What is Run Expectancy? Definition, Formula, and Example
Run Expectancy (RE) is a sabermetric metric that calculates the average number of runs scored from a specific base-out state to the end of an inning.
What is Run Expectancy?
Run Expectancy (RE) is a foundational sabermetric concept that quantifies the exact mathematical value of every base-out state in a baseball inning. It calculates the average number of runs that score from a specific situation—such as a runner on second base with one out—until the end of that inning. By using historical data to map out the run-scoring probability of all 24 possible base-out states (8 base states multiplied by 3 out states), analysts can determine the exact run value of any offensive event or the run-prevention value of any defensive play.
How it is Calculated / Measured
To calculate Run Expectancy, analysts aggregate decades of play-by-play data—often millions of half-innings—to find the average runs scored from each of the 24 base-out states. The base states are: bases empty, runner on first, runner on second, runner on third, runners on first and second, first and third, second and third, and bases loaded. Each of these 8 states is paired with 0, 1, or 2 outs.
The RE matrix (often called the RE24 table) is generated by taking the total runs scored from a specific state to the end of the inning, and dividing it by the number of times that specific state occurred. The Run Expectancy of a plate appearance is calculated by subtracting the RE of the base-out state before the pitch from the RE of the base-out state after the play, plus any runs that scored on the play.
Formula: Run Value = (RE_after + Runs_Scored) - RE_before
Worked Example
Using a standard modern MLB RE24 matrix, the Run Expectancy for a bases-empty, no-outs state is approximately 0.461 runs. The Run Expectancy for a runner on first base with no outs is 0.831 runs.
If a batter hits a leadoff single, the base-out state changes from "0 outs, bases empty" to "0 outs, runner on first." The run value of that single is 0.831 - 0.461 = 0.370 runs.
Now consider a sacrifice bunt. The batter moves the runner from first to second, but makes an out. The state changes from "0 outs, runner on first" (0.831 RE) to "1 out, runner on second" (0.699 RE). The run value of this play is 0.699 - 0.831 = -0.132 runs. This mathematical proof is exactly why modern front offices forbid bunting; giving up an out costs the team over a tenth of a run on average.
Why it Matters
Run Expectancy is the mathematical engine powering advanced analytics. It directly drives Win Probability Added (WPA) and Run Expectancy on the 24 base-out states (RE24). Front offices use RE24 to evaluate hitters independent of their teammates' failures or successes; a player who consistently moves the needle from low-RE states to high-RE states provides immense offensive value. For fantasy baseball and DFS players, understanding RE states clarifies why managers pinch-hit certain players in high-leverage spots, and why elite on-base skills directly correlate to RBI opportunities.
Limitations / Common Misconceptions
The primary limitation of Run Expectancy is that it is context-neutral and based on league averages. The RE matrix assumes an average lineup follows the current batter. If Aaron Judge is batting followed by the bottom of the Yankees order, the actual run expectancy is lower than the chart suggests. Conversely, if the top of a high-powered lineup follows a walk, the actual expectancy is higher. RE also does not account for the specific pitcher on the mound; it measures the mathematical state, not the personnel.
A common misconception is that Run Expectancy predicts future games. RE is a historical average of past events used to assign objective value to specific plays, not a crystal ball for predicting exact runs in tomorrow's game.
Related Terms
In Legends Deck
In Legends Deck, Run Expectancy formulas heavily influence our in-game simulation engine. When a player's card triggers a specific outcome, the resulting mathematical impact on the inning's run probability mirrors historical RE24 matrices. High-OBP players carry higher in-game valuations because they consistently shift the game into higher Run Expectancy states, giving your virtual lineup the exact statistical edge real MLB managers rely on.