I read something alarming in the daily “Best of GoComics” e-mail this morning. It was a panel of Dave Whamond’s Reality Check. It’s a panel comic, although it stands out from the pack by having a squirrel character in the margins. And here’s the panel.
Certainly a solid enough pun to rate a mention. I don’t know of anyone actually doing a March Mathness bracket, but it’s not a bad idea. Rating mathematical terms for their importance or usefulness or just beauty might be fun. And might give a reason to talk about their meaning some. It’s a good angle to discuss what’s intersting about mathematical terms.
And that lets me segue into talking about a set of essays. The next few weeks see the NCAA college basketball tournament, March Madness. I’ve used that to write some stuff about information theory, as it applies to the question: is a basketball game interesting?
- How Interesting Is A Basketball Tournament? leads the series off. From it I answer: 63.
- What We Talk About When We Talk About How Interesting What We’re Talking About Is fills in a bit of context. I answer 63 what.
- But How Interesting Is A Real Basketball Tournament? starts to shade the answer, reflecting things like how the number 1 seed nearly always beats the number 16 seed. It had never happened, when I wrote this essay. The number 16 beat the number 1 seed for the first time, I think, last year.
- But How Interesting Is A Basketball Score? This doesn’t relate to the essay, but a few weeks ago I read a book about the New York Original Celtics, who played — and invented — much of professional basketball in the 1910s and 1920s, and it’s all fascinating but it also mentions newspaper clippings of, like, the greatest game anyone had ever seen and the score was 28 to 25. (The game had much less offense and much more defense back then, plus you couldn’t necessarily count on the hoop having features like a backboard or stuff.)
- Doesn’t The Other Team Count? How Much? Earlier I put up an answer about how interesting one team’s score was. The tricky part is the other team has a score, too, and you know it’s not the same as the first team’s. So, how to account for that?
- A Little More Talk About What We Talk About When We Talk About How Interesting What We Talk About Is as I circle back around to the 63 or some other number that’s appeared before, and I name just what the 63 of things are.
Along the way here I got to looking up actual scoring results from major sports. This let me estimate the information-theory content of the scores of soccer, (US) football, and baseball scores, to match my estimate of basketball scores’ information content.
- How Interesting Is A Football Score? Football scoring is a complicated thing. But I was able to find a trove of historical data to give me an estimate of the information theory content of a score.
- How Interesting Is A Baseball Score? Some Partial Results I found some summaries of actual historical baseball scores. Somehow I couldn’t find the detail I wanted for baseball, a sport that since 1845 has kept track of every possible bit of information, including how long the games ran, about every game ever. I made do, though.
- How Interesting Is A Baseball Score? Some Further Results Since I found some more detailed summaries and refined the estimate a little.
- How Interesting Is A Low-Scoring Game? And here, well, I start making up scores. It’s meant to represent low-scoring games such as soccer, hockey, or baseball to draw some conclusions. This includes the question: just because a distribution of small whole numbers is good for mathematicians, is that a good match for what sports scores are like?