Expected Earned Runs Over a Projected Workload

You have a pitcher with a known Earned Run Average (ERA) from a historical period, and you need to estimate how many earned runs that pitcher will allow over a different number of innings in the future. The translation is a direct linear scaling, expressed as your expected earned runs over a projected workload. Use the formula: Expected Earned Runs = (ERA × Projected Innings Pitched) / 9. The result is a long-run average, not a prediction for a single game.

The Worked Calculation

Take a pitcher who has a 4.50 ERA over 200 innings pitched. That ERA, as defined by MLB Rule 9.16 and Rule 9.02, means the pitcher allowed 4.50 earned runs per nine innings. The per-inning rate is 4.50 divided by 9, or 0.5 earned runs per inning. Now project that rate onto a future workload of 90 innings. Multiply the per-inning rate of 0.5 by 90, or use the formula directly: (4.50 ERA × 90 IP) / 9 = 405 / 9 = 45 earned runs.

Why This Is a Long-Run Estimate, Not a Single-Game Prediction

The handoff context for this translation treats the result as a long-run estimate. The formula assumes the pitcher's true skill level, as measured by the historical ERA, stays constant. It also assumes that future conditions, team defense, ballpark, luck on batted balls, match those of the historical period. A single appearance can easily produce 3 earned runs or 8, even if the long-run expectation is 5. Use the projection for season planning, roster decisions, or workload distribution, not for betting on one game.

Step 1: Confirm the ERA Is Reliable

Before you multiply, check the sample size. FanGraphs states ERA is not reliable below 50 innings for starters and 30 innings for relievers. A 4.50 ERA over 10 innings is a meaningless number. If the sample is too small, the expected earned runs projection will be highly uncertain. You are better off using a predictive stat like FIP, xFIP, or SIERA for that pitcher instead of their raw ERA.

Step 2: Convert ERA to a Per-Inning Rate

ERA is expressed per nine innings. To get the rate per single inning, divide by 9. For a 4.50 ERA, the rate is 0.5 earned runs per inning. This is the number you will scale.

Step 3: Multiply by the Projected Innings

Multiply the per-inning rate by the number of innings in the projected workload. If the projected workload is 90 innings, multiply 0.5 by 90 to get 45 earned runs. The formula (ERA × Projected IP) / 9 gives the same result directly.

Step 4: Apply the Failure Case Check

If the projected workload is large relative to the historical sample, the estimate becomes more sensitive to a change in the pitcher's skill. A pitcher with a 4.50 ERA over 200 innings who then switches to a team with a poor defense may allow 55 earned runs over 90 innings, not 45. The formula is linear and deterministic, but the real world is not.

The Arithmetic Is Simple; the Context Is Not

The formula Expected ER = (ERA × Projected IP) / 9 is a straight proportional scaling. Double the projected innings, and the expected earned runs double. The simplicity hides several assumptions that fail in practice. The estimate assumes the ERA itself is a stable measure of the pitcher's runs-allowed rate. But ERA is noisy, context-dependent, and influenced by factors outside the pitcher's control: the quality of the defense, the ballpark's park factor, and the scorer's judgment of earned versus unearned runs.

The Sample-Size Failure

The most common failure case is small-sample overconfidence. A pitcher with a 2.00 ERA over 10 innings has an expected earned runs projection of (2.00 × 90) / 9 = 20 earned runs for a 90-inning workload. That number looks precise, but the underlying ERA is meaningless. FanGraphs recommends a minimum of 50 innings for starters and 30 innings for relievers before treating an ERA as reliable. Apply that threshold before you run the calculation.

The Reliever Problem

For relievers, the projection is even less reliable. Reliever ERA is more volatile because relievers often enter with inherited runners on base. Those inherited runners, if they score, count as earned runs against the reliever's ERA even though a different pitcher put them on base. MLB Rule 9.16 defines the scoring correctly, but the expected value calculator in your head, the linear scaling, does not adjust for inherited runners. A reliever projected for 30 innings may allow more earned runs than the formula suggests because a few inherited-runner appearances can spike the actual total.

What Goes Wrong

A reliever enters the game with a runner on second base. That runner later scores on a single. The run is earned under the scorer's judgment because the reliever allowed the hit that moved the runner. The run counts against the reliever's ERA, but the runner was not the reliever's responsibility to begin with. Over a projected workload, the linear formula will undercount expected earned runs for relievers who regularly enter with inherited runners.

What to Do Instead

If you must project earned runs for a reliever, use their FIP (Fielding Independent Pitching) or SIERA (Skill-Interactive ERA) instead of raw ERA. Both stats exclude defensive contributions and inherited-runner effects. FanGraphs provides xFIP, which replaces actual home-run rate with a league-average rate, for an even more predictive projection. For a reliever with a 3.50 FIP over 30 innings, the expected earned runs for a future 30-inning workload is (3.50 × 30) / 9 = about 11.7 earned runs, which is a more honest estimate than the ERA-based projection.

Comparing ERAs Across Eras or Levels

If you translate a pitcher's ERA into expected earned runs and then compare that number to a different pitcher from a different league or season, you introduce a league-average mismatch. The 2023 MLB average ERA was 4.33. The 1968 MLB average was 2.98. A 3.50 ERA in 2023 translates to expected earned runs of (3.50 × 90) / 9 = 35 earned runs over 90 innings. A 3.50 ERA in 1968 is the same arithmetic, but the performance level is completely different. The 1968 pitcher is significantly worse than league average, while the 2023 pitcher is better than league average. Use ERA+ (park- and league-adjusted ERA) to normalize before projecting across eras.

High School and Softball Contexts

The same failure applies to high school and softball comparisons. NFHS and NCAA rules differ from MLB on earned-run judgment. Softball uses 7-inning games, not 9. A 2.00 ERA in softball over 7-inning games means 2.00 earned runs per 9 innings, but the pitcher only plays 7 innings per game. The linear formula still works, (2.00 × 70 IP) / 9 = 15.6 expected earned runs over 70 innings, but comparing that number to a baseball pitcher's projection without adjusting for game length is invalid.

Use It For

• Season-level roster planning: estimating how many runs a starting pitcher might allow over a projected 180-inning season.
• League officials verifying software output for partial-inning calculations.
• Fantasy or simulation leagues that need a baseline expected runs number for a pitcher over a defined workload.

Skip It For

• Single-game or single-appearance betting.
• Comparing pitchers from different leagues, eras, or ballparks without adjusting for park factor or league-average ERA.
• Any reliever with fewer than 30 innings of data.
• Pitchers who have changed teams, ballparks, or leagues since the historical period.

The single most common error is treating the expected earned runs number as a precise forecast. It is a long-run central tendency, not a guarantee. If the pitcher's skill has changed, or if the context differs, the estimate will be wrong. Check the sample size, check the context, and treat the result as a planning tool, not a prediction.

Projected Innings Pitched	Expected Earned Runs	Sample Reliable?
90	45	Yes (200 IP historical sample)
50	25	Yes (200 IP historical sample)
30	15	Marginal (minimum for reliever)
10	5	No (10 IP historical sample is too small)
5.667 (5.2 IP)	2.83	No (partial inning, small sample)

Before you multiply, confirm that the pitcher's ERA comes from a reliable sample, at least 50 innings for a starter, 30 innings for a reliever. If the sample is too small, do not use the formula. Find the pitcher's FIP or SIERA from FanGraphs instead, and use that stat in the same linear scaling. That single check will prevent the most common failure case: small-sample overconfidence that turns a 2.00 ERA over 10 innings into a misleading projection of 20 earned runs over 90 innings.