All Possible Bowling Scores

TL;DR: there are 301 different scores you can receive while playing 10-pin bowling. One score is more likely than the others.

Today we went bowling. I am not good at bowling. A few of the people in our group bowled games over 150. I did not.

As I was contemplating the meaning of life after another missed spare, I started to try to put together a mental model for bowling scores would land in a typical distribution curve.

I found an amazing website when I got home. It answered exactly zero of my questions, but it did help me better understand the importance of closing frames if you want to break 100. As in, it's impossible to bowl over 90 unless you get at least one spare.

Here's what I learned:

in terms of all possible scores in ten-pin bowling, the mode score is 77. It occurs as the result of 172,542,309,343,731,946 possible scoring combinations—or roughly 3% of all possible game outcomes. And guess what my score was in my first game of the night?

Is there a lesson here?

Yes. Bowling sucks and math (specifically statistics) is the worst.

But seriously,

I think that this clearly demonstrates for me how misleading looking at the Mode (or Median, or Mean) of a given dataset can be.

It doesn't seem too dissimilar from business, where if you look at all the possible ways problems could be approached or solved, the bar is really, really, low.

When looking at all possible outcomes, we certainly need to have a higher standard than just "above average."