The Deceptiveness of Percent Effectiveness
Antimicrobial Product Claims Don’t Mean What You Think They Mean
If you asked most people if a given consumer product advertised as 99.9% effective at reducing microbial contamination (“kills 99.9% of germs” would be a more common wording) does a good job of killing “germs” they would almost certainly say yes. They might even think it does a fantastic job, after all 99.9% is a huge proportion of the germs that might be present. I don’t blame most people for thinking this, and it is true that 99.9% of something is a big chunk of that thing. However, in terms of antimicrobial effectiveness a 99.9% reduction may actually be translated as not effective at all or only barely effective. The same can be said of 99.99% and even 99.999% in some cases. How is this possible?
To understand this requires at least some basic knowledge of microbiology, mathematics (percentages and logarithms), and large numbers. These four topics are not exactly high on the list of most peoples favorite subjects and ignorance of them runs deep. This is exactly why deceptive marketers have stepped in to fill the gap with product claims that sound great on the surface, but on closer inspection, are less than meets the eye. Let’s walk through them each one at a time.
(Author’s note: For simplicities sake in the following discussion by antimicrobial I am referring to antimicrobial for bacteria, and specifically pathogenic bacteria of concern to humans. Similar principles apply for viruses, and they are generally more resistant to antimicrobials than bacteria, but techniques used to measure antimicrobial effectiveness with viruses are different and other technical differences related to growth/replication etc. complicate that discussion. Suffice to say the general message about deceptiveness of claims holds and is even exacerbated in the case of viruses.)
Bacteria grow exponentially. One becomes two, two becomes four, four becomes eight, etc. This is also sometimes referred to logarithmic growth or bacterial doubling (in reality there are multiple phases to bacterial growth lag, log, stationary, and death, but I am ignoring these for sake of simplicity). The upshot of this is that bacterial populations can reach very large numbers very quickly. See link below for more on this.
Three Important Lessons Taught By One Cleverly Designed Thought Experiment
The Problem of Human Overpopulation, Bacterial Population Dynamics, and Our Inability to Comprehend Big Numbers
With doubling times on the order of 20 minutes or less under ideal conditions for pathogens like E. coli O157:H7 or Salmonella huge numbers can be reached very quickly. A million may seem like a big number, and it is but a million bacteria is a drop in the bucket, and that number can easily be found on a tiny patch of your own skin, or on a surface in your home, or in a food you eat or just about anywhere and everywhere. The other important point here is that for some common human pathogens the infectious dose (number of bacteria required to make you sick) is quite low, as low as 1 for some pathogens and more commonly in the 10–1000 range. Keep that in mind as you continue.
Five million is a large number. It is a 5 followed by six zeroes or 5,000,000. Large numbers like this are often written in a different way, 5 x 10⁶ (five times ten to the sixth), which is 5 times 1 million, which is 5 million (5 x 10⁶). In microbiology bacterial populations are almost always written out in this format because they span a very large range of numbers from as low as 1 (1 x 10⁰) to 1000 (1 x 10³) to 100,000 (1 x 10⁵) to one billion (1 x 10⁹) or even higher in some rare cases.
(note: You may also sometimes see these numbers written as for example 5e6. eX means the same as 10 to the X power. I can’t remember actually why this is the case, but I am sure it makes total sense and is not in the least bit confusing or stupid).
In case you were wondering the units we use in microbiology to express bacterial counts are called colony forming units (CFU) and these are most often shown per milliliter or (CFU/ml). Basically the CFU/ml number tells you how many bacteria can be grown and counted on an agar plate out of one milliliter of liquid. No need to delve into the details here and all you need to know for purposes of this discussion is that bacteria counts/populations are typically expressed as CFU/ml and can be very, very large numbers.
A percent of something is 1/100th of that thing. One per cent is one per hundred. Stupid right?
How is a cent a hundred (I guess because a penny is one one hundredth of a dollar) and why does 1/100th of a thing get its own special designation that everyone talks about when 1/10th of a thing or 1/1000th of a thing does not? Great question but it is what it is.
