Without evidence of benefit, an intervention should not be presumed to be beneficial or safe.

- Rogue Medic

Ambulance Crash ‘Caused by’ Overtime?


 

Was this crash caused by paramedics working an extra shift, or two, or three, or . . . ?

Does management’s math work (as reported)? Does management’s math (as reported) suggest that management does not understand math (or that a mistake was made reporting the story)?
 

HONOLULU (HawaiiNewsNow) – An ambulance crash at Ala Moana Center involved overworked paramedics on overtime.[1]

 

A paramedic on overtime? Oh, no! In many places, it seems that paramedics (who get paid more than basic EMTs) have to work more than one job to just be able to live paycheck to paycheck. Part of the problem is that we humans spend money unwisely (as a species, we are horrible at money management). Part of the problem is that EMS often does not pay well. If pay is low, people will work other jobs – or they will not be able to continue to pay their bills and complications ensue.

Here is the math problem.
 

The city wants to reduce chronic vacancies which lead to back-to-back shifts by changing the length of the shift from eight to 12 hours. The move would mean the city’s 22 ambulances could be run with one-third less staff each day, allowing other medics to have much-needed time off, but sources said the United Public Workers union is holding up the negotiations.[1]

 

If shifts are changed from 8 hours to 12 hours, there will be one third fewer shift changes, but that should not affect the number of calls the ambulances run. If the ambulances are not currently busy, changing the schedules might reduce the amount of time crews are not on calls, but so would cutting shifts. That does not seem to be an option, so this appears to be a bit of bad math that nobody in management has corrected.

If I work six 8 hour shifts a week, I am working 48 hours a week.

If I work four 12 hour shifts a week, I am still working 48 hours. I am only cutting the number of shifts in a week, not cutting the hours worked in a week.

If I work nine 8 hour shifts a week, I am working 72 hours a week. If I work six 12 hour shifts a week, I am still working 72 hours.

Should I expect to be any less tired if my shifts are divisible by 12, rather than by 8?

Will the proposed schedule result in fewer ambulances on the street at peak times. Someone will still have to pick up the patients. If ambulances are not currently busy, this could result in treating and transporting the same number of patients with fewer paramedics, but that can also be achieved with 8 hour shifts. Ambulance contracts often mandate that a certain percentage of response times be under X minutes. If management is able to get that to change, that could result in fewer crews on the street, but working much harder, and might be seen as a success by shortsighted management.
 

[youtube]8NPzLBSBzPI[/youtube]
 

We can speed up what we do, but at some point we will increase the rate of errors. This is to be expected and should not be blamed on the employees. Management deserves the blame. The role of management is to help the income producing employees to do their jobs, not to blame the employees for bad management.

I have worked for people who manage this way – and not just in EMS, but we do seem eager to make excuses for bad management.

If management is not capable of competence with simple math (as was reported here), what are their other weaknesses?

If management isn’t able to manage with 8 hour shifts, will Goldilocks come to the rescue when the shifts are 12 hours long?

Footnotes:

[1] First responders hurt in ambulance accident at Ala Moana
Posted: Jul 12, 2014 11:40 PM EDT
Updated: Jul 13, 2014 4:45 AM EDT
Hawaii News Now
Article

.

1 + 1 = 3 Sometimes – Pharmacology Fun

 

Does 1 + 1 always equal 3?

No.

If you do not give all of the medication in a syringe, vial, ampule, you are rounding off. This is where significant figures matter.[1]

1+1 does equal 3 for sufficiently high values of 1.

For those who do not understand this –

Consider a morphine syringe with a volume of 1 ml that contains a total dose of 10 mg.

We intend to give 1 mg.

Can we give exactly 1 mg?

I cannot.

We give an approximation of 1 mg.

What is considered to be 1 mg?
 


 

0.50001 mg should be rounded to 1 mg if we are not using decimal places. We probably do not have the precision to measure that accurately. If we did, we should use all of the significant digits in our documentation.

I am using this as an example to point out that with no decimal places 0.50001 mg is 1 mg.

We round off to the nearest significant digit.

If we are not using decimals, then 1.49999 mg is also 1 mg.

We will not be measuring that as carefully, either.

What we will be doing is trying to get close to 1 mg, but that could be 1.4 mg, or 1.3 mg, or 1.2 mg, or 1.1 mg, 0.9 mg, or 0.8 mg, or 0.7 mg, or 0.6 mg, or 0.5 mg.

