Triangles and the Twins

After their victory over the White Sox last night the possible scenarios (all in all 21 games involving the Twins or Tigers = 2,097,152 scenarios) for the Twins look like so:

0.9% of the scenarios have the Twins clinching the division on the road in the Detroit series.

9.6% of the scenarios result in a game 163 (tie atop the division)

15.0% of the scenarios have the Twins winning the division in 162 games.

So 1 in 4 possible scenarios result in the Twins playing more than 162 games this season.  After this summer, I guess I’ll take it.

In calculating those numbers I used Pascal’s triangle (and probably did more math by hand than was absolutely necessary) to figure out the distribution of outcomes.  I remember when my fourth grade teacher presented us with that triangle and asked us if we could find the pattern.  I pored over it for quite a while before I noticed how to construct a line from the line before it.

I was enthralled.  One of my classmates and I created an enormous replica of the triangle for the hallway outside our classroom with around 30 rows of binomial coefficients.  I spent an inordinate amount of time on this.  Then the school’s open house rolled around and I found my dad checking out the triangle, he had been trying to figure out the pattern for a solid five minutes.  I guess it’s obvious where I get it from.

3 thoughts on “Triangles and the Twins

  1. I am feeling just a little down
    Nothing I can wrap reasons around
    But I can ignore it if I look real hard
    And make perfect triangles out of every three stars
    Sometimes I make burns on my arms
    Cause it moves that feeling from my heart to my arms
    And I’m driving and it keeps me awake
    I have so many more triangles to make
    Now that I have planted the seed
    Maybe those triangles will form without me
    Surround the world in their crystalline ache
    And freeze the heroes into glassy mosaics

    “Triangle Song” – Thin White Rope

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