The one and the one hundred can be anything, and I mean anything, solid, liquid, gel, made up fictional entity, anything). For example, 1g in 100ml is 1%, 1 apple in 100 apples is 1%, 1 bacteria in 100 bacteria is 1%, etc. 1Q from Star Trek TNG in 100 Q is 1%. By the same token 50g in 100ml is 50%, as is 50 apples in 100 apples, and 50 bacteria in 100 bacteria. The two things don’t have to be the same either. 50 apples in a mix of 100 apples and oranges is still 50% of the total fruit present. Importantly, it also does not have to be out of a hundred though it is always broken down and expressed as such, 250 apples out of 500 apples is still 50%, 50 out of every 100 is another way you could say the same thing. A percent is essentially just a way of expressing how big a proportion out of one hundred something is. It is also confusing as all get out and really stupid as I already mentioned above. However, for whatever reason, people are “used to” seeing and working with percentages. At least they think they are and for many things like 25% off discounts they work just fine and are fairly straightforward and not deceptive in the least. When it comes to microbiology and large numbers however they can be very misleading.
Lets take the example case of a 99.9% reduction product claim. In this example we will set a starting bacterial population of 5 million which as I discussed above is a not at all that unusual or a particularly large number as far as bacterial populations go. To solve this problem first, we need to determine what is 99.9% of 5,000,000 (5 x 10⁶)?
Get out your calculator and actually plug in the numbers. Type a five than type six zeroes then hit the times button then hit zero then hit the little point button that looks just like a period, then nine three times, 5,000,000 x 0.999 (remember 99.9% is 99.9/100 or 0.999). After hitting the equal button the result will be 4,995,000 (4.995 x 10⁶).
Now what is the difference between 5 x 10⁶ (the number of bacteria we started with) and 4.995 x 10⁶ (the number of bacteria we killed)? That difference represents the number of bacteria still remaining. At first blush you would think that killing that huge a number of bacteria would surely eliminate any potential risk of infection or illness and there must be almost no bacteria remaining alive. However, if you actually do the math
(get out your calculator again and do it. Seriously, it’s way easier that way)
, that number is 5,000 (5 x 10³). There are still 5,000 bacteria remaining even with a 99.9% effective antimicrobial. Remember what I said above in the microbiology section about the infectious dose for many common human pathogens, Five thousand is more than enough to get you sick. What if we do the same math for a 99.99% effective antimicrobial? The situation improves, but not by as much as you might think. In this case there would be 500 bacteria remaining, and even at 99.999% you still would have 50 bacteria remaining (in both cases for some pathogens that is still enough to make you sick).
Good old logarithms. The Eurythmics of math.
I never thought it would be possible to hate a log until I was introduced to logarithms in math class in 7th or 8th grade (I can’t remember which likely because the memories are so traumatic or possibly because I blacked out from boredom and did not wake up again until a grade later.) Does the period go inside or outside of the parentheses? I can never freakin remember that for some reason. Probably because of all those damn logarithms. Stupid logarithms.
In any event, in addition to inducing comas, logarithms can be helpful in understanding percent effectiveness claims and microbiological populations. This is because every log10 (note: this applies to log base 10 only and the little 10 is supposed to be subscript but I cant figure out how to do a subscript in Medium’s text editor so fuck it. There are other log base values possible but for the most part they are useless and stupid and so I ignore them.) change represents a ten fold change in something. A change from 1 to 10 is a one log increase, 1 to 100 a two log increase, 1 to 1000 three logs, etc. and so on. The same applies in the reverse, a change from 1000 to 1 is a three log decrease.
Time to see what you have learned. Nothing? Crap. Oh well I will just go ahead and tell you what you should have learned then by discussing the example above of the 99.9% effectiveness claim.
A change from five million (5,000,000) to five thousand (5,000) is a three log decrease. Were you able to figure that out on your own? No? Congratulations you are a normal person that sucks at logarithms. A 99.9% reduction translates to a three log reduction.
Can you guess how man logs a 99.99% reduction translates to? Maybe you should try calculating or thinking instead of guessing. That usually works better. The answer is four you big dummy.
99.999% is a five log reduction, etc. and so on. At this point, if you are still awake, you might be asking yourself where is all of this heading. It’s heading straight to hell at warp factor seven. Nah. It is actually heading to the following point. Remember what I said way up in the microbiology section, or maybe the large numbers part, I can’t actually remember as it was so long ago. In any event I said something somewhere about bacterial population numbers being large, very large, ranging from 1 to 1 billion or higher. Populations of a million are commonplace. How many logs are there in a million smart guy or gal? Huh? It should be obvious unless you are a dullard that there are six logs in a million. You didn’t get that? Because you are a dullard probably.
Taking three logs out of six logs still leaves three logs (1000) remaining and take my word for it three logs is a lot of logs, plenty of logs to make you sick. It’s so obvious even a PhD in micro and molecular biology like myself can understand it. What’s your problem? Dummy.
And there you have it. I guess. What was I talking about again? Oh yeah, percent effectiveness claims are very misleading. Get it?