Tag Archives: probability

Punxsutawney Phil is worse than a coin flip in predicting the weather

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How well does Punxsutawney Phil predict the duration of winter? Not so well according to one source:

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Phil’s track record is not perfect. “On average, Phil has gotten it right 40% of the time over the past 10 years,” according to the National Centers for Environmental Information, a division of the National Oceanic and Atmospheric Administration, which manages “one of the largest archives of atmospheric, coastal, geophysical, and oceanic research in the world.”

The three-month temperature outlook for February through April 2023 calls for above normal temperatures across the eastern and southern US and below normal temperatures for the northwestern US, according to the Climate Prediction Center…

Despite his mixed record when it comes to actually forecasting the weather, there’s no doubt Phil’s fans still hold him in high regard.

After all, his full title is Punxsutawney Phil, Seer of Seers, Sage of Sages, Prognosticator of Prognosticators, and Weather Prophet Extraordinary.

In other words, Phil is worse than a coin flip in predicting the coming weather. This is not good; any expert would hopefully be better than that.

However, there is some evidence that many expert predictions about the future are not great. How well can people predict the future performance of the stock market or natural disasters or geopolitical change? Not so well. And it is not just that it is difficult to predict the future; we think we can predict the future so it can be even more damaging when projections are wrong.

I suspect very few people care if Punxsutawney Phil is right or wrong. They like the tradition, the ritual, a festive gathering in the middle of winter. Still, Phil offers a window into our own abilities and confidence about knowing the future…and it is a cloudy window at best.

Thinking about probabilistic futures

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When looking to predict the future, one historian of science suggests we need to think probabilistically:

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The central message sent from the history of the future is that it’s not helpful to think about “the Future.” A much more productive strategy is to think about futures; rather than “prediction,” it pays to think probabilistically about a range of potential outcomes and evaluate them against a range of different sources. Technology has a significant role to play here, but it’s critical to bear in mind the lessons from World3 and Limits to Growth about the impact that assumptions have on eventual outcomes. The danger is that modern predictions with an AI imprint are considered more scientific, and hence more likely to be accurate, than those produced by older systems of divination. But the assumptions underpinning the algorithms that forecast criminal activity, or identify potential customer disloyalty, often reflect the expectations of their coders in much the same way as earlier methods of prediction did.

Social scientists have long hoped to contribute to accurate predictions. We want to both better understand what is happening now as well as provide insights into what will come after.

The idea of thinking probabilistically is a key part of the Statistics course I teach each fall semester. We can easily fall into using language that suggests we “prove” things or relationships. This implies certainty and we often think science leads to certainty, laws, and cause and effect. However, when using statistics we are usually making estimates about the population from the samples and information we have in front of us. Instead of “proving” things, we can speak to the likelihood of something happening or the degree to which one variable affects another. Our certainty of these relationships or outcomes might be higher or lower, depending on the information we are working with.

All of this relates to predictions. We can work to improve our current models to better understand current or past conditions but the future involves changes that are harder to know. Like inferential statistics, making predictions involves using certain information we have now to come to conclusions.

The idea of thinking both (1) probabilistically and (2) plural futures can help us understand our limitations in considering the future. In regards to probabilities, we can higher or lower likelihoods regarding our predictions of what will happen. In thinking of plural futures, we can work with multiple options or pathways that may occur. All of this should be accompanied by humility and creativity as it is difficult to predict the future, even with great information today.

Interpreting a 50% chance of rain

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We have had multiple days recently where there is a threat of rain all day. The hourly forecast from yesterday was not unusual:

One of my first thoughts in seeing such a forecast is to say that there is a 50/50 chance of rain. Flip a coin. With this in mind, I would not necessarily stay inside but I would be prepared when going outside.

The idea of a meteorologist flipping a coin when predicting rain is tempting. This could lead to thinking that the meteorologists do not really know so they are just guessing.

However, this is not exactly how this information works. If I look at the hourly forecast and see 0% chance of rain or even anything under 20-30%, I am not going to worry about rain. The probability is low. In contrast, if I see 70% and above I might alter my behavior as the probability is high.

The 50/50 information is still very useful even if it leaves a reader unsure if there will be rain or not. It is not conclusive information but it is not no information or just a guess. With rain at 50%, bring an umbrella, have a coat, or do not stay too far away from shelter but do not just stay inside.

