Percentages are Confusing

The word ‘percentage’ has a pretty simple and specific meaning, but the meaning of the word is gradually becoming more generic, like Kleenex or Xerox. Whether it’s the Mythbusters or Hockey Night in Canada the word percentage is increasingly used to just mean ‘ratio’ or portion. That’s a shame because it adds ambiguity to all the traditional uses of the word. It’s wrong, and should be corrected.

The meaning of percentage is encoded in the word itself. ‘Percentage’ means ‘per hundred’ (from the Latin for hundred) so when you say “50 percent” you are saying “50 per 100, or half.

The save percentage of a goalie is pretty simple to calculate. If there were 100 shots on goal and the goalie stopped 97 of them then the goalie has a 97% save percentage. The general formula, useful when the number of shots wasn’t exactly 100, is:

Save Percentage = 100 * saves / shots

Multiplying by 100 is what changes the number from being the ratio of saves to shots, or the portion of shots that were stopped, to the percentage of shots that were stopped. The rule is simple: if you don’t multiply the ratio by 100 then it’s not a percentage.

A save percentage of 97% is pretty good. A save percentage of 1% or lower would be implausibly bad. Even if the goalie just lay down in the crease and had a nap they could probably stop more than 1% of shots.

Some frustrated Vancouver Canucks fans might feel like Roberto Luongo’s 2011 Stanley Cup performance was pretty bad, but the Hockey Night in Canada stats still seem a bit cruel:

image

In game four Luongo stopped 22 out of 28 shots, and let in 6 goals. The Hockey Night in Canada summary would have us believe that Luongo stopped 22 out of 2,800 shots!

.786% = 100 * 6 / 2800

If they want to display it as a number between 0.000 and 1.000 then that’s fine – but don’t call it a percentage. Or, if you want to call it a percentage, move the decimal point over, as demonstrated in this beautifully photo-shopped image:

image

Wow. 66.7%? That’s really bad. I’ll bet that Tim Thomas could have laid down in the net and had a nap and still would stopped that high a percentage of the shots.

About brucedawson

I'm a programmer, working for Google, focusing on optimization and reliability. Nothing's more fun than making code run 10x faster. Unless it's eliminating large numbers of bugs. I also unicycle. And play (ice) hockey. And juggle.
This entry was posted in Math. Bookmark the permalink.

One Response to Percentages are Confusing

  1. Pingback: More Confusion with Percentages | Random ASCII

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s