Earned and Unearned Runs Explained: How ERA Is Really Computed
How the official scorer decides which runs count against a pitcher's ERA, by rebuilding the inning without errors, with worked examples, the passed-ball rule, relievers and the limits of the statistic.
A pitcher can allow three runs and have an earned run average of zero for the game. He can also allow three runs on three home runs and be charged with all three. The difference lies in a bookkeeping rule that most fans know only in outline: a run is earned when the pitcher is held responsible for it, and unearned when a fielding mistake made it possible. Every earned run average you have seen is built from that single distinction.
The rule looks simple and is not. Deciding which runs are earned means the scorer has to imagine the inning without the errors, and the answer sometimes surprises people, because one misplayed grounder can wipe out runs that scored later in the same inning and apparently had nothing to do with it. This article reconstructs the logic step by step, works through four sample innings, covers relievers and the strange case of the passed ball, and ends with what the statistic can and cannot tell you.
The definition and the formula
Earned run average, or ERA, is the number of earned runs a pitcher allows per nine innings. The formula is earned runs times nine, divided by innings pitched. A pitcher who gives up 3 earned runs in 7 innings has an ERA for that game of 3 times 9, divided by 7, which is 3.86. A pitcher who gives up 5 earned runs in 6 and two thirds innings has 5 times 9, divided by 6.667, which is 6.75.
Innings are counted in thirds because the unit is the out. A line of 6.1 means six and one third innings, and 6.2 means six and two thirds. They are not decimals, which is the most common arithmetic mistake in hand calculations; convert the tenths digit to thirds before you divide. The stat calculator on this site does the conversion for you.
The nine is a convention. It scales the statistic to the length of a regulation game so that a pitcher who threw 40 innings and one who threw 200 can be compared on the same scale. It does not mean the pitcher is expected to go nine. ERA became an official league statistic in the early 1910s, with the National League first, and the underlying idea of separating a pitcher's runs from his fielders' mistakes is older than that. The rule that governs it today is Rule 9.16 of the Official Baseball Rules, which is where the scorer's duties are laid out.
The one idea: rebuild the inning
Every ruling in this area flows from one instruction. The scorer imagines the inning as if the defence had made no errors, with no passed balls and no catcher's interference, and decides which runs would have scored in that cleaned-up version. Those runs are earned. Any run that would not have scored in the clean version is unearned.
The reconstruction has three working parts.
First, a batter who reached base on an error is treated as if he had been put out. He is out for the purposes of counting the three outs of the inning, which matters because the cleaned-up inning ends sooner than the real one did.
Second, a runner who advanced because of an error is held at the base he would have reached without it. If a single moves a runner from first to second and an error on the throw moves him to third, the scorer gives the pitcher credit only for second.
Third, once the cleaned-up inning has three outs, nothing after that point can count against the pitcher. Every run that scored after the inning "should" have ended is unearned, however clean the hits that produced it.
Only fielding errors, passed balls and catcher's interference are removed. Walks, hit batters, wild pitches, balks and stolen bases stay in the reconstruction, because the rules treat them as part of the pitcher's work. An error by the pitcher himself counts as an error just like anyone else's, so a pitcher who throws a bunt away is not charged with an earned run that depends on it.
Four worked innings
The best way to see the rule is to run it.
Inning one: the error that erases everything. Batter A hits a ground ball and the shortstop throws it away, so A is on first with no outs. Batter B singles. Batter C strikes out. Batter D doubles, scoring A and moving B to third. Batter E grounds out, scoring B, and Batter F flies out. Two runs scored. Now rebuild: A is treated as out, so after A there is one out. B singles, C strikes out (two outs), D doubles and puts B on third, and E's ground out is the third out. The inning ends in the reconstruction with no runs. Both runs are unearned, and the pitcher is charged with zero earned runs for the inning despite allowing a single, a double and two scoring plays.
Inning two: the error that costs one run. Batter A reaches on an error. Batter B hits a two-run home run. The next three batters are retired. Two runs scored. Rebuild: A is out, B hits a home run with nobody on base, and that is one run. One run is earned and one is unearned. The pitcher is charged with one earned run.
