Doesn’t The Other Team Count? How Much?

I’d worked out an estimate of how much information content there is in a basketball score, by which I was careful to say the score that one team manages in a game. I wasn’t able to find out what the actual distribution of real-world scores was like, unfortunately, so I made up a plausible-sounding guess: that college basketball scores would be distributed among the imaginable numbers (whole numbers from zero through … well, infinitely large numbers, though in practice probably not more than 150) according to a very common distribution called the “Gaussian” or “normal” distribution, that the arithmetic mean score would be about 65, and that the standard deviation, a measure of how spread out the distribution of scores is, would be about 10.

If those assumptions are true, or are at least close enough to true, then there are something like 5.4 bits of information in a single team’s score. Put another way, if you were trying to divine the score by asking someone who knew it a series of carefully-chosen questions, like, “is the score less than 65?” or “is the score more than 39?”, with at each stage each question equally likely to be answered yes or no, you could expect to hit the exact score with usually five, sometimes six, such questions.