Run Expectancy and RE24: Valuing Every Base-Out State

Every half-inning of baseball is a position you can describe in two numbers: which bases are occupied, and how many outs there are. There are eight ways to arrange the runners — from empty bases to bases loaded — and three out totals, zero, one, and two. Multiply them and you get exactly twenty-four distinct situations. Baseball calls them base-out states, and the entire modern understanding of in-game value is built on a single table that puts a number next to each one.

That number is run expectancy: given a base-out state, how many runs does the average team go on to score from that point to the end of the inning? Answer it for all twenty-four states and you have the run-expectancy matrix — the quiet, unglamorous backbone underneath sacrifice-bunt math, stolen-base break-evens, and a play-by-play hitting stat called RE24. It is, in a real sense, the periodic table of run scoring.

The twenty-four base-out states

Start with the bookkeeping, because the structure is the whole point. The bases can be empty; a runner can stand on first, second, or third alone; runners can occupy any pair (first-and-second, first-and-third, second-and-third); or the bases can be loaded. That is eight configurations. Each of those can occur with nobody out, one out, or two outs. Eight times three is twenty-four, and every legal moment of an inning — before the third out ends it — lives in exactly one of those cells.

The trick is that we don’t guess what each cell is worth. We measure it. Take years of recorded play-by-play, find every time a team was in, say, a runner-on-second, one-out state, and average how many runs that team scored for the rest of that inning. Do it for all twenty-four states and the matrix fills itself in from history rather than intuition. The values shift a little with the run environment — a high-offense season pushes every cell up, a pitching-dominated one drags them down — but the shape stays remarkably stable.

Reading a representative matrix

Here is a small, deliberately rounded version of the matrix. Treat these as representative figures for a typical modern run environment — the exact decimals vary by season and by source, and you should never quote them as a specific year’s official numbers. The point is the pattern, not the third decimal place.

Two regularities jump out, and they govern everything that follows. First, reading across any row, run expectancy falls hard as outs pile up — outs are the scarcest, most precious resource in the inning, and burning one roughly halves what you can expect to score. Second, reading down any column, advancing runners raises the number, but never by as much as an out costs. A runner on second with nobody out (about 1.10) is worth more than a runner on first with nobody out (about 0.85), but the gap is far smaller than the cliff you fall off by recording an out.

RE24: crediting a play by what it changed

Once you have the matrix, you can value any single play with one subtraction. RE24 — the “24” is a nod to the twenty-four states — scores a play as the run expectancy of the state it created, minus the run expectancy of the state it started in, plus any runs that actually crossed the plate during the play. In words: a play is worth how much it improved your run-scoring outlook, plus whatever it banked immediately.

The beauty of the construction is that it credits the things batting average and even wOBA ignore: a walk with the bases loaded forces in a run and is worth a great deal; the same walk with two outs and nobody on is worth a sliver. RE24 sees the difference because it knows the state. Summed over a season, a hitter’s RE24 tells you how many runs better or worse than average he was, given the exact situations he actually batted in.

A worked example

Make it concrete with a clearly hypothetical play, using the representative numbers above. Suppose a hitter comes up with a runner on first and nobody out — a state worth roughly 0.85 expected runs. He doubles into the gap; the runner on first comes around to score, and the batter ends up on second. The new state is a runner on second, nobody out, worth about 1.10, and one run has already scored.

Run the arithmetic: RE24 equals (1.10 − 0.85) plus the 1 run that scored, which lands at about +1.25 runs of credit for that one swing. That is an enormous number for a single play — which is exactly right, because a run-scoring double with nobody out is one of the best things a hitter can do. Now flip it. Suppose instead the hitter, with that same runner on first and nobody out, lays down a textbook sacrifice bunt: the runner moves to second, the batter is out, and the state becomes a runner on second with one out, worth about 0.65. RE24 is (0.65 − 0.85) plus zero runs — roughly −0.20. The “successful” sacrifice handed back two-tenths of a run.

Why the sac bunt usually loses

That negative number is not a fluke of the example; it is the general rule, and it is the whole reason the sacrifice bunt nearly went extinct. The bunt trades a high-expectancy state (runner on first, nobody out) for a lower one (runner on second, one out) because the out it spends costs more than the base it buys. The run-expectancy matrix turned a century of accepted strategy into an arithmetic mistake, visible the moment you put the two cells side by side. Stolen bases get the same treatment: a steal raises expectancy modestly, a caught stealing torches it, and the break-even success rate falls straight out of the matrix.

RE24 is what happens when you apply that logic to every event in a game rather than just bunts, building a player’s seasonal value one base-out subtraction at a time.

RE24 versus context-neutral stats and WPA

It helps to place RE24 between two neighbors. On one side sit context-neutral stats like wOBA, which assign every double the same value no matter when it happened — cleaner for measuring a hitter’s underlying skill, precisely because they strip out the situation. RE24 deliberately keeps the situation: it rewards the bases-loaded double over the bases-empty one. That makes it a better account of what a player’s plate appearances were actually worth, and a worse predictor of future performance, since being handed high-leverage spots is not a repeatable skill.

On the other side sits Win Probability Added. RE24 values plays in the currency of runs; WPA values them in the currency of wins. A two-run double in a 12–1 blowout has a healthy positive RE24 — runs are runs — but a trivial WPA, because the game was already decided. The matrix doesn’t know the score or the inning; it only knows the base-out state. That is its strength for measuring run production and its blind spot for measuring drama.

The bottom line

The run-expectancy matrix is twenty-four numbers that quietly answer most of baseball’s strategic questions. RE24 is what you get when you let those numbers grade the game one play at a time: every event is worth the change in expectancy it produced, plus the runs it scored. It is why the bunt lost its job, why a bases-loaded walk is a real event and a meaningless-spot walk nearly isn’t, and why “how many runs is this worth?” finally has a defensible answer. Learn to read the matrix and you are reading the language the rest of the sport’s strategy is written in.

Sources & Further Reading

• Retrosheet — the play-by-play record from which run-expectancy matrices are computed.
• FanGraphs — RE24 leaderboards and the run-expectancy framework behind them.
• Tom Tango, Mitchel Lichtman & Andrew Dolphin, The Book: Playing the Percentages in Baseball — the canonical treatment of base-out states and run values.
• SABR — historical and methodological writing on run expectancy.