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Michael Lynch: ‘Peak Oil’ Errors Can Teach Us About Covid Statistics

General Ideas

Back when I was a college student, I went to the movie theater to see the Vietnam-era movie “Go Tell the Spartans,” and one scene struck me: an intelligence office (bespectacled naturally) was explaining to his boss, Burt Lancaster, why he estimated one village to be particularly dangerous, despite the low number of violent incidents there. I shouted, “He’s taking the second derivative!” which led to the other few members of the audience to look at me clearing thinking, “Nerd!” (Yes, I was and am.)

Which brings me to the current pandemic and the statistics that are often presented. The New York Times provides excellent graphics showing daily cases and deaths, along with the moving average. Massachusetts, however, tends to show cumulative cases over time. The latter is not very useful, because I want to know the current status of the pandemic in my area, not the entire history of infections in one number. In other words, I don’t want the number, I want the rate of change, or, even better, the rate of change in the rate of change.

The best way to think of this is to consider distance, speed and acceleration. Distance to a place is useful, but the distance you cover in a unit of time, which is speed, is the first derivative, that is rate of change. The rate of change in the rate of change, or second derivative, is acceleration (or if negative, deceleration). What the intelligence officer was trying to show to Burt Lancaster was the acceleration in violent incidents.

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The geologists who started the recent round of peak oil concerns failed to understand this. (The chapter in my book discussing this is titled, “Get thee to a statistics class.”) One in particular published graphs showing cumulative discoveries and cumulate production, marveling at how closely they resembled each other and treated it as predictive of production. But any intro class in statistics will tell you that this is an invalid approach, yielding minimal if any information. I can easily tell you that next year’s GDP will almost always be close to this year’s GDP; no one says GDP next year will be $21 trillion, they talk about the growth rate, that is, the first derivative.

This can be easily demonstrated with some oil industry statistics. The figure below shows cumulative oil production in the United Kingdom, and it looks impressive: nice smooth growth over time, and one is tempted to extrapolate the line into the future. A curve of cumulative discoveries would look very similar, which led some peak oilers to think they could use discovery data to predict production, just by shifting the curve the right the appropriate number of years.

But the use of cumulative numbers means that the scaling is very large: 30 billion barrels on the Y-axis, which dwarfs annual data and, even more, annual changes in the trend. Most graphs of cumulative data look similar, growth that turns into a rising slope, and cumulative Tootsie Roll sales would look like oil discoveries, if cumulated over a lengthy period.

The next figure shows annual production for the U.K., which fluctuates quite a bit, fluctuations that are hidden by the use of cumulative data. Viewing the first graph above, it is hard to see the dip in the late 1980s or the acceleration in the mid-1990s. The second figure below shows the annual change, which provides much more information about the direction of production.

That the peak oil arguments gained such headway despite reflecting some very basic analytical errors goes a long way towards demonstrating the superficial way so much writing and punditry looks at research. Every time I see a local news show discuss health research involving a few dozen people and some insignificant factor like the dietary effect of eating while standing instead of sitting, I am reminded that not only do most in the media have a poor understanding of statistics and research, but so does much of the public. The flood of stories about medical research, often contradictory, tends to confuse the public and is one factor behind the skepticism towards expert opinion.

Of course, it is rarely the experts who are wrong but the presentation of their results in the popular media, which is driven, in part, by public interest. The book The Rock from Mars describes how NASA scientists describe the geology of a meteorite that originated from Mars and resembled, in a superficial way, organic processes. This was immediately hailed as evidence of life on Mars, which was not what the scientists had claimed. Little surprise that “LIFE ON MARS” headlines got a lot more attention than “INTERESTING GEOLOGY OF METEORITE” ever would have.

So, although the Commonwealth of Massachusetts does an excellent job of collecting pandemic data, I would prefer that their presentation of it, especially at the county level, would show daily changes rather than cumulative. (Yes, I know it’s more work they don’t need at this time.)


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