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The Worldly Philosophers
The desire for safety lies over and against every great and noble enterprise.
Any politician would prefer a dead body to a frightened voter.
—John Dunster, UK Health and Safety ExecutiveWikipedia[1]:75

A risk is a situation where the outcome is uncertain, more specifically carrying some chance of loss or injury.

In many of life's situations, the possibilities of benefit include some risk, such as investing in a business or trusting another person. 'Risk management' is the science of minimizing the risk inherent in a given endeavor. Colloquially, 'risky behavior' means activities that are perceived as having a high risk-to-benefit ratio, especially if the risks can easily be reduced by simple means. The application of risk analysis spans several broad fields, including economics, medicine, the environment, and engineering. Because of the economic, health, policy and consequent regulatory aspects of risk analysis, there are frequently political implications. Parts of game theory study the risk versus reward aspect of artificial and real-life situations.

When analyzing risk, it is important to consider both the type of risk (e.g. death, specific diseases, economic loss), and the target population (e.g., local residents, workers, national population, world population, or biodiversity). The risk calculation is likely to be different depending on which type and population one considers, and oftentimes one wishes to consider multiple risk combinations.[1]:9-49 Because of a variety of factors, public perception of risk can diverge substantially from the reality of risk.[1]:75-89 For example catastrophic airplane crashes garner a lot publicity, but individual auto fatalities usually don't, but commercial airplane travel is substantially safer than automobile travel on a per-mile basis.[2]

Absolute risk[edit]

In its simplest form, absolute risk (R) can be expressed as the ratio of the expected affected population divided by the total population. A more accurate assessment of risk takes into account time (t), benefits (B) and cost (C) and standardizes them on to a common scale (using factors α, β, and γ:[1]:94

α(B, t) B(t) - β(C, t) C(t) - γ(R, t) R(t)

A further refinement can then be made to reflect that benefits in the near term are usually more valuable than those in the long term, just as risk in the distant future are less concerning than those in the present. The adjustment is made to what is called the Net Present Value (NPV):[1]:94

NPV = Σ D(t) {α(B, t) B(t) - β(C, t) C(t) - γ(R, t) R(t)}

where D(t) is a discounting function. For economists, D(t) is usually equal to 1/(1 + r)2, where r is the discount rate.[1]:94

For shorter-term adjustments for the NPV, such as in banking or business, the discount rate is usually set at around the estimated inflation rate for the time period in question.[3] Interest rates should not be relied upon for long-term risk assessments "because interest rates and expectedreturns are not observed for the requisite long horizons."[4]

For long-term adjustments for the NPV, setting the discount rate can be problematic and highly consequential, particularly for risks that involve potential catastrophic events such as nuclear waste disposal[1]:94-95 or climate change. Setting the discount rate too low for long-term risks, particularly for climate change, can result in dramatically larger negative externalities for future generations.[5][6]:26 The sensitivity of the discount rate for long-term catastrophic risks explains at least in part how Exxon simultaneously knew about and internally took action against the costs of global warming while simultaneously participating in a public denialist/coverup campaign for decades to prolong its profits.[7][8][9]

Relative risk[edit]

The group exposed to treatment (left) has half the risk (RR = 4/8 = 0.5) of an adverse outcome (black) compared to the unexposed group (right).

Relative risk is the ratio of the risk risk associated with one activity over another (often expressed as a percentage) — such as "going for a drive" compared to "doing nothing". It is the most common value quoted in the media due to the virtue of it being inevitably the largest and most dramatic value available. Although scientists usually report it as a ratio of probabilities, results are commonly discussed as percentages. On its own, the relative risk of an activity or medical intervention is essentially meaningless, it must be used in conjunction with absolute figures — a 100% increase may sound dramatic, but it can be put in context by saying this is a change from 1 in 100,000 to 2 in 100,000. Furthermore, the reference category matters. A 100% change with one reference group sounds much more impressive than the 50% reduction if the two groups were reversed. To make the value even higher, the popular press usually quote the risk relative to doing nothing, as doing nothing is sometimes erroneously perceived to be risk free while doing anything at all will change it.