Rare events may happen multiple times due to the law of truly large numbers plus the law of combinations

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Rare events don’t happen all the time but they may still happen multiple times if there are lots of chances for their occurrence:

Improbability Principle tells us that we should not be surprised by coincidences. In fact, we should expect coincidences to happen. One of the key strands of the principle is the law of truly large numbers. This law says that given enough opportunities, we should expect a specified event to happen, no matter how unlikely it may be at each opportunity. Sometimes, though, when there are really many opportunities, it can look as if there are only relatively few. This misperception leads us to grossly underestimate the probability of an event: we think something is incredibly unlikely, when it’s actually very likely, perhaps almost certain…

For another example of how a seemingly improbable event is actually quite probable, let’s look at lotteries. On September 6, 2009, the Bulgarian lottery randomly selected as the winning numbers 4, 15, 23, 24, 35, 42. There is nothing surprising about these numbers. The digits that make up the numbers are all low values—1, 2, 3, 4 or 5—but that is not so unusual. Also, there is a consecutive pair of values, 23 and 24, although this happens far more often than is generally appreciated (if you ask people to randomly choose six numbers from 1 to 49, for example, they choose consecutive pairs less often than pure chance would).

What was surprising was what happened four days later: on September 10, the Bulgarian lottery randomly selected as the winning numbers 4, 15, 23, 24, 35, 42—exactly the same numbers as the previous week. The event caused something of a media storm at the time. “This is happening for the first time in the 52-year history of the lottery. We are absolutely stunned to see such a freak coincidence, but it did happen,” a spokeswoman was quoted as saying in a September 18 Reuters article. Bulgaria’s then sports minister Svilen Neikov ordered an investigation. Could a massive fraud have been perpetrated? Had the previous numbers somehow been copied?

In fact, this rather stunning coincidence was simply another example of the Improbability Principle, in the form of the law of truly large numbers amplified by the law of combinations. First, many lotteries are conducted around the world. Second, they occur time after time, year in and year out. This rapidly adds up to a large number of opportunities for lottery numbers to repeat. And third, the law of combinations comes into effect: each time a lottery result is drawn, it could contain the same numbers as produced in any of the previous draws. In general, as with the birthday situation, if you run a lottery n times, there are n × (n ? 1)/2 pairs of lottery draws that could have a matching string of numbers.

Rare events happening multiple times within a short time also tends to provoke another issue in human reasoning: we tend to develop causal explanations for having multiple rare events. These multiple occurrences can still be random but we want to know a clear reason why they occurred. Having truly random outcomes doesn’t mean outcomes can’t be repeated, just that there is not a pattern to their occurrence.

Fun with statistics: people flock to stores that sold winning lottery tickets in the past

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Ahead of the recent large Powerball jackpot, stores that sold winning tickets in the past experienced an increase in business:

When word got out that a southeast Pennsylvania 7-Eleven sold a $1 million Powerball ticket on Saturday, customers hoping to experience some luck of their own flocked to the store…

At a Casey’s General Store in Bondurant, Iowa, everyone knows it’s the place where a $202.1 million Powerball jackpot ticket was sold to a local woman in September. Asked what types of questions the store gets when the jackpots get huge, assistant manager Debra Fetters said: “Does lightning strike twice here?”…

“When you get those stores where they’ve actually seen someone win, they’re very enthusiastic about it. They know about the game, they have regular customers. A lot of it really does come down to great retailers that support the lottery, understand that there are winners on both sides.”

Linda Hamlin, also of the New Mexico Lottery, noted the story of “Millionaire Mary” Torres of Albuquerque. After she sold a $1 million winning Powerball ticket to an Albuquerque man in May 2011, she became known as a good luck charm. Her customers followed her to another store a few miles away.

And the article ends with this quote:

“Humans tend to be superstitious about things,” said Strutt of the Multi-State Lottery Association. “We all have our ways to ensure our best luck. But every ticket has the exact same chance of winning.”

What would happen if this argument, that their odds of winning do not increase, was presented to these purchasers who go back to the place of past winners? Would they say the numbers aren’t right or say it doesn’t matter? Perhaps this is a sort of Pascal’s Wager for Powerball: it doesn’t increase my odds of winning to shop at this particular location, but it can’t hurt!

This could be chalked up to superstition but it is also the result of humans looking for patterns where there aren’t any. Two things make where the winning person bought the ticket stand out: (1) there are few big winners and (2) the big prizes are noteworthy. Put these two together and all of the sudden people start seeing trends even though there is little data to work with. But, then you have news coverage a few years ago about a woman in Texas who won the lottery four times – four data points make a much better pattern than a one-time winner!