Baseball’s Earned Run Average (ERA): Nothing More Than a Complex Fraction

Now that baseball season is underway, many of you may be wondering how that statistic called earned run average (ERA) is calculated. You may be aware that this statistic reflects a pitcher’s runs allowed or earned per nine innings. But did you know that this statistic is nothing more than a complex fraction in mathematics and can be calculated with a little trick?

Earned run average can be a pitcher’s best friend or worst nightmare. Regardless of how this stat is actually calculated, the lower the number, the better for the caster. In fact, a pitcher who can finish the season with an ERA under 2 would be very pleased, as long as the pitcher has thrown at least 50 or more innings. A pitcher with few appearances could have a very favorable ERA if he didn’t allow runs; whereas a pitcher who pitched 1 inning but allowed 10 runs, he would have a disastrous ERA.

However, how did we arrive at this calculation, and what does this have to do with complex fractions? A complex fraction that you may remember is a fraction that contains in the numerator, denominator, or both, another fraction. That is why it is considered complex. The earned run average in baseball is calculated by taking the total earned runs and dividing it by the number of innings pitched divided by nine. That “double division” in the last sentence is where our complex fraction comes in.

Let’s see this calculation with an example. Mariano Rivera of the New York Yankees is supposed to have thrown 72 innings. Let’s also assume that during these innings he has allowed 6 earned runs. The way to get his ERA is as follows: we divide 6 by 72 divided by 9 or ERA = 6 / (72/9). Since 72/9 is 8, the calculation simplifies to ERA = 6/8 or 0.75; Not bad for an earned run average. In this calculation, we first perform the calculation 72/9, but we could use the principle that dividing is the same as multiplying by the reciprocal. This is a good trick to get the ERA.

The way we do this is this: we convert 6/(72/9) to 6*(9/72) which becomes 54/72, and this simplifies to 3/4, or 0.75. So, to get the ERA fast, take the earned runs and multiply by 9; then divide by the number of innings pitched. To see this, assume that Johann Santana has allowed 18 earned runs in 100 innings pitched. His ERA will be 18 * 9/100 or 162/100 or 1.62. Now that you’re up to speed on this nifty way to gain ERA, you can show his friends that he’s a true baseball fan.