into approximately 60 risk factors, which are then used to create lists of buildings that are most vulnerable to fire.” Ranking buildings based on vulnerability seems reasonable, but once you start to forecast events in a complex system, challenges arise.

Think of the difficulty of forecasting the winner of game seven in the 2016 world series. Relatively, this is a simple problem; you only have 50 participants playing a defined game for a limited time. Your participants all have plenty of descriptive and predictive data from a relatively sterile environment. Yet the outcome of the game was largely unknown until the end.

Contrast the simple baseball problem to forecasting the complex behavior of a city with one million residents over a limitless time frame. We have taken a model stretched to its limits with a simple system and tried to expand it beyond imagination to fit a complex system.

Complex systems vs simple systems

Probability works, forecasting works — in the right domain, simple systems. The Cynefin framework defines simple systems as the “known knowns.” Like the baseball game, simple systems are stable with identifiable, repeatable, and predictable causes and effects, such as predicting mileage on a fire engine over the next five years. In simple systems, you study the history, forecast the future, and plan.

Opposed to complex systems, in which cause and effect are only detectible in hind-sight. These systems are inheritably unpredictability due to the massive numbers of variables and influences. This is where Murphy’s Law comes from. Simple systems are easy to dissect and understand, but Complex systems “are impervious to a reductionist, take-it-apart-and-see-how-it-works approach because your very actions change the situation in unpredictable ways.” In complex systems probability is limited, forecasting creates a false sense of confidence, and Murphy’s Law reigns true.

Cities are complex systems. Human behavior is a complex system. Fires starting in cities driven by human behavior is exponentially complex. Be very skeptical of anyone with a mathematical model claiming to forecast the future of a complex system who can’t confidently forecast the winner of the next Super Bowl.

“All models are wrong; some are useful.” — George Box

Probability is a brilliant methodology originally designed for sterile games of chance, evolving into a dazzling mathematical domain. Probability works in the proper context, but can produce deadly results if it is overleveraged. In the words of author Charles Wheelan, “Probability doesn’t make mistakes; people using probability make mistakes.” The finance industry and the fire service has been burned by over-leveraged forecasting models. The math is amazing, the results are elegant, but the consequences are catastrophic if they are applied to the wrong domain. Don’t let the math surpass your wisdom.

Epilog — Pascal’s wager

Pascal, the father of probability understood the limitations of his methodology in real life. When asked to bet on God’s existence, Pascal did not consider the probability, odds, or evidence of god’s existence. Pascal considered the consequences of being wrong, and just choose the least consequential option. Pascal concluded accepting god’s existence and being wrong had no consequences greater than the alternative. But denying god’s existence and being wrong came with massive consequences, including an eternity burning in hell.

Pascals wager

Pascal, the father of probability, claims when a rational person is dealing with an unknown, they should consider the consequences, not the odds. Evidence suggest Pascal understood Murphy’s law and was a true risk manager.

Eric Saylors teaches courses on this topic for Elite Command Training

And can be followed on Twitter at @saylorssays

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