Reliever chain: Link 1 proves, Link 2 does not, and the premise inverts

The causal insight is right -- the game is a sequence and the matchup does
shift mid-game. The direction is backwards, measured on 93,663 plate
appearances from 1,238 games pulled free from statsapi.

LINK 1 PROVES. Starter batters-faced, point-in-time from his own prior
starts only, clustered on the pitcher: MAE 3.2226 -> 2.7990, delta
-0.4236, CI [-0.6006,-0.2731] at 0.9995 corrected for 107 tests, 1,706
starts across 204 pitchers. It finds the tail the chain needed -- early
exits are a 23.2% base rate, model-flagged starts are 34.0% early, lift
+10.8pp.

Scope correction inside Link 1: the order specifies fatigue x GAME
SCRIPT, but game script is not available at grade time -- whether he gets
hit tonight is the thing being projected, not an input to it. Only the
workload half is measured; the in-game half is recorded as a live feature,
out of scope, rather than quietly folded in.

LINK 2 DOES NOT PROVE, twice over. Model accuracy 17.2% vs an 8.6%
baseline -- doubling it sounds good and is not, since naming a specific
arm is wrong five times in six. And structurally the entity is the
BULLPEN: 39,629 post-starter plate appearances across 30 clubs is 30
readings, below the 40-cluster floor, the same permanent ceiling as park
geometry and team defence. LINK 3 NOT RUN, per the order's own rule.

THE PREMISE IS REFUTED, and this chains on nothing so it was safe to
measure:

  vs STARTER  n=48,492  hit rate 0.2444 +/-0.0038
  vs BULLPEN  n=35,760  hit rate 0.2373 +/-0.0044

The pen is 0.7pp HARDER. The specific effect the chain exists to exploit
-- early exit making later at-bats softer -- is +0.0010 on 35,760 PAs. A
well-powered null, not a sample problem.

What IS real is times through the order: TTO1 0.2351 -> TTO2 0.2515 ->
TTO3 0.2518. A starter does decay as the lineup sees him again, but that
advantage is SURRENDERED when he leaves, not extended -- the pen is
harder than his second and third time through. A modern bullpen is a
queue of fresh specialists throwing one inning each; there is no tiring
arm to punish.

So the insight survives inverted, and Link 1 stays valuable for the
opposite reason it was built: a likely early hook predicts the hitter
LOSES his third-time-through look (0.2518 -> 0.2373 on that PA). The
mispricing is on hitters who get an EXTRA look at a starter going deep.

BUILT: predictionGate.js + tests -- the two-part gate for a continuous
prediction. factorGate binarises outcomes for Brier, which would destroy
a target like batters faced. Same discipline, same THEATER verdict, real
scale.

PRE-REGISTERED NOT RUN: Link 2' using a PA-weighted bullpen AGGREGATE
rather than a named arm. Recorded rather than substituted in -- running
Link 3 on a swapped-in Link 2 is the assumed-link failure the order
forbids. Given the premise result its expected value is now low.

PARALLEL TRACK logged: total_bases n=948 pooled, BOMBER x TB 340, short
by 160. Sample-readiness only, not a verdict.

