This week’s topic is probably going to be the shortest I’ve written since starting this BLOG at the start of 2003. I’m not going to get into specifics because they tend to complicate things more than necessary.
As well, I know I’ve covered some of this before, but it keeps coming up. What’s worse is that the clueless keep pontificating about it as though their musings are facts when they’re nothing more than guesses based on intuitive logic.
However, even the densest among us occasionally stumble into something factual—and I can be as dense as the best of them when it comes to topical cluelessness.
But most of the time it’s more a matter of people winding aimlessly through the valley of intuitive logic. And the problem is that it greatly increases the likelihood of them being smacked between their eyes by the two-by-four of counter-intuitive reality.
I’m talking about mathematical “CHANCES,” often called the ODDS of something happening. The topic could be anything: the chances of being assaulted, murdered, killed in an automobile accident, winning a lottery, getting laid, or how many times a professional athlete will say “ya know” during an interview.
But, as stated above, I’m not going into topical specifics, only an explanation of the process, along with some clarifying technical definitions.
First we have to understand that CHANCES, PROBABILITIES, and ODDS are the same things expressed in different ways. But it’s impossible to calculate any of them without first knowing the number of occurrences and the number of potential occurrences.
And even after we do this, we also have to make sure to express the chances as both a one-shot chance and chances over a lifetime. The former may make the chances appear as reasonably safe, but the latter puts them into realistic perspective.
For example, let’s say that last year 10-people were killed while trying to cross a certain intersection and that data show that approximately 28,000 attempt to cross each year.
So we calculate the CHANCES of a fatality at that intersection by dividing the number of potential fatalities (28,000) by the number of actual fatalities (10). The answer is 2,800 and the chances of becoming a pedestrian fatality at that intersection are 1 in 2,800.
Using the same data, we can express the CHANCES as a PROBABILITY by dividing the number of actual fatalities by the number of potential fatalities. And doing so (10 divided by 28,000) results in 0.000357143, which is the decimal probability of being killed trying to cross that intersection.
And by multiplying this by 100, we get a percentage probability of 0.0357%, which when rounded to the nearest one HUNDREDTH, translates to chances of about four ONE HUNDREDS of ONE percent of being killed trying to cross that intersection.
But if we divide 1 by the decimal probability of 0.000357143, we get 2,800, which we earlier described as the CHANCES of being killed while trying to cross that intersection. So, once again, CHANCES and PROBABILITIES are the same things expressed in different terms.
ODDS are technically defined as a ratio of the chances of something NOT happening to the chances of it happening. So if the chances of a fatality at that intersection are 1 in 2,800, the odds against it are 2,799 to 1.
But either way we look at it, on an individual basis, we have a pretty good chance of getting to the other side of that intersection unharmed. So the tendency is for people to wonder what’s the big deal, those 10 people should have been more careful.
And perhaps this is true, but if we express the chances of surviving this intersection as a projection over a lifetime of attempted crossings, it paints a more realistic picture.
If the average life expectancy in the USA during the year for which we’re doing the analysis was 78.6 years, simply divide the one-shot chances (1 in 2,800) by 78.6 years to arrive at the lifetime chances (1 in about 35) of being killed while trying to cross that intersection.
It’s not such a rosy picture after all. Perhaps there is something about this intersection that is inherently dangerous and needs to be fixed.
This methodology applies to virtually every human endeavor involving the taking of chances. Just for emphasis, apply it to the chances of winning the Power Ball.
The chances of winning with one ticket during a single drawing are 1 in 175,223,510. Over a lifetime, though the odds are much better, about 1 in 2.23-MILLION (playing a single ticket, of course.)