How precisely can we measure the amount?

If we tend to underestimate the doses we are giving, we could be giving a couple of doses of 1.3 mg.

1.3 + 1.3 = 2.6, which is rounded to 3.

1 + 1 = 3.

If I gave 1.3 mg and 1.3 mg to the same patient, I gave 1 mg + 1 mg and the

1.4 can be rounded off to 1.

If there are no significant digits beyond the 1, then the value of 1 is anywhere from 0.6 to 1.4.

Add a couple of 1s that add up to 2.5, or greater, and you have 3.

1.2 + 1.3 = 2.5, which is rounded to 3.

When rounded to one significant digit, 1.2 = 1, 1.3 = 1, 1.4 = 1, and 2.5 = 3.

That is not what we generally think of when we think of 1 + 1 = 3.

We assume a precision that may not be there.
 


 

Error bars do not always result in excess.

We can end up with a small number due to wide error bars.

1+1 can equal 1 for sufficiently low values of 1.
 


 

So,

      how

            accurate

                  are

                        we?

Footnotes:

[1] Significant figures
Wikipedia
Article

.

Creation Mathematicians Demand Equal Time for Biblical Pi in the Classroom

 

Pi – 3.14159 . . . . is infinitely long.

Has anyone ever seen a number that long.

Pi is irrational.

Let the kids decide for themselves.

Teach the controversy!

This is in the Bible twice. The third time makes it true.
 

We should let the students decide - as long as they only use religion to question math and not math to question religion.

We should let the students decide – as long as they only use religion to question math and not math to question religion.


 

23 And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about.[1]

 

2 Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about.[2]

 

30 divided by 10 = 3. Pi = 3. Only a literal interpretation is acceptable.

3.14 . . . is something like half the Number of the Beast. This is clearly Satan’s work – or half of satan’s work.

Education controversy expert Michelle Bachmann had this to say about promoting the Bible in math classrooms.
 

“I support Biblical Pi,” Bachmann told reporters in New Orleans following her speech to the Republican Leadership Conference. “What I support is putting all math on the table and then letting students decide. I don’t think it’s a good idea for government to come down on one side of math issue or another, when there is reasonable doubt on both sides.”[3]

 

We can’t have students questioning received wisdom.

If we allow that, the next thing we know, they might be actually measuring the diameter of a circle and comparing that with the circumference and deciding for themselves.

Students need to just memorize and recite information.

Questioning authority is bad, unless the authority is teaching something I don’t like.

Footnotes:

[1] Bible
1 Kings 7:23 – King James Version (KJV)
Passage

[1] Bible
2 Chronicles 4:2 – King James Version (KJV)
Passage

[3] Bachmann: Schools should teach intelligent design
June 17th, 2011
06:52 PM ET
CNN Political Reporter Peter Hamby
Article

Here is the original Bachmann quote (the quotes from 1 Kings and 2 Chronicles are real and have not been altered) –

“I support intelligent design,” Bachmann told reporters in New Orleans following her speech to the Republican Leadership Conference. “What I support is putting all science on the table and then letting students decide. I don’t think it’s a good idea for government to come down on one side of scientific issue or another, when there is reasonable doubt on both sides.”.”

 

Intelligent Design is just the fraud of trying to create a legal loophole to get around the law.

Is Biblical Creationism (Intelligent Design) any less silly than Biblical Pi?

.

Definitely Certain


ResearchBlogging.org

Also posted over at Research Blogging. Go check out the rest of the research blogging there.

This study was looking at the use of MDCT (MultiDetector Computed Tomography) scanners to assess for the presence of appendicitis in patients with a physical exam/history suggestive of appendicitis (as the study’s title suggests). It provides an interesting look at how good the self-assessments were of the accuracy of the scans.

Definitely positive = 556/567 or 98% positive.

Claiming to be definitely right and being right 98% of the time is pretty accurate. Still, it is not 100%, which is what definitely suggests.

Probably positive = 85/103 or 83% positive.

Equivocally positive = 24/38 or 63% positive.

Equivocally negative = 25/27 or 93% negative.

Probably negative = 170/174 or 98% negative.

Definitely negative = 1958/1962 or 99.8% negative.

Too often we will look at just the rare, but well publicized error. We ignore what may be an otherwise overwhelming history of accuracy. We are frequently far less accurate in our assessment than those we condemn.

