There are times in our lives when it feels like something should happen more often than it does, but the math proves that it’s actually on track.
For example, the Atlanta Braves made it to the postseason 14 straight times (1991-2005) but only won the World Series once. It feels like if you make it 14 years in a row, you should probably win 3-4 championships in that time, right? In actuality, with eight teams making it each year, they should have won just 1.75 championships in that time. So yes, their solo championship was less than expected, but even two championships during that 14 year run would have been more than they mathematically should have earned.
It’s like tossing a coin. If you flip it five times and they’re all heads, what are the odds of heads on the sixth toss? 50%.
As Joseph Bertrand has said, “the coin has neither memory or consciousness“.
I wish the Braves would have won more titles during that run, but they weren’t as disappointing as it seems at first glance. All things being even, they had a 12.5% chance of a championship each season, so I’m glad one of them worked out for them.
That happens too often
On the other hand, you have events that are seemingly very unlikely yet occur far more frequently than you’d expect because there are tons of opportunities to come up. If there is some feat that only happens “once in a million”, and a million people try it, odds are someone will beat those huge odds.
It’s like playing Powerball, where the odds of winning are 1 in 292,201,338, but yet people win all the time. How do people keep beating those odds?
In the book “Seeking Wisdom“, author Peter Bevelin put it this way:
We underestimate how many opportunities there are for “unlikely” events to happen. Surprises and improbable events happen if they have enough opportunities to happen.
Lottery odds can be fun to look at. I might guess that the next drawing will pull the numbers 1 2 3 4 5 6, and that looks like a silly bet to make. However, it has literally just as good a chance of coming up as a more random mix like 2 11 34 45 58 9, even though the latter set feels more likely.
Cards have never been sorted like that before
If you properly shuffle a deck of cards, the odds are essentially 100% that the order of cards you just created has never been seen before and will never be seen again, simply because the odds are so drastically low.
It doesn’t feel right, but it is. This video explains it a bit more:
My hope is that if the Braves get on another run of postseason appearances they’ll win more often then they did last time, but I already know that it’s unlikely to be true.
In the meantime, I’ll enjoy the fact that they won it all last year and they’re the reigning champions for at least the next few months.
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