Inning three: the error that does not matter. With two outs, the first baseman drops a throw and the batter is safe at first. The next batter hits a home run. Rebuild: the batter who reached on the error is treated as the third out, so the inning is over before the home run. Both runs are unearned. This is the case that surprises people most, because the home run was a legitimate hit that no fielder could have stopped. The rule gives the pitcher the benefit of the doubt: with the error removed, the inning would have ended.
Inning four: the error that does not change the result. The leadoff batter doubles. The next batter grounds to second base, and the throw to first is wild: the batter is safe and the runner moves from second to third. The third batter singles, and the runner scores from third. Rebuild: the runner who doubled stays at second, because the error is what moved him up. The batter who reached on the error is treated as out. The single would have scored the runner from second anyway, so the run is earned. Now change the ending. If the third batter had hit a fly ball deep enough to score the runner from third, the reconstruction holds him at second, where a fly ball would not have scored him, and the run would be unearned. The scorer's question is always the same: what would have happened without the error?
What the pitcher owns
The following table shows how common events fare in the reconstruction. It is a summary; the scorer's judgment still applies to close calls.
| Event | Treated in the reconstruction as | Effect on earned runs |
|---|---|---|
| Hit, including an infield hit | Hit | Pitcher owns it |
| Walk, intentional walk, hit batter | Walk or hit batter | Pitcher owns it |
| Wild pitch, balk | Pitcher's fault | Pitcher owns the advance |
| Stolen base | Steal | Pitcher owns the advance, unless an errant throw helped |
| Fielding error | Batter out, or runner held back | Run unearned if it depended on the error |
| Passed ball | Same as an error | Run unearned if it depended on it |
| Catcher's interference | Same as an error | Run unearned if it depended on it |
| Dropped foul fly | Batter treated as retired | Later hits by that batter do not count against the pitcher |
| Sacrifice bunt or fly | Out, runner advances | Pitcher owns the advance |
The dropped foul fly is the odd one out. The error did not put a runner on base, but it gave the batter another chance at the plate, and the scorer treats him as if he had been retired.
The same pitch, two charges: passed ball and wild pitch
The line between a wild pitch and a passed ball causes more arguments in the scorebook than almost any other. The pitch can be identical. The question is whether a catcher could have stopped it with ordinary effort, and the scorer decides. If the pitch was so far off target that the catcher could not reasonably handle it, it is a wild pitch and the pitcher owns whatever it does. If the catcher should have caught it, it is a passed ball, which the rules treat like an error.
The consequences are concrete. Say a runner is on second base with one out. The pitcher throws a pitch in the dirt and the runner takes third. A sacrifice fly then scores him.
- If the pitch was ruled a wild pitch, the runner's advance to third belongs to the pitcher. The run is earned.
- If the pitch was ruled a passed ball, the reconstruction holds the runner at second. The sacrifice fly would not have scored him from second, so the run is unearned.
The same logic applies to a third strike. A batter who strikes out on a pitch that gets away from the catcher can run to first if first base is open or there are two outs. If the catcher is charged with a passed ball, the batter is treated as out in the reconstruction. If it was a wild pitch, he is treated as a baserunner who reached through the pitcher's fault. The full rules for who gets the blame are covered in wild pitches, passed balls and stolen bases in the scorebook.
A related decision comes earlier in the chain: whether a ball put in play is a hit or an error at all. If the scorer rules that an ordinary play should have been made, the batter is treated as retired for earned run purposes. How the scorer makes that call is the subject of hit or error, the official scorer's rules.
Relievers and inherited runners
Replacing the pitcher mid-inning adds a layer. The rule is that the scorer reconstructs the whole inning from its first batter, regardless of who was pitching, and then assigns each run to the pitcher who was responsible for the runner who scored.
Responsibility follows the runner, not the batter at the plate when he scored. If a starter leaves with runners on first and second and a reliever allows a single that scores both, those two runs are charged to the starter, because he put the runners on base. The reliever is charged only with runs scored by batters he put on. The reliever's own earned run average does not carry the inherited baserunners, which is why a reliever can come in, allow a run-scoring hit and still finish the outing with a perfect ERA.
