How PQS works
Full details in the paper: Pitch-Quality Surplus (PQS): measuring hitter value net of pitch quality · code: zenodo.21972304
The problem
wOBA, xwOBA, and wRC+ all condition on what the hitter did. None of them condition on what the pitcher threw.
A home run off a 99 mph fastball with late movement is treated identically to one off an 88 mph hanging
slider — but those are not the same skill.
Expected run value, pitches only
We train a gradient-boosted model to predict Statcast's delta_run_exp (the run value of a pitch's
outcome) using pre-contact information only:
- release speed, spin rate, extension
- movement: horizontal and induced vertical break
- location: plate_x, plate_z
- context: ball/strike count, handedness platoon (stand × p_throws), pitch type
Leave-one-year-out scoring
To score the 2025 season we train on 2022–2024 and predict every 2025 pitch — so no hitter is ever graded by a
model that saw him. This repeats for each season (four models total).
pqs_pitch = delta_run_exp − expected_rv(pitch)
The metrics
| Metric | Meaning |
|---|
| PQS | Counting runs of surplus — actual run value above what his pitches implied |
| PQS/100 | Surplus per 100 pitches faced (rate stat) |
| PQS+ | PQS/100 scaled so league average = 100 |
| TPS/100 | Surplus per 100 against the toughest tercile of pitches — who produces vs. elite stuff |
| MPS/100 | Surplus per 100 against the softest tercile — how fully he punishes mistakes |
Fantasy translation
- Underrated board: high PQS+ with lagging surface stats → buy-low / waiver targets.
- Overrated board: negative surplus on regulars → sell-high / fade.
- Tough-diet specialists: TPS leaders → keepers for playoff-stretch matchups.
Honest limitations
- Expected RV is context-light by design: it knows the pitch, not the park, umpire, or baserunners.
- Diet is partly schedule-driven (facing the Dodgers helps nobody's PQS) — that's the point, but it means small-sample PQS is noisy.
- We publish qualification thresholds (1,500 pitches for public boards) precisely because below them the metric lies.