Sunday, March 30, 2008

Appreciating The Math

There's an interesting article in today's NY Times on the math behind Joe DiMaggio's 56 game hitting streak. The line that got me thinking was:

"in 1941 Joe DiMaggio had an 81 percent chance of getting at least one hit in each game"

Lets translate to poker:

Joltin' Joe has pocket aces and his opponent pocket kings. DiMaggio is an 80-20% favorite to win the hand. If the aces hold up, his hitting streak continues. If the aces get cracked, his hitting streak is over.

Somehow Joe's pocket aces held up 56 hands in row!


Who wins 56 in a row without their aces getting cracked?

Fact is there's only been three times in history when aces have actually held up at showdown.

- My grandfather won't talk about WW2 but he has told me in great detail about the night he saw pocket aces win in Springfield, Mass. in 1938. His brother confirms this story.

- Che Guevara's pocket aces were in big trouble after Victor Dreke flopped a set in the Congo in 1965, but Guevara took down a huge pot when a third ace came on the turn.

- Everyone remembers Mindy Cohn's pocket aces holding up against Kim Fields' flush draw on the set of The Facts of Life in 1982.

And that's it.

Of course bad luck aside, a hand that is an 81% favorite should win.

Yet the fun math is to run some trials of an 81% favorite versus a 19% dog.

If we have them square off 4 times, an 81% favorite will win all 4 in a row only 43% of the time.

Math is desperately trying to tell us there's a 57% chance DiMaggio WON'T get a hit 4 games in a row. Even at his phenomenal 81% success rate.

So not only does DiMaggio have to win 4 in a row (which he will only do 43% of the time), he somehow has to repeat this success 14 times in a row!

What 43% thing happens 14 times in a row?

Can you imagine how much money I would have lost betting against DiMaggio in 1941?

I don't know what .43 to the 14th power looks like but if this was a standardized test I'd recommend finding an answer real close to .81 to the 56th power.

Good luck with that.


genomeboy said...

While it is an interesting analogy, you seem to overlooking the fact that he typically had between 3-5 chances each game of having the AA he held in the on deck circle hold up once the pitches started to fly. Thus, it would seem a lot more likely that his streak could continue, as long as he was not intentionally walked...

Robert said...

The 81% success rate doesn't overlook the number of at bats in each game. This 81% is already based on his getting the 3 to 5 at bats per game.

The big distinction to make mathematically is to consider each game as only 1 trial. Not 3 to 5. Thus Joe isn't 81% every time he comes to the plate. He's "only" 35.7%. (His batting average for the season).

So sticking with the poker analogy he's not holding AA each time he sits in the on deck circle. It's more like a monster flush draw.