If we do not measure what we are doing, we probably will be wildly inaccurate in our estimation of our performance.

Patient selection was performed without knowledge of subsequent clinical, surgical, or pathology findings after MDCT. No patient was excluded for suboptimal MDCT evaluation.[1]

The total number of equivocal (positive and negative) interpretations was 65.

That is 65/2871 or just over 2% of the total were equivocal interpretations and none were excluded due to low quality. In other words, there was no weasel factor.

It is noteworthy that the preoperative MDCT interpretation was true-negative in nearly one half of the clinically suspected cases in our series for which pathology findings were negative at appendectomy, outnumbering false-negative MDCT findings by 26 to 10. If surgery had been avoided in all 26 cases, the rate of negative findings at appendectomy would have decreased from about 8% to 4%.[1]

Paying attention to the interpretation would have cut the unnecessary surgery rate in half, but we do not know what the outcome would have been for the 10 patients with appendicitis, but negative interpretations.

In examining EMS interventions, we need to take assess our ability to identify what we are treating in a similarly thorough manner.

Do we use smaller doses when we are less confident in our assessments?

Do we reassess more frequently when we are less confident in our assessments?

Do we look for more definite indications when we are less confident in our assessments?

If not, why not?

Footnotes:

[1] Diagnostic performance of multidetector computed tomography for suspected acute appendicitis.
Pickhardt PJ, Lawrence EM, Pooler BD, Bruce RJ.
Ann Intern Med. 2011 Jun 21;154(12):789-96.
PMID: 21690593 [PubMed – in process]

Pickhardt PJ, Lawrence EM, Pooler BD, & Bruce RJ (2011). Diagnostic performance of multidetector computed tomography for suspected acute appendicitis. Annals of internal medicine, 154 (12), 789-96 PMID: 21690593

.

Mathematically Annoying Advertising

xkcd 870 explains a bit of the problem of trying to get people to understand how bias misleads us in research.

The mouse-over text reads –

I remember the exact moment in my childhood when I realized, while reading a flyer, that nobody would even spend money solely to tell me they wanted to give me something for nothing. It’s a much more vivid memory than the (related) parental Santa talk.

Of course this study, that only superficially addresses the question, is the final word on ________. After all, it confirms my beliefs.

Of course some stranger has decided to set up a business to give me something for free. After all, I’m a unique and special snowflake.

If you are not able to tell if I am using sarcasm, then consider that the subtitle for xkcd is – A webcomic of romance, sarcasm, math, and language.

.

More Examples of Errors Due to Confirmation Bias

The government is often a great source of logical fallacies, since politicians pander to the biases of the electorate. Here is one example.

“The increases in youth drug use reflected in the Monitoring the Future Study are disappointing,” said Gil Kerlikowske, director of the White House Office of National Drug Control Policy. “Mixed messages about drug legalization, particularly marijuana, may be to blame. Such messages certainly don’t help parents who are trying to prevent kids from using drugs.[1]

If mixed messages (as opposed to chanting the party line?) are the explanation, or a large part of the explanation, then marijuana use should be increasing faster than the use of other drugs measured.

The MTF survey also showed a significant increase in the reported use of MDMA, or Ecstasy, with 2.4 percent of eighth-graders citing past-year use, compared to 1.3 percent in 2009. Similarly, past-year MDMA use among 10th-graders increased from 3.7 percent to 4.7 percent in 2010.[1]

What were the changes in the rates of marijuana use?

Most measures of marijuana use increased among eighth-graders, and daily marijuana use increased significantly among all three grades. The 2010 use rates were 6.1 percent of high school seniors, 3.3 percent of 10th -graders, and 1.2 percent of eighth-graders compared to 2009 rates of 5.2 percent, 2.8 percent, and 1.0 percent, respectively.[1]

Notice the data are comparing daily use with past year use. This is not a useful way to look at data. Probably the most relevant number to look at, if we are interested in the effect of anything, is past 30 day use. The daily user is not likely to alter his behavior because of much and the same is true for someone who only rarely uses a drug. Those using more frequently are the ones we are most interested in discouraging from increasing their use to daily use.

If we look at these data, what can we conclude?