When an error was made before the reliever entered, the reconstruction runs through the whole inning. If the cleaned-up inning would have ended before the reliever's batters came to the plate, the runs scored after that point are unearned for the reliever as well. The goal is that no pitcher is penalised for an inning that would already have been over.
One modern wrinkle: since 2020 the major leagues have used, in regular-season games, a runner placed on second base at the start of each extra inning. That runner is not the pitcher's doing, and the rules treat a run scored by him as unearned.
Why unearned runs have become rarer
Unearned runs depend on how often fielders make errors, and errors have declined sharply over the history of the game. The historical record gives team totals that let us measure this directly. In 1914, the American League allowed 3.69 runs per nine innings, of which 2.73 were earned, so about 26 percent of all runs allowed were unearned. In 1968 the American League allowed 3.42 runs per nine and 2.98 earned, so about 13 percent were unearned. In 2000 the American League figures were 5.34 and 4.91, about 8 percent unearned.
The trend has an obvious reading. Teams made fewer errors as the decades passed, so the gap between runs and earned runs narrowed. It also means that comparing pitchers from different eras on ERA alone gives older pitchers a boost relative to the runs they actually allowed, because a quarter of their runs were erased from the ledger. The lowest seasons on record are covered in the lowest ERAs in baseball history.
Where ERA misleads
The statistic is useful, and it has well-known limits. Here are the main ones.
The scorer's judgment. Whether a play was an error, a hit or a passed ball is a human decision, and the earned-run total inherits that uncertainty. A different call on one play can move a pitcher's ERA.
The defence behind him. ERA removes errors, but not the quality of the defence. A team with excellent range turns more balls in play into outs, and its pitchers benefit without any error being recorded. A team with poor range allows more hits that are not errors, and its pitchers pay for them in ERA.
The ballpark. Park effects are not part of the formula. A pitcher who calls a pitcher-friendly park home has his ERA flattered by it.
The era. An ERA of 3.50 means one thing in a league that scores three and a half runs per game and another in one that scores five. Two adjusted measures exist for that. ERA+ compares a pitcher's ERA to the league average, adjusted for park, with 100 as average and higher as better. Fielding-independent pitching, or FIP, ignores the defence altogether and uses only strikeouts, walks, hit batters and home runs, on the theory that those are the outcomes a pitcher controls most directly; its basic form is 13 times home runs, plus 3 times walks and hit batters, minus 2 times strikeouts, divided by innings, plus a constant that puts it on the ERA scale.
Small samples. A reliever with 60 innings who has one outing in which he allows five earned runs in an inning adds well over half a run to his ERA. That is why rate titles carry an innings qualifier: a pitcher must throw at least one inning per scheduled team game to qualify for a league ERA title.
Common questions
Can a pitcher lose a game with an ERA of 0.00? Yes. If every run he allowed was unearned, he has no earned runs and an ERA of zero, but the runs still count on the scoreboard and he can still take the loss.
Are unearned runs counted anywhere? Yes. They count in the team's runs allowed, in the game result, and in the stat called runs allowed per nine innings, often shortened to RA9. They are left out only of earned run average.
Does a no-hitter require no earned runs? No. A no-hitter is about hits. A pitcher can throw one and still allow runs on walks and errors. The rules are covered in what counts as a no-hitter or a perfect game.
Does the same logic apply in the postseason? Yes. The scoring rules are the same in every game, and postseason earned run averages are computed the same way.
What if the pitcher's own error starts the trouble? It is treated like an error by any other fielder, so any run that depended on it is unearned.
Do earned runs decide who gets the win, loss or save? No. Those decisions depend on the score and the lead, not on whether runs were earned. See the save rule, the hold and the win for the details.
Where to go next
If you keep score at the park, the logic here is built into the scoresheet, and the scoresheet tool lets you practice marking errors and runs. For another piece of the scorer's craft, read counts, walks and strikeouts. To check any pitcher's earned run average against the record, the leaders page lists the current standings.