The use and misuse of 'relative risk', is best shown with an example — and there are plenty to chose from. For example, one of the many, many headlines that appear on almost every issue of the Daily Mail. Based on a British Medical Journal article,[10] the Daily Mail headline initially screamed, "How pills for your headache could kill",[11] but was subsequently moderated to "Ibuprofen can raise risk of heart attack".[12] The article itself initially contained the statement, "British research revealed that patients taking ibuprofen to treat arthritis face a 24% increased risk of suffering a heart attack."[11] but was subsequently modified to "The results showed the risk of heart attack increased by 24 per cent in those taking ibuprofen and by 55 per cent in those on diclofenac."[12]

In context, this headline refers to the use of ibuprofen and other painkilling pills, and the increased risks of heart attacks observed (specifically in men over the age of 50, but they usually neglect this fact too). 24% seems like a very dramatic result. Indeed, the headline alone indicates that you should stop using these painkillers if you want to even survive! However, the risk increase quoted is meaningless without the context of the absolute risks. The study in question had further limitations since it was just a single study, the author herself called the findings 'suggestive', and that confounding factors could not be fully corrected for.[10]

In terms of absolute risk and the natural frequencies (the most meaningful real-world numbers, rather than more abstract percentages), the risk of a heart attack may start as only about 10 in 1000 for all individuals.[13] This is 1%, so while it's likely that you'll not have a heart attack, it's not completely impossible. The risk of a heart attack is very fluxional and there are much higher and lower risk groups based around age, lifestyle and general health. A relative increase of 24% would raise this to 1.24%, in terms of real numbers this is about 12-13 heart attacks per 1000 people, an increase of just 2 per 1000 (a risk difference). And the study shows that this is only for intensive users of the drug. So out of 1000 people who are taking intensive doses of pills, we would expect two extra deaths on top of the ten that happen anyway.

Although this increase is significant, it is far more meaningful and far less scaremongering than the relative risk of 24% that was originally given. The causes behind heart attacks are complex and mostly related to general health (levels of exercise, smoking and drinking habits, quality of diet). There will always be a risk associated with medical treatments but these must be weighed using real numbers, not meaningless percentages designed to look large and impressive.

See also[edit]


  1. 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Risk/Benefit Analysis by Richard Wilson and Edmund Crouch (1982) Ballinger Publishing Company. ISBN 0884106675.
  2. Here's Why Flying Is the Safest Mode of Transportation by Elizabeth Preske (August 12, 2017) Travel + Leisure.
  3. NPV and Inflation Xplaind.
  4. The Rising Cost of Climate Change: Evidence from the Bond Market by Michael D. Bauer & Glenn D. Rudebusch (July 2020) Federal Reserve Bank of San Francisco. Working Paper 2020-25. doi:10.24148/wp2020-25.
  5. The Economics of Climate Change: A Primer by Jan Hatzius et al. (19 January 2020 | 5:25PM EST) Goldman Sachs.
  6. The Economics of Global Climate Change by Jonathan M. Harris & Anne-Marie Codur (2004) Global Development And Environment Institute, Tufts University.
  7. The Climate Deception Dossiers (July 9, 2015 update) Union of Concerned Scientists.
  8. Deception Dossiers: All Documents Union of Concerned Scientists.
  9. Factsheet: Heritage Foundation ExxonSecrets.org (archived from June 7, 2019).
  10. 10.0 10.1 Risk of myocardial infarction in patients taking cyclo-oxygenase-2 inhibitors or conventional non-steroidal anti-inflammatory drugs: population based nested case-control analysis by Julia Hippisley-Cox (2005) The British Medical Journal 330:1366. doi:10.1136/bmj.330.7504.1366.
  11. 11.0 11.1 Risky Business by Ben Goldacre (June 20, 2005) Bad Science.
  12. 12.0 12.1 Ibuprofen can raise risk of heart attack by Jenny Hope (Last updated at 09:50 10 June 2005) Daily Mail.
  13. Alcohol Use And Alcohol Use Disorders In The United States: Main Findings From The 2001–2002 National Epidemiologic Survey On Alcohol And Related Conditions (NESARC) U.S. Alcohol Epidemiologic Data Reference Manual Volume 8, Number 1. (January 2006) National Institute on Alcohol Abuse and Alcoholism. Table 2-1. Rate per 1,000 population of selected past-year health conditions, by sex and age group, according to drinking status1 in the past year, United States, 2001–2002.]