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.