Baseball Must Balance

Before baseball events are classified, attributed, or valued, the underlying game state must balance. A runner who holds first, second, or third base holds one, two, or three runner-bases. A runner who completes the circuit banks four runner-bases as a run. Bases are conserved in the accounting sense: at every resolved-play boundary, the runner-bases brought into the play plus the signed runner-base change during the play must equal the runner-bases banked as runs, erased when runners are retired, or carried forward by unretired runners. Thus each play satisfies Bₖ₋₁ + gₖ = 4rₖ + eₖ + Bₖ. Summed over a half-inning, this local balance telescopes to I + G = 4R + S + E, and therefore NRB = G − E = 4R + S − I. Here I and S are the opening and closing runner-base totals, G is signed runner-base change before disposition, R is runs, and E is runner-bases erased by retirements. NRB is net runner-bases. With offense assigned the positive sign, every offensive entry also has an equal-and-opposite entry in the opponent-facing account. None of these quantities depends on whether a play is later described as a particular batting, baserunning, pitching, or fielding event. Those classifications belong to a later layer. The claim is not that this identity evaluates players or predicts wins. The claim is that baseball statistics should begin with a primitive, auditable ledger of what the game produced and extinguished before assigning names, responsibility, or value.