On April 23, 1999, Fernando Tatis of the St. Louis Cardinals hit a
grand slam home run against Chan Ho Park of the Dodgers. That's not an
overly rare event. However, Tatis didn't hit just one grand slam off
of Park. He hit TWO. And they were in the same inning. No Major League
player had ever done this before and no one has done it since. The
chances of being a witness to such a thing must be so high to make it
unlikely that anyone would ever see it. And yet it happened.

David Hand's book The Improbability Principle tries to explain how
such seemingly unlikely events not only do happen, they almost have to
happen. Hand's "principle" is actually just his way of synthesizing
several different mathematical laws of probabilities. He does an
excellent job of explaining complicated topics in a clear and engaging
manner.

One of the most important laws to take from the book is The Law of
Truly Large Numbers. Essentially, if you give some event enough
chances to occur, it will happen. So if you think someone winning the
lottery twice is impossible, it isn't. People have done it--and with
big jackpots. Why? Because there are a lot of lotteries in the world.
There are so many that by chance one person will take home two big
payouts.

There is also the Law of Near Enough. Many things that humans think
are coincidences are just our way of drawing parallels between things
that are close. Say that I know the value of pi to 20 digits. You know
it to 10 digits. We both think we know the value of pi. But we don't
both know the exact same number. But for most people it's near enough.

Hand also mentions probability levers. Certain outside influences can
change the probability of an event occurring. In the case of Tatis'
two grand slams, he was playing in an era when there were many home
runs hit. He was also facing the same pitcher twice who was tiring
because he was throwing many more pitches than normal. Both of those
factors made the two grand slam home runs a bit more likely, albeit
still highly unusual.

Our brains are trained to look for patterns and coincidences it seems.
But our brains aren't as well trained at figuring out probabilities.
We go to casinos and play roulette and bet on numbers that haven't
come up recently because "they're due." Basketball players keep
passing the ball to a teammate who may have made two shots in a row
because "he has a hot hand." But, these can all just be random
variations. It just happens.

The Improbability Principle may make you think that everything is
random. Weird coincidences may seem a little less special, but you may
also feel special knowing the reason why that is so.