What ratio determines a pitcher's ERA?

This explains it pretty well http://www.freemathhelp.com/earned-run-average.htm...

It's basically the number of earned runs time 9, divided by the number of innings pitched. Things can get a little complicated when you start using 1/3's of an inning, but that's the gist of it.

ERA stands for Earned Run Average, and it's calculated over a 9 inning period. 2 runs in 6 innings would equal an ERA of 3, because you're averaging to give up one run every 3 innings. Now, whenever you see a pitcher's ERA in a box score, that's their ERA for the entire season, so it's not going to change drastically if you have a lot of innings pitched, unless of course, you give up a ton of runs.

earned runs per 9 innings pitched.

The ratio is

Earned runs allowed, divided by innings pitched, multiplied by 9.

This is the formula to calculate ERA: (Earned Runs/Innings Pitched) x 9.

((Earned runs * 9) / Innings pitched)