Some common probabilistic misunderstandings linked to Covid-19
Note: this is a short adaptation of a section of ‘Outlines of a probabilistic evaluation of possible SARS-CoV-2 origins’ by G. Demaneuf and R. De Maistre, https://zenodo.org/record/4067919.
‘BSL-4 labs are very safe. It makes no sense at all to point to a potential leak out of the the Wuhan BSL-4.’
The Wuhan BSL-4 is actually largely irrelevant to the discussion about a possible lab-leak being the origin of Covid-19 outbreak. Indeed most of the work on SARS-Like BatCovs was done at the required level BSL-3 (for cell culture), not at all at BSL-4. It is also worth remembering that China had already done years of work on SARS-like BatCovs even before it opened its BSL-4 in 2017.
So one can basically simply ignore the Wuhan BSL-4 and instead focus on BSL-3s where most of the work one SARS-like viruses was done.
‘BSL-3 labs are very safe. They do not leak.’
BSL-3 labs do leak. In the space of 2 years there were for instance not one but four Lab Acquired Infections (LAI) - some with small outbreaks - in BSL-3 labs working on SARS in China.
The best international stats we have show that assuming a baseline risk of Lab Acquired Infection of 0.2% per year is reasonable in Canadian and US BSL-3 labs when working with this kind of pathogens (doing cell cultures) . Further a 20% chance of outbreak given LAI seems also reasonable for SARS-CoV2. All together, this gives a roughly 0.04% chance of outbreak per year per lab actively working on SARS-like viruses due to an LAI.
Additionally, the 4 SARS LAIs observed in China in 2003–04 would actually point to the fact that such an estimate fell rather short of the actual risk in China at the time.
‘Whatever the LAI risk in China was in 2003–04, the situation has very much improved and the risk of an LAI in a Chinese BSL-3 lab is very small’
First for sure the Chinese risk is no less than the US or Canadian risk, with a reference baseline 0.2% risk of LAI per year for an average BSL-3 lab.
Secondly, unfortunately Chinese authorities and experts have continuously been fighting to reinforce the security of their BSL-3 labs. Some top Chinese experts have continuously denounced the too common lack of maintenance budgets (sometimes inexistent), the lack of personal trained in bio-safety (often part-time), the prestige BSL-3 labs quickly built without coordination and operating procedures, and much more.
As a conclusion, for sure many of the 112 or so BSL-3s labs in China as of Sep 2020 are very well run, but the overall picture still shows local signs of a fairly immature system that needs improving.
‘Since we know that a SARS-like epidemic in China is much more likely to be triggered by a natural encounter with some animal rather than by any lab accident, saying that the recent epidemic may have been caused by a lab accident is simply unscientific and not worth discussing.’
This misunderstanding is often repeated in the current debate [55, 56]. It is true that for China as a whole the risk of a SARS-like community outbreak triggered by a purely random zoonotic event is likely higher than a lab-induced one.
To put these into quick numbers, a typical baseline for Lab-Acquired Infection (LAI) in a US BSL-3 lab is 0.2% per year. So considering less than 10 BSL-3 labs in China working on SARS-like BatCovs and supposing a risk at par with US labs, we would get roughly less than a 2% risk of a SARS-like BatCov LAI in China per year, which would give rise to an even lower risk of community outbreak caused by an uncontained BatCov LAI (given the roughly 20% chance of an outbreak given an LAI). By contrast intuitively the probability of a zoonotic SARS-like outbreak in China is much more than these 2%, as exemplified by SARS (2003) and possibly Covid19 (2019).
However when one consider an outbreak that starts in Wuhan, the relative probabilities totally pivot. Using a lottery analogy, Wuhan bought a large portion of the lab-induced ‘SARS-like community outbreak’ lottery tickets as it has a large chunk of the labs actively working on SARS-like BatCoVs in China (3 labs out of a total of 9 in China is a defensible count), but it purchased less than 1% of the China random zoonotic community outbreak tickets (based on a population rescaling argument).
As a result Wuhan itself is more likely to be holding a ‘winning ticket’ from the lab lottery than from the natural encounter lottery. From this we can see that the relative probabilities (natural vs. lab induced) for a community outbreak in China as a whole do not extend to a community outbreak that actually started in Wuhan — quite the contrary. Hence it is unfortunately misleading to generalize the China odds to the Wuhan odds.
Additionally there is good circumstantial evidence to believe that the 0.2% baseline is very conservative when applied to a highly transmissible coronavirus and to variable lab safety conditions. Indeed it is impossible to explain otherwise how 6 SARS LAIs could have happened in only 2 years (2003–04), with 4 incidents in Chinese labs, if these LAIs were universally governed by such a low baseline probability.
‘If you suppose that a community outbreak happens in China, then by definition it must happen somewhere. So there is no point saying after the fact that there was a small chance that it happened in Wuhan, of all places. It had to happen somewhere and it just happened in Wuhan by chance.’
An easy way to see why this is incorrect is to notice that for the Wuhan community outbreak to be a purely neutral after-the-fact random observation, then the rest of China must look like Wuhan. Hence given that we are considering 3 BSL-3 lab-complexes in Wuhan actively working on coronaviruses and given that Wuhan has 1% of China’s population, this means that the argument would be correct if China had at least 300 BSL-3 lab-complexes actively working on coronaviruses.
Interestingly, if told that 300 lab-complexes were actively working on SARS-like coronaviruses in China, most people at this stage would not intuitively consider the odds of a lab-related origin for a SARS-like community outbreak somewhere in China to be negligible (compared to a purely random zoonotic event) without even needing a more detailed inspection of individual probabilities. But crucially this is exactly the same odds as when considering the probability of an observed first community outbreak in Wuhan with 3 active BSL-3 lab-complexes against a purely random zoonotic community outbreak there.
