Main question: Why does a particular highway have roughly the same number of automobile-related deaths every year if a car crash is unexpected and dependent on the actions of individual drivers?
More detail: in Tennessee, they have those electronic signs on the interstate that occasionally show the number of roadway fatalities in the state for the current year and beneath that it will show the previous year. The numbers are almost always close, within a reasonable margin of error and accounting for both slightly more drivers on the road each year fur to population growth.
Having been in a serious car crash, I understand the seemingly arbitrary way a sequence of events can play out depending on multiple factors such as driver awareness, vehicular dependency, roadway conditions, weather, etc. Even a highly skilled and fully focused driver in a perfectly functional car on a road with no issues can be involved in a crash, say due to a different driver’s condition, a deer running out into the road, or a sudden gust of wind blowing a newspaper onto their windshield and obscuring their vision for a few seconds.
This may by a multi-part question, but it’s been in the back of my mind for years now and I woke up today wondering about radioactive decay so I started reading about isotope decay. That’s not really what this question is about though, but the seemingly random probability of an isotope decaying in an independent manner (not related to the actions of any other isotopes nearby) made me kind of connect these two ideas and start to wonder about it again.
So getting back to the roadway fatalities, in this case for the state of Tennessee, I found the 20 year statistical data at the site linked below. It shows some ups and downs over the years, presumably with the reductions coming from improved safety features in cars, yet the total number for 2020 (1,221) is closer to the total for 2001 (1,251) than it is to the total for even the previous year 2019 (1,148).
So despite population growth and enhanced safety features, we are kind of right back where we started, or rather, where we’ve always been.
I could also expand this question to cover other events that should ideally never occur, such as murder. Why does something as abominable and world-shattering like murder, at least from an individual perspective, happen with roughly the same frequency and rate when looking at a large sample size? Shouldn’t something like that be the exception and not the norm? Is it somehow related to density?
This has me wondering about probability, fate, design, and all sorts of things both rational and irrational.
Anyway, thanks for reading this. Even if nobody responds, I think it’s helped to just get it out in writing for the next time I think about this in a few months.
TLDR: Why do independent actions and events that deviate from the norm happen with almost certain predictability?
In: Mathematics
The key point that you aren’t getting, which is obvious from your tldr, is that these events aren’t random in the way you think they are.
It’s also the key behind using statistical methods to predict much larger populations, like using a sample of 1,300 people to reasonably accurately reflect the opinions of a pool of voters that’s more like 180 million or something.
Let’s take your example of road fatalities in Tennessee. Tennessee has millions of people driving on the roads. They drive, in total, about 55 billion vehicle-miles a year. The roads in Tennessee are not changing very quickly. The driving habits of the people in Tennessee aren’t changing very quickly. The weather in Tennessee isn’t changing very quickly. The safety features of the cars in Tennessee aren’t changing very quickly. So why wouldn’t you expect there to be almost exactly the same number of bad things happening every year?
You are correct that any given accident can be interpreted as the end result of a long sequence of events, some of which are relatively rare. But I think you’re fundamentally underestimating how many of those possible events there are. This isn’t a problem with you. Human beings are extremely bad at dealing with very big numbers. But that’s what’s going on. Whether a specific person gets in a car accident can’t be predicted with a high degree of certainty (although I’m sure you would agree that a given person getting in an accident is much more likely if the roads are icy, even if that’s all you know). But how many people over an entire state, in an entire year, getting car accidents is pretty easy to predict based on the history because of all the things that don’t change much from year to year.
Let me give you an example that might help. The odds of dealing a royal flush in poker are about 1 in 650,000. This means that if you shuffle your deck randomly and you deal out 650,000 hands, the likelihood that you’ll get at least one royal flush is about 63% (I can explain why it’s not 100%. If you care, but it’s not important to my point here).
If you are a casino and you deal 650 million hands of poker a year, you know you should end up dealing about 630 royal flushes per year. If you end up with a number that’s a lot bigger or a lot smaller, you should get concerned about whether you’re not shuffling fairly or whether somebody’s cheating. Actually, there are specific statistical ways to figure out whether the number you get is so much different from what you expect that something is wrong or different.
How are you able to predict such a rare event with pretty good accuracy? The answer is, there are so many opportunities for it to happen that you end up getting a bunch of rare events. You don’t have to know the exact conditions of how the royal flush was dealt, how the deck was shuffled, etc. to make this prediction. In fact, that’s kind of the whole point.
The bottom line is just that, when you’re talking about 55 billion miles traveled by vehicles, it doesn’t matter that crashes are rare and each crash can be decomposed into a bunch of steps, any one of which might have prevented the crash if it was different. All of those other chances get built in to your observed frequency. Unless something changes in the factors that drive the road fatalities, no pun intended, you’re going to get the same every year.
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