Defense and bullpen rest don't fix game totals

The question

Our game totals and moneyline don’t yet beat the simplest possible guess: the league-average total, and the home team winning about 53% of the time. Two missing inputs looked like the obvious fix: how good each team’s defense is, and how tired each bullpen is.

Defense: real, but too small to see

• On 6,902 team-games from 2025 and 2026, a team’s defense does predict the runs it allows, even after accounting for its pitchers and the hitters it faced. Each run of measured defense saved about 0.87 runs, close to the 1.0 theory says.
• Out of sample, the gain was small and its interval touched zero.
• On the replayed games, adding defense made the served total slightly worse (typical miss 4.623 runs against 4.611).

Why it can’t help yet: the two defenses together move a game’s expected total by about 0.28 runs, while game-to-game noise in a total is about 4.6 runs. Seeing a gain that size reliably would take on the order of 13,000 games.

Bullpen rest: no signal at all

Relief pitches thrown in the previous one or three days, and the number of arms who pitched back-to-back, said nothing about runs allowed in the 7th inning and later. If anything, a tired pen allowed slightly fewer late runs. On the replay, the term made both markets a touch worse.

What it means

Neither change shipped. Game totals and the moneyline stay Research only: we show them as projections, never as plays. Bullpen fatigue is still shown on game pages as context, because it is useful to know, but it doesn’t move a number.