What Is ERA in Baseball? Formula, Examples and Earned Runs

ERA, or earned run average, is the number of earned runs a pitcher allows per nine innings. The formula is earned runs x 9 / innings pitched, so a pitcher who gives up 65 earned runs in 180 2/3 innings has a 3.24 ERA.

It is the oldest and most quoted pitching stat in baseball, and it is simpler than it looks once you know two things: what makes a run earned, and how to read innings pitched, because a box score that says 6.1 does not mean six and one tenth. This guide covers both, with every step of the arithmetic shown, then explains ERA+ and FIP, the two adjusted numbers you will see next to ERA on most stat pages.

The ERA formula

The Official Baseball Rules define it in Rule 9.21(e): multiply the earned runs charged to a pitcher by 9, then divide by the innings he pitched, including fractions of an inning.

ERA = (earned runs x 9) / innings pitched

Why nine? Because a regulation game is nine innings, so ERA answers a practical question: if this pitcher threw a whole game at his usual level, how many earned runs would he allow? A 3.00 ERA means three earned runs per nine innings, on average.

The rulebook even includes its own worked example: 9 1/3 innings and 3 earned runs gives a 2.89 ERA. Check it: 3 x 9 = 27, and 27 divided by 9.333 is 2.893, which rounds to 2.89. Lower is better, and ERA is normally shown to two decimal places.

Reading innings pitched: why 6.1 means 6 1/3

Each out a pitcher records is one third of an inning. MLB's glossary puts it plainly: every out adds a third of an inning to the total, a double play adds two thirds, and a batter who reaches on an error adds nothing because no out was made.

Box scores do not print thirds as fractions. They use a shorthand where the digit after the dot is the number of extra outs:

• 6.0 means 6 full innings (18 outs)
• 6.1 means 6 1/3 innings (19 outs), or 6.333 as a true decimal
• 6.2 means 6 2/3 innings (20 outs), or 6.667 as a true decimal
• There is no 6.3, because a third out completes the inning and the total becomes 7.0

That shorthand is the single most common source of wrong ERA calculations. Before you divide, convert .1 to one third and .2 to two thirds.

Worked examples, step by step

The pitchers below are hypothetical. The point is the arithmetic.

A single start: 6.1 innings, 2 earned runs

First, convert the innings: 6.1 means 6 1/3, which is 6.333 innings, or 19 outs. Next, multiply earned runs by 9: 2 x 9 = 18. Then divide: 18 / 6.333 = 2.842. Rounded to two decimals, the ERA for the start is 2.84.

Check with the outs shortcut: 2 x 27 = 54, and 54 / 19 = 2.842. Same answer.

A full season: 180.2 innings, 65 earned runs

Convert the innings: 180.2 means 180 2/3, which is 180.667 innings. In outs, that is 180 x 3 + 2 = 542. Multiply earned runs by 9: 65 x 9 = 585. Divide: 585 / 180.667 = 3.238, which rounds to a 3.24 ERA.

Outs check: 65 x 27 = 1,755, and 1,755 / 542 = 3.238. Same again.

The mistake to avoid

If you type the box score figure straight into a calculator, you treat 6.1 as six and one tenth. For the single start, 18 / 6.1 = 2.951, which rounds to 2.95 instead of the correct 2.84. Over a full season the error shrinks, because the fraction is a smaller share of the total: 585 / 180.2 = 3.246, or 3.25 instead of 3.24. Small, but wrong, and enough to flip a tight ERA race.

Earned runs vs unearned runs

Not every run counts against ERA. An earned run is one the pitcher is held responsible for. Under Rule 9.16, the official scorer reconstructs the inning as if there had been no errors or passed balls, giving the pitcher the benefit of the doubt, and any run that would not have scored in that cleaner version of the inning is unearned.

Runs are usually ruled unearned in situations like these:

• The runner who scored reached base on a fielding error
• The run scored after the inning should already have ended, had a fielder made a routine play
• A passed ball (the catcher's fault, not the pitcher's) let the runner advance into scoring position or score
• The batter reached on catcher's interference and later scored
• In regular season extra innings, the automatic runner who starts on second base scores; MLB rules treat that runner as if he reached on an error, though no error is charged

What does not make a run unearned: walks, hit batters, wild pitches, balks and stolen bases. The rulebook is explicit that a wild pitch is solely the pitcher's fault and counts toward earned runs just like a walk. For more on the extra-inning runner rule, see our guide to how many innings are in a baseball game.

