Ties and percentages

I was looking at the NFC standings yesterday, particularly the NFC North, the Chicago Bears’ division. The hated Packers are at the top of the division with a 4-1-1 record and a winning percentage of .750.

NFC Standings from Week 7

(Screenshot taken this morning from ESPN.)

How does a 4-1-1 record turn into .750? I guess the obvious answer is that the tie is treated as half a win and

4+½6=.750

But for some reason, my initial thought was more complicated. I thought of it as the weighted average of the winning percentage of non-ties with the winning percentage of ties:

56(.800)+16(.500)=.750

(There may be a philosophical argument as to whether a tie truly constitutes a .500 winning percentage, but I’m just going to accept it as a given.)

The calculation works out the same, of course, because

56(.800)+16(.500)=5(.800)+1(.500)6=4+½6=.750

I think this says something about me and my tendency to overcomplicate things. On the other hand, it’s always nice to be able to work out a solution in more than one way.

If you find that referring to numbers like .750, .800, and .500 as “percentages” a tiny bit off-putting, you’re my kind of people. But it’s common in sports to divide one number by another and call it a percentage—a tribute to the elasticity of language.

Two other common features of sports percentages:

  1. They are always (?) written to three decimal places. I think this was arrived at through experience—enough digits to distinguish close races but not enough to waste space.
  2. They are always spoken as if the decimal point isn’t there. The examples above are “seven-fifty,” “eight hundred,” and “five hundred.”

Baseball also uses “average” to express one number divided by another: batting average and earned run average come to mind. But it also has the slugging percentage, which isn’t remotely like a percentage.

I’m a big fan of “modulus,” mainly because of its many uses in engineering mechanics, e.g., Young’s modulus, bulk modulus, and section modulus. But I don’t expect to see it on ESPN anytime soon.