| Now that baseball season is well under way, many | | | | number of innings pitched divided by nine. That |
| of you might be wondering how that statistic | | | | "double division" in the last sentence is where our |
| called the earned run average (era) is computed. | | | | complex fraction comes in. |
| You might know that this stat reflects a pitcher's | | | | Let's see this calculation with an example. Suppose |
| allowed, or earned, runs per nine innings. But did | | | | Mariano Rivera of the New York Yankees, has |
| you know that this stat is nothing more than a | | | | pitched 72 innings. Let's also assume that during |
| complex fraction in mathematics and can be | | | | these innings he has allowed 6 earned runs. The |
| calculated with a nice little trick? | | | | way to get his ERA is as follows: we divide 6 by |
| The earned run average can be a pitcher's best | | | | 72 divided by 9 or ERA = 6/(72/9). Since 72/9 is |
| friend or worst nightmare. Regardless of how this | | | | 8, the calculation simplifies to ERA = 6/8 or 0.75; |
| stat is actually calculated, the lower the number | | | | not too shabby an earned run average. In this |
| the better for the pitcher. Indeed a pitcher that | | | | calculation, we performed the 72/9 calculation first |
| can end the season with an ERA of under 2, | | | | but we could use the principle that dividing is the |
| would be very pleased, provided the pitcher | | | | same as multiplying by the reciprocal. This is a |
| threw at least 50 or more innings. A pitcher with | | | | nice little trick to getting the ERA. |
| few appearances could have the ERA work very | | | | The way we do this is as follows: we convert 6 |
| favorably if he did not allow any runs; while a | | | | (72/9) into 6*(9/72) which becomes 54/72, and |
| pitcher who threw for 1 inning, yet allowed 10 | | | | this simplifies to 3/4, or 0.75. Thus to get the |
| runs, would have a disastrous ERA. | | | | ERA quickly, take the earned runs and multiply |
| Yet how do we get to this calculation and what | | | | them by 9; then divide by the number of innings |
| does this have to do with complex fractions? A | | | | pitched. To see this, suppose Johann Santana has |
| complex fraction you might recall, is a fraction | | | | given up 18 earned runs in 100 innings pitched. His |
| which contains in either the numerator, the | | | | ERA will be 18*9/100 or 162/100 or 1.62. Now |
| denominator, or both, another fraction. This is | | | | that you are aware of this neat little way to get |
| why it is considered complex. The earned run | | | | the ERA, you can show your friends what a real |
| average in baseball is computed by taking the | | | | baseball fan you are. |
| total of earned runs and dividing that by the | | | | |