Regression to the Mean
Why is the world going to hell, Harold?
It seems a right of passage for people of a certain age–typically over 40–to look around them and ask certain questions:
“What’s with kids these days?”
“Why aren’t things like they used to be?”
“Why is no one moral anymore?”
“Does NO ONE have any work ethic?”
This isn’t exaclty, new. Listen to this modern voice:
The children now love luxury; they have bad manners, contempt for authority; they show disrespect for elders and love chatter in place of exercise. Children are now tyrants, not the servants of their households. They no longer rise when elders enter the room. They contradict their parents, chatter before company, gobble up dainties at the table, cross their legs, and tyrannize their teachers.
That sage of modernity? Socrates, (470-399 BC). Only 2400 or so years ago.
So, it seems of the same tenor to posit: “Why is the world going to Hell?”
From my historical perspective: It’s simply Regression Towards the Mean
What is that?
Regression towards the mean simply posits that, over time, results even out towards the less extreme. One can see this with dice. With one die, one has an equal chance of encountering any of its six faces. Things get slightly more interesting with two dice. Here’s a chart of probabilities for a single throw of two fair dice:
| Total | Probability |
|---|---|
| 2 | 1/36 |
| 3 | 2/36 |
| 4 | 3/36 |
| 5 | 4/36 |
| 6 | 5/36 |
| 7 | 6/36 |
| 8 | 5/36 |
| 9 | 4/36 |
| 10 | 3/36 |
| 11 | 2/36 |
| 12 | 1/36 |
The something/36 works like this: There are 6x6=36 combinations out of two fair dice, the numerator (the something) is the number of combinations that make that total. For example, only two 1’s (“Snake Eyes”) can make a total of two, so it’s 1 out of 36. Likewise, only two 6’s (“Boxcars!”) can make 12. Seven is the most common result, since it can be 1+6, 2+5, 3+4, 4+3, 5+2, or 6+1, thus 6 out of 36.
Anyway, if you throw dice a few times, you might expect get a 6,7, or 8 about half the time (44.44…% to be exact). Writing a small program bears this out:
package main
import (
"fmt"
"math/rand"
"time"
)
const MAX_TRIALS = 10000000000
var outcomes = [...]uint64 { 2,12, 3, 3, 11, 11, 4, 4, 4, 10,10,10,5,5,5,5,9,9,9,9,6,6,6,6,6,8,8,8,8,8,7,7,7,7,7,7 }
func main() {
for i:=1; i < MAX_TRIALS ; i*=10 {
runTrials(i)
}
}
func runTrials(iterations int) {
var sum = uint64(0)
var k int
seeded_rand := rand.New(rand.NewSource(time.Now().UnixNano()))
for i:=0; i < iterations; i++ {
//each time, choose a random index out of 36
k = seeded_rand.Intn(36)
sum += outcomes[k]
}
fmt.Printf("Iterations: %10d, Mean value: %1.10f\n", iterations, float64(sum) / float64(iterations))
}
Results show that we quickly establish a mean close to 7 in as few as 10 iterations:
» ./dice
Iterations: 1, Mean value: 5.0000000000
Iterations: 10, Mean value: 5.7000000000
Iterations: 100, Mean value: 6.9100000000
Iterations: 1000, Mean value: 6.9840000000
Iterations: 10000, Mean value: 7.0034000000
Iterations: 100000, Mean value: 7.0012500000
Iterations: 1000000, Mean value: 7.0006190000
Iterations: 10000000, Mean value: 6.9994839000
Iterations: 100000000, Mean value: 7.0003509300
Iterations: 1000000000, Mean value: 7.0000477900
ZZZZZ…
Okay, so the point here is: Over big enough numbers, things become mediocre. I’d posit the same happens with Societies.
Think about it: If you study ancient history or medieval history the line keeps appearing:
Life was nasty, brutish, and short.
Read: Life is usually bad. If it’s not, you’re by definition in an outlying condition. You’re living a “Snake eyes” or “Boxcars” roll.
Thing is…that can’t last forever, societally. Everything trends back towards mediocrity given long enough time.
So What?
If your life is really bad right now, it will probably get better, with no input from you. The infamous “Bad luck comes in threes” is really no more surprising than rolling three successive double-6’s at Monopoly. It happens. It just doesn’t happen often, thanks to probability.
Similarly, if your life is really good right now, it won’t last. Setbacks and various chaotic things will affect you. This isn’t necessarily divine retribution, it’s just continuous rolls of the dice.