Green = Marijuana use 2009
Purple = Marijuana use 2010
Orange = Ecstasy use 2009
Maroon = Ecstasy use 2010

The year to year increase is small. The year to year increase of marijuana is not much more than the year to year increase of ecstasy. Are there Mixed messages about drug legalization affecting ecstasy that might explain this?

Not that I am aware of, but if there are, please let me know.

What explains the increase in ecstasy use if the increase in marijuana use is significantly due to Mixed messages about drug legalization? If the effect of Mixed messages about drug legalization are insignificant, why mention this?

Because it confirms the bias of the people selling this idea. The War on Drugs is tens of billions of dollars of our money each year. That is a strong incentive to keep us hooked on our addiction to the War on Drugs.

As long as we are keeping kids from getting hooked on drugs, getting them hooked on lies may not be a bad trade off.

Did you notice that the quote only mentioned use of ecstasy in the 8th grade and 10th grade? Why not mention the 12th grade?

Because the use of ecstasy in the 12th grade decreased and not by just a tiny percentage of use.

Maybe if we look at the rate of change, things will show that there has been a greater change with marijuana this year than there was last year. This could be evidence of Mixed messages about drug legalization.


Green = Marijuana increase/decrease in use from 2008 to 2009
Purple = Marijuana increase/decrease in use from 2009 to 2010
Orange = Ecstasy increase/decrease in use from 2008 to 2009
Maroon = Ecstasy increase/decrease in use from 2009 to 2010

Let’s look at the percentage changes this year (changes from the 2009 numbers to the 2010 numbers) and compare them with the percentage changes last year (changes from the 2008 numbers to the 2009 numbers).

For 8th grade, the percentage change this year was close to twice as much as the percentage change the previous year. That is significant.

On the other hand, for 10th grade, the percentage change this year was only one third as much as the percentage change the previous year. That is probably also significant, but in the opposite direction.

For the 12th grade, the percentage change this year was only five eights as much as the percentage change the previous year. That is probably not significant, and in the opposite direction, but the reality is that these numbers are not demonstrating any significant trend. The numbers go up. The numbers go down. They go in different directions in the same time period. This is not a pattern. This is confirmation bias, which is just a way of fooling ourselves and fooling others with nonsense.

The ecstasy numbers were also supposed to have increased significantly. Let’s look at the change in use during the same time periods. Do they show the significant increase that was claimed?

For 8th grade, the percentage change this year was a huge increase. The percentage change the previous year was a decrease. That must be significant.

For 10th grade, the percentage change this year was almost three times as much as the percentage change the previous year. That also must be significant.

For 12th grade, the percentage change this year was negative by over 20% from the previous year. The percentage change the previous year was zero. If that is significant, then what about the other numbers that are significant in the opposite direction?

We are finding patterns that support our biases. We do not appear to be finding data that has any predictive potential.

If anything, this year, there appears to be an unusually large increase in the use of marijuana and ecstasy among 8th grade students; A split on the use among 108th grade students, with the rate of ecstasy use increase rising by 3 times as much, while the rate of marijuana use increase rises by only 1/3 as much; And 128th grade students have a smaller increase in the use of marijuana, but no increase in the use of ecstasy – a large drop in the use of ecstasy.

How should we interpret any of this? If we were to accept the notion that the potential legalization of marijuana is a major influence on the data, and there is no good reason for someone not on the receiving end of money from the War on Drugs to accept that –

Then 8th grade students are much more influenced by the political considerations than 10th grade students.

10th grade students are much more influenced by the political considerations than 12th grade students.

12th grade students – the only ones who might be old enough to vote – are not at all influenced by the political considerations of the potential legalization of marijuana.

Just how high were the people who came up with this interpretation?

Red is 12th grade. Blue is 10th grade. Green is 8th grade.

The perception of regular marijuana use as a great risk has been dropping since about 1990. It is foolish to suggest that efforts to legalize marijuana have produced some sudden change.

The perception of marijuana being easy to obtain rose from about 1990 to 1996, then has dropped down to where it had been. No significant change with efforts to legalize marijuana.

Since the 12th grade students have overwhelmingly considered marijuana easy to obtain for as long as this data has been tracked, what does that say about the effectiveness of those tens of billions of dollars spent every year?

Ineffective. Maybe even counterproductive.

