Archive for September 17th, 2008

Per mille measurements

September 17, 2008

Surely you’ve heard of percent, and probably have a sense of its etymology: per centum = per 100, for describing fractional quantities in their equivalent form as parts out of 100. For example, since \frac{3}{4} = \frac{75}{100}, we say that 3/4 = 75%.

But are you familiar with per mille ? Denoted by the symbol ‰, per mille measures parts per 1000, or equivalently tenths of a percent. Thus 3/4 = 750‰.

Per mille measurements occur in a variety of contexts, typically ones in which small-scale changes in value are relatively significant, and so are worth the extra scrutiny that per mille units allow. Typical examples include roadway grades (or gradients), water salinity, and (perhaps most familiarly for our US readers) baseball batting averages.

Chipper Jones (of the Atlanta Braves) currently leads the Major Leagues in batting average: he has a total of 156 hits, out of 427 at-bats, for a batting average of \frac{156}{427} \approx .365339578....

Given that he’s only had 427 at-bats, not all that many digits are significant digits in the decimal expansion; baseball statisticians universally round off such expansions at the third place: his batting average is .365, which one could call 365 per mille.

A perfect batter, one who got a hit every single time at bat, would have a batting average of 1. But saying that the batting average is “one” might be misleading, in a context in which baseball fans typically describe a .365 hitter as batting “three hundred sixty five” — it seems “one” might be thought of as .001 as a batting average.

So the culturally accepted practice is to say that a perfect batter is “batting 1000”. And indeed, their batting average of 1 is also 1000 per mille.

Sadly, as the following photo attests, the phrase “batting 1000” is still sometimes subject to misinterpretation:

Perhaps we should incorporate the phrase “per mille” into our daily lexicon, for the common good. (Or maybe this just means that it is really hard to hit a baseball when you’re wearing a big furry mouse costume.)