A two-out error, reconstructed

The rulebook's own illustration works like this. With two outs, the shortstop boots a routine ground ball and the batter reaches first. The next hitter homers. The pitcher then strikes out the third hitter. Two runs scored, but neither is earned, because without the error the ground ball would have been the third out and the inning would have ended at zero.

Change one detail: if the batter reached on catcher's interference instead, one of the two runs (the home run hitter's) is earned. The scorer cannot assume the batter would have made an out, because he never got to finish his turn at bat.

One more rule worth knowing: runs belong to the pitcher who put the runner on base. If a starter leaves with a runner on first and the reliever gives up a double that scores him, that run goes on the starter's line, not the reliever's.

Why it matters: one start, two numbers

Say a hypothetical starter goes 6.0 innings and allows 4 runs, 2 of them unearned. His ERA for that game is 2 x 9 / 6 = 3.00. His runs allowed per nine innings, a stat called RA9 that counts every run, is 4 x 9 / 6 = 6.00. Same outing, very different picture, which is why some analysts prefer RA9 for describing what actually happened.

ERA+: adjusting for league and ballpark

A 3.50 ERA in a pitcher-friendly park during a low-scoring season is not the same as a 3.50 ERA in a thin-air hitter's park when offense is booming. ERA+ corrects for that.

MLB's glossary describes ERA+ as the league ERA, adjusted for park factors, multiplied by 100 and divided by the pitcher's ERA. The result is scaled so that 100 is league average, and higher is better. A 150 ERA+ is about 50 percent better than average.

A simple illustration with made-up numbers: if the park-adjusted league ERA is 4.00 and our pitcher's ERA is 3.20, then 4.00 x 100 / 3.20 = 125, roughly 25 percent better than average. A pitcher with a 5.00 ERA in the same setting gets 4.00 x 100 / 5.00 = 80, or about 20 percent worse than average. Notice that ERA+ flips the direction: for raw ERA lower is better, for ERA+ higher is better.

FIP: ERA without the defense

ERA still depends on the fielders behind the pitcher. A great defense turns hard grounders into outs, a poor one lets them through, and the scorer's error calls do not catch every misplay. Fielding independent pitching, or FIP, tries to strip that out by using only the outcomes a pitcher controls most directly: strikeouts, walks, hit batters and home runs.

MLB's glossary gives the formula as ((13 x HR) + (3 x (BB + HBP)) - (2 x K)) / IP + a constant. The constant changes every season and exists only to put FIP on the same scale as ERA; FanGraphs notes it is generally around 3.10.

A hypothetical season, using 3.10 as an illustrative constant: 180 innings, 18 home runs, 50 walks, 6 hit batters, 180 strikeouts.

Home runs first: 13 x 18 = 234. Walks plus hit batters: 3 x (50 + 6) = 3 x 56 = 168. Strikeouts: 2 x 180 = 360. Combine them: 234 + 168 - 360 = 42. Divide by innings: 42 / 180 = 0.233. Add the constant: 0.233 + 3.10 = 3.33 FIP.

If that pitcher's actual ERA were well above 3.33, analysts would suspect bad luck or poor defense. If it were well below, they would expect it to drift upward.

What ERA does well and where it misleads

As a rough feel for the numbers, the rule-of-thumb chart in the FanGraphs stat library puts an excellent ERA around 2.50, great around 3.00, average around 3.75, and poor around 4.30 or higher, and it suggests shading those marks about half a run lower for relievers. Those are general guides, not official categories, and league scoring changes every year. ERA+ is the better tool for a fair comparison.

ERA quick reference

A checklist for working out or reading any ERA:

• Formula: earned runs x 9 / innings pitched
• Convert innings first: .1 = one third, .2 = two thirds, never tenths
• No-decimal shortcut: earned runs x 27 / total outs
• Unearned runs (errors, passed balls, catcher's interference, the extra-inning automatic runner) do not count
• Walks, wild pitches and balks still produce earned runs
• ERA+: 100 is league average and higher is better
• FIP: ERA-scaled estimate using only HR, BB, HBP and K

On the hitting side, the matching all-in-one number is OPS. Our guide to OPS in baseball walks through it with the same step-by-step approach, and if you want to know why pitchers fear runners on base, read up on what a balk is.