Footnotes:

[1] Teen marijuana use increases, especially among eighth-graders
NIDA’s Monitoring the Future Survey shows increases in Ecstasy use and continued high levels of prescription drug abuse
NIDA
Tuesday, December 14, 2010
NIH News Release

[2] Monitoring The Future
Drug and Alcohol Press Release: Text, Figures, & Tables
Web page with link to PDFs of the various data provided

Free PDF of the data on past 30 day use of all drugs from monitoringthefuture.org

.

More on Drug Calculations

I am making a pun at my own expense. Not More on Drug Calculations, but Moron Drug Calculations.

And I am the moron.

In my last post, Current Drug Shortages, I was pointing out ridiculing concerns about the use of 1:1,000 epinephrine IV, since it should never be given through an IV to a live patient, except as a drip. This is true. It is not considered wrong by the FDA (Food and Drug Administration), but that is something the FDA should change.

The problem is with my calculation of the drip rate. I wrote, not just once, that putting 1 mg of epinephrine in 250 ml NS (Normal Saline) would produce a concentration of 4 mg/ml.

I hope that everybody reading this has noticed the mistake I made. You don’t need to be a math whiz to be able to figure out that when you dilute 1 mg/ml by adding 250 ml, you do not get a more concentrated solution. Dilution produces a less concentrated solution.

If the same mistake were being made by a student in an ACLS (Advanced Cardiac Life Support) class, and this mistake has been made plenty of times, I would ask the student some questions, because many of these mistakes cannot be made with the supplies that are in a crash cart or EMS drug bag.

For example, plenty of students have stated that they would give one gram of epinephrine. I have never seen a crash cart or EMS drug bag with even 100 mg of epinephrine. You have to do some restocking to get that much. In the hospital, that means somebody running to the pharmacy to get 1,000 mg. If they state 1:10,000, that means 10 liters, and it is unlikely that the pharmacy carries epinephrine in 1:10,000 concentration in liter containers. 1,000 preloaded syringes of 1:10,000 epinephrine may be more than is available in the pharmacy. Anyway, once I state, A coworker points out that we do not have enough epinephrine to give 1 gram of 1:10,000 epinephrine, the student usually realizes the mistake and corrects the mistake without any further need for hint or for explanation.

I have seen several instructors immediately state that the student killed the patient. I don’t know what kind of dream world these instructors live in, but it appears to be a sadistic one with no grasp on the reality. If the student does not have the capability to actually give 1 gram of epinephrine, then how can the student kill the patient with 1 gram of epinephrine?

I hear the excuse that the student has to learn somehow. This suggests that pointing out the drug calculation is not embarrassing enough to make it memorable. This suggests that a petty and unrealistic comment by an instructor is in some way an example of great teaching. It is not.

However, what I did was much worse than a student making a simple mistake in a stressful moment – a mistake that could not lead to the administration of the wrong dose to the patient. Well, JCAHO might try to make it possible, just so they can penalize people for this.

What I did was tell people that this impossible concentration is the correct concentration.

This is going to mislead and confuse people. It will get others to laugh at me. I should be decreasing confusion, not contributing to confusion. I do not have the same excuse as a student being tested in an ACLS class. I had plenty of time to check everything and in the unreality of the internet anything is possible, right up until it is tried in the real world.

There is one other problem with the drug concentration of 4 mg/ml.

The concentration of 1:10,000 epinephrine is 0.1 mg/ml. I cannot create a concentration of 4 mg/ml, unless I add even more concentrated epinephrine to this 0.1 mg/ml concentration. 4 mg/ml is 40 times more concentrated than 1:10,000 epinephrine.

If you do not understand this, assume that you add 1,000 mg epinephrine to 250 ml NS, you get 4 mg/ml. That works, but only as long as you do not consider the amount of solution that is already included with the epinephrine. For 1:10,000 that means 10 liters of solution with the 1,000 mg, so you do not end up with 4 grams/250 ml or 4 mg/ml. You end up with 1 gram in 10,250 ml or 97.6 mcg (MICROgrams)/ml. Ordinary 1:10,000 epinephrine is 100 mcg/ml (0.1 mg/ml or 100 mcg/ml – not significantly different from what we end up with).

The concentration of 1:1,000 epinephrine is 1 mg/ml. The same concentration problem exists, except that 4 mg/ml is only 4 times more concentrated than 1:1,000 epinephrine.