‘There is still nothing proving that the COVID-19 community outbreak was caused by a lab-related accident, whatever the probabilities. So it makes no sense to talk about a possible lab accident.’
This misunderstanding seems to be surprisingly common in the debate about COVID-19. It is easy to see why it is wrong: there is simply nothing proving that the outbreak is actually a purely random zoonotic event either.
The too-often accompanying assertion that, when considering China as whole, a natural origin SARS-like community outbreak is anyway much more likely than a lab-induced SARS-like community outbreak — so that the probabilities are actually as good as a proof — offers no support at all here since it is based on another misunderstanding (see Misunderstanding #5).
‘There may be very roughly a 1 in 10 year probability for a random SARS-like community outbreak in China but we know that coronaviruses outbreaks are more common (MERS, SARS pig, etc) across the world. We also know that populations living close to bat colonies in China carry antibodies for SARS-like coronaviruses, so this is only the tip of the iceberg and outbreaks involving SARS-like coronaviruses are much more common than that’.
This misunderstanding is based on three possible confusions.
There is first a confusion on the probability of interest, which is the probability of a non-lab related (1) community outbreak of a (2) human (3) SARS-like coronavirus (4) in Wuhan. If we consider the attribute ‘community outbreak’ for instance, there is no point considering a probability based on local non-outbreaks because there is no meaningful way to translate that denser probability distribution into the probability of a proper SARS-like outbreak. These local non-outbreaks are fundamentally different: they are effectively only detected through some antibodies in a small fraction of rural populations living close to bat colonies (2.7% in the study reported in Ning Wang et al , 0.7% in the study reported by Hongying Li et al ) — antibodies which are not only conspicuously absent in the Wuhan population but also suggest that ‘infections were subclinical or caused only mild symptoms’. 
The second confusion is a logical one. Local non-outbreaks in these populations living close to bat colonies, as inferred by antibodies, are by definition local. So one would have to contrive an exclusively directed scenario where someone in such a community got infected with SARS-CoV2 (or a an early strain of it), for some reason remained asymptomatic, did not create a local outbreak but somehow led to an outbreak in Wuhan and nowhere else along the way, and particularly not back home if home that was. This would have to involve some very directed travelling from such a local community to Wuhan. Interestingly the people who do such directed travelling between these communities and Wuhan are quite likely often involved with bat coronavirus studies.
The third confusion is a cognitive confusion between risk awareness and the actual level of risk. Specifically, the knowledge that bat-colonies are natural reservoirs of SARS-like coronaviruses and that some people living close to bat colonies often have antibodies for SARS-like coronaviruses has certainly dramatically increased our awareness of the possible mechanisms of a SARS-CoV-like spillover, but it has not in itself proportionally increased the risk level itself. In the same way (taking a much more extreme example) that our tracking of asteroids over the last 30 years has not increased the risk of the earth being hit by one. What may have much more impact on the actual risk level are the trends governing the intensity of the possible contacts between populations and bats (possibly through an intermediate animal host), land use and the development of transport links.
Most importantly, whatever the theoretical debates, in the end we have only at most two non-lab related occurrences of human SARS-like community outbreaks in China over 16.5 years. Based on the above discussion these 2 events provide the best available signature of the actual outbreak distribution applicable to Wuhan via a rescaling argument based on population proportion (Wuhan vs. China).
Notes & References:
 The following paper compares the bat CoV antibodies in 218 residents from four villages in Jinning County, Yunnan province, located 1.1 to 6 km from bat caves with a control group made of 240 people living in Wuhan. 6 residents in Jinning returned a positive test for Bat CoV antibodies, none in Wuhan. Ning Wang: Shi-Yue Li, Xing-Lou Yang, Hui-Min Huang, Yu-Ji Zhang, Hua Guo, Chu-Ming Luo, Maureen Miller, Guangjian Zhu, Aleksei A. Chmura, Emily Hagan, Ji-Hua Zhou, Yun-Zhi Zhang, Lin-Fa Wang, Peter Daszak, Zheng-Li Shi. ‘Serological Evidence of Bat SARS-Related Coronavirus Infection in Humans, China’. Jan 2018. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6178078/
 Klotz, Sylvester. “The Consequences of a Lab Escape of a Potential Pandemic Pathogen”. Aug 2014. Available from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4128296/
 Eliza Barclay. ‘Why these scientists still doubt the coronavirus leaked from a Chinese lab’. Apr 2020. Available from: ’https://www.vox.com/2020/4/23/21226484/wuhan-lab-coronavirus-china
 Joe Pompeo. Vanity Fair. “The Discussion Is Basically Over”: Why Scientists Believe the Wuhan-Lab Coronavirus Origin Theory Is Highly Unlikely”. May 2020. Available from: https://www.vanityfair.com/news/2020/05/why-scientists-believe-the-wuhan-lab-coronavirus-origin-theory-is-highly-unlikely
 Hongying Li, Emma Mendelsohn, Chen Zong, Wei Zhang, Emily Hagan, Ning Wang, Shiyue Li, Hong Yan, Huimin Huang, Guangjian Zhu, Noam Ross, Aleksei Chmura, Philip Terry, Mark Fielder, Maureen Miller, Zhengli Shi, Peter Daszak.‘Human-animal interactions and bat coronavirus spillover potential among rural residents in Southern China’. Nov 2019. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7148670/