Hook & Leverage

Two targets. Leverage: the average absolute win-probability swing of a plate appearance in a game state, relative to an average PA. Penalty: xwOBA by the starter’s batter number after removing batter and pitcher quality.

• Every 2024–26 regular-season plate appearance (≈550k): inning, half, outs, runners, score, and Statcast per-pitch win probability
• xwOBA per PA (expected outcome for balls in play; actual for walks and strikeouts)
• Batter number and pitch count within each start; who started the game
• Keystone Stuff and batter-adjusted xwOBA allowed for relievers; days since last appearance
• The 2027 staff: Pittsburgh’s from the Winter Plan (decisions feed), any other club’s from its roster as it stands

• Leverage: mean |ΔWin%| by inning × half × outs × bases × score (±4), backing off to coarser states with fewer than 60 PAs
• Penalty: each starter PA’s xwOBA minus the batter’s and pitcher’s season quality (lightly shrunk), averaged by batter number
• Hook: a starter’s first two passes (shrunk toward average) + the league third-time step + his own excess, shrunk by the k its year-over-year reliability implies (k = n̄(1 − r)/r ≈ 2,000 PAs)
• One comparator for every call: the relief bar, the 2027 pen’s arms ranked 4–8 by skill plus a second-look penalty. Two times through at +.010, third time OK at −.005, a tandem only if also +.020 the first time
• Each gap carries a standard error (his sample, his own excess, the bar’s arms); a call within one of a line is a toss-up. Runs at the plan’s 2027 innings (an arm behind the rotation at its injury branch’s starter innings), over the wOBA-per-run scale measured on 2025–26 plate appearances (the Matchup Engine’s, ≈1.20)
• A starter whose 2026 ended on the injured list is also graded on 2024–25 alone, so the page can say whether his call rests on the injury season
• Platoon check: the relief bar re-weighted to the batters a starter’s third time presents (by his hand), each arm’s same-side/opposite-side split shrunk toward the league’s for his hand by the k its 2025 → 2026 reliability implies. Shown beside the calls, which stay on the unadjusted bar
• An arm in the 2027 pen with no 2026 relief record counts toward the bar as a league-average reliever, the same average every graded arm is shrunk toward
• Shortened outings (two times through and tandems, a tandem priced on the second and third times through) share a 60-inning bullpen cap with the batters development and health leashes hand over; the leashes come first, then the outings that save the most runs. Each injury branch’s new starter must fit what’s left
• 25 or younger: a development call with a leash (22 batters), its run cost, a first-two-pass goal that would take his third time off the hook, and a velocity goal
• Back from a major arm injury (a 60-day arm stint in 2025–26, or the season before lost to the IL): a starter sent a third time gets the same 22-batter leash, priced, and so does one whose shorter outing the cap can’t take (those starters get the cap before the run calls). Shorter arm stints and 25%+ innings jumps are shown on the row, not acted on
• Reliever skill: Keystone Stuff and batter-adjusted xwOBA (2026, with 2024–25 at half weight), weighted by what predicted the next season best (fit on 2024 → 2025, tested on 2025 → 2026); the 2027 pen is ranked into a ladder. Its ± counts the xwOBA sample and Stuff’s year-to-year noise (2025 → 2026), so neighbors in the ladder are often a toss-up
• Forward test: each starter’s expected third-time xwOBA built from 2024–25 alone (his passes, the league step and the shrinkage) against his 2026 third-time results
• Back-to-back fatigue: each back-to-back against his rested outings within 14 days (the table shows both means), called only on 5+ back-to-backs and a 0.5 mph drop

• The 60-inning bullpen cap is an assumption (about one extra relief inning every three games), not measured.
• No in-game signals such as velocity loss, command, or how hard the last inning was.
• Leverage measures what is at stake, not what comes next. A manager may save an arm for a bigger spot later.
• The adjustment for pitcher quality is season-level, so it misses how a starter is throwing that day.
• The three-batter minimum isn’t modeled. The platoon mix is checked (relievers face more same-side hitters than a starter’s third time through) but the calls use the unadjusted bar; it moves a bar a few points at most, and each club’s page names any call it would change.
• The 25-and-under development rule is a club choice the data can’t test: one season of third-time results doesn’t repeat.
• The 22-batter leashes (development and health) are club settings the model prices, not model outputs; whether a leash prevents re-injury is a medical question the data can’t answer.

• Runs allowed by batters faced the third time through, before vs. after adopting the rule
• Leverage alignment (skill vs. entry LI) by month during the season
• Reliever velocity and injury rates on back-to-back days