For 1:1,000, assume that you add 1,000 mg epinephrine to 250 ml NS and you get 4 mg/ml. For 1:1,000 that means 1 liter of solution with the 1,000 mg, so you do not end up with 4 grams/250 ml or 4 mg/ml. You end up with 1 gram in 1,250 ml or 800 mcg (MICROgrams)/ml. Ordinary 1:1,000 epinephrine is 1,000 mcg/ml (1 mg/ml or 1,000 mcg/ml – there is a more significant difference between 800 mcg/ml [0.8 mg/ml] and 1,000 mcg/ml [1 mg/ml]).

Either way, I was suggesting something that is impossible with standard concentrations of epinephrine. It was suggested to me that I was trying to engage in a bit of homeopathy, by pretending that dilution leads to greater strength. 🙁

Dilution does not lead to greater strength.

This is probably the reason that I made this mistake, other than just not thinking, and I wasn’t thinking. We learn the lidocaine clock for calculating concentrations of drips that we use in EMS. Lidocaine commonly comes in a package of 100 mg/10ml for IV push in cardiac arrest. It doesn’t improve outcomes, but that is a different discussion. If you add 100 mg/10ml lidocaine to 250 ml NS, you end up with 100 mg in 260 ml or 3.85 mg/ml. This should also be rounded off to 4 mg/ml, even though it is a much bigger difference from the 4 mg/ml. The reason is that both are not significant differences.

Mixing 1 in 250 will give you a 4/1,000 concentration. Since we can move the decimal (by changing the prefix) to give a 4/1 concentration we need to remember to make sure we are still dealing with the right amounts when we have completed our calculations. Any time we end up with numbers that seem as if they require a lot of drug, or very little drug, we need to consider the possibility, even the likelihood, that we made a decimal point (prefix) error.

Thank you to Matt J for pointing out my huge mistake. I will correct it on the original post, too.

.

What Math Do We Need To Know?

An interesting and very short – less than 3 minutes – presentation from a professor of mathematics about what we should be teaching in math class.

I can’t leave you hanging like that without telling you a little bit about what 2 standard deviations means. But first you should read what he said in, If Arthur Benjamin got an extra minute on stage ….

Now to what 2 standard deviations means. This is easiest if you look at a bell curve. Bell curves only represent normal distribution. You’ve seen this curve before.

Dark blue is less than one standard deviation from the mean. For the normal distribution, this accounts for 68.27 % of the set; while two standard deviations from the mean (medium and dark blue) account for 95.45%; three standard deviations (light, medium, and dark blue) account for 99.73%; and four standard deviations account for 99.994%. The two points of the curve which are one standard deviation from the mean are also the inflection points.[1]

Here is another way of looking at the same information, just rotated to the side


The red circles with tails are the Greek letter Sigma, which is the symbol for standard deviation. The data points (dots) on the left are far too few to produce the smooth curve that appears on the right (which is just the bell curve from above with different colors and flipped on its side, so that the standard deviation bars approximately match). No the numbers on the left are not grades of a class from paramedic school before grading on a curve.

Why is it important to understand the concept of 2 standard deviations?

Anything outside of 2 standard deviations is unlikely. Anything outside of 3 standard deviations is rare.

In the video, he mentions the financial mess. One of the big problems was that bankers were making sub-prime loans that initially were just a tiny part of their business. As long as they remained a tiny part of the business, that was not a problem. Grouped in with an overwhelming number of safer loans, they would not present a huge problem, even if they all failed at once.

Mortgage writers were apparently ignoring the increasing proportion of loans that were sub-prime. They went from between 2 and 3 standard deviations to around 1 standard deviation. now it did not even take a coordinated failure of these loans to cause a huge problem, but the mortgage writers kept acting as if things had not changed. They were making their consistent commission. They were selling the risk to people with even less understanding of statistics. On the other hand, they were selling a risky asset, rather than keeping it as an investment. So, maybe they were not so unaware.

When the problem loans were only a few percent of business, the risk was small. You can see from the bell curve, that only a little of the shaded area is there. As the percent of problem loans increased, the chance of many failing at the same time increased. It was not a question of if, but when.

Things changed. Not a little bit, but a lot. The change was ignored.

We do the same thing in EMS in many ways.

We claim that some risk is small, insignificant.

We do this for many things.

We ignore the accumulation of rare, or just unlikely, risks.

We act surprised when the inevitable happens.

We blame someone else.

Footnotes:

^ 1 Standard Deviation
All of the graphs are from Wikipedia.
Article

.