Counter and frozen clusters byte-identical.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01W1sivYNqY2TS5ftykmHBU9
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# The reliever chain — Link 1 proves, Link 2 does not, and the premise inverts
**The causal insight is right: the game is a sequence and the matchup does shift
mid-game. The direction is backwards.** Measured on 93,663 plate appearances from
1,238 games, the bullpen is *harder* than the starter, not softer.
---
## The chain, link by link
### LINK 1 — starter pull timing: **PROVES**
Target is batters faced, because that is what decides how many of a hitter's
plate appearances come against the starter rather than the pen. Point-in-time:
each start predicted only from that pitcher's starts strictly before it, shrunk
toward the league mean by prior-start count. Baseline is the league mean — the
naive "a starter goes about six."
```
1,706 starts · 204 pitchers · clustered on the pitcher · 107 cumulative tests
MAE 3.2226 (baseline) -> 2.7990 (model) delta -0.4236
CI [-0.6006, -0.2731] at 0.9995 VERDICT: PROVES
```
It finds the tail, which is what the chain needed: early exits (≤20 batters
faced) occur at a **23.2%** base rate, and among model-flagged starts they occur
at **34.0%** — lift **+10.8pp**.
**Scope correction made here:** the order specifies fatigue profile × *game
script* ("getting hit → pulled early"). Game script is not available when a prop
is graded — whether he gets hit tonight is the thing being projected, not an
input to it. Using it would be reading the answer. Only the fatigue/workload half
is measured above; the in-game half is a LIVE feature, recorded as out of scope
rather than quietly folded in.
### LINK 2 — reliever identity: **NOT PROVEN**, on two independent grounds
Predict which arm throws a given post-starter plate appearance. Baseline: the
team's most-used reliever to date. Model: the arm that team has most often used
*in that inning* to date — the cheapest expression of bullpen role.
```
39,629 post-starter plate appearances · 30 bullpens
baseline accuracy 8.6% -> model accuracy 17.2%
VERDICT: PENDING_SAMPLE — 30 independent clusters < 40
```
1. **On merit.** Doubling the baseline sounds good and is not: naming a specific
arm is **wrong five times out of six.**
2. **Structurally.** Bullpen usage is a team-level process — same manager, same
arms, same roles all season — so the entity this prediction rides on is the
club, and there are 30. Row count cannot create replication that does not
exist. **The same permanent ceiling as park geometry (30 venues) and team
defence (26 teams).**
### LINK 3 — shifted matchup: **NOT RUN**
Per the order's own discipline, a link that does not prove does not feed the
next. Link 3 needs the reliever's profile, and Link 2 cannot say whose profile it
is.
---
## The premise, tested directly — because that chains on nothing
This required no unproven link, so it was safe to measure, and it is the finding
that matters most:
| | n | hit rate per PA | ±95% |
|---|---|---|---|
| vs **STARTER** | 48,492 | **0.2444** | 0.0038 |
| vs **BULLPEN** | 35,760 | **0.2373** | 0.0044 |
| bullpen \| starter exited early | 14,672 | 0.2379 | 0.0069 |
| bullpen \| starter went normal | 21,088 | 0.2369 | 0.0057 |
**The bullpen is 0.7pp HARDER than the starter**, and the intervals barely
overlap. The specific effect the chain was built to exploit — an early exit
making later at-bats softer — is **+0.0010, indistinguishable from zero on 35,760
plate appearances.** That is a well-powered null, not a sample problem.
### What IS real: times through the order
| | n | hit rate |
|---|---|---|
| TTO 1 | 21,596 | 0.2351 |
| TTO 2 | 18,426 | **0.2515** |
| TTO 3 | 8,278 | **0.2518** |
A starter does decay as the lineup sees him again: **+1.6pp from first look to
second.** But that advantage is **surrendered when he leaves, not extended**
the pen (0.2373) is harder than the starter's second and third time through
(0.2515).
The mechanism is a modern bullpen: a queue of specialists throwing max effort for
one inning each, fresh, often handedness-matched. There is no tiring arm to
punish.
### The insight survives, inverted
The sequence framing is correct and the edge is real — it just points the other
way. **A hitter's soft spot is a starter still in the game on the third time
through, and an early hook takes it away.** So Link 1 remains valuable, for the
opposite reason it was built: flagging a likely early exit predicts that a hitter
*loses* his third-time-through look (0.2518 → 0.2373, a 1.45pp shift on that
plate appearance) — a downgrade signal, not an upgrade.
That is also market-relevant in the way the order wanted, with the sign flipped:
if a line is set on the starter's matchup, the mispricing is on hitters who will
get an *extra* look at a starter going deep.
---
## Built
- `src/services/model/predictionGate.js` (+ tests) — the two-part gate for a
CONTINUOUS prediction. `factorGate` binarises outcomes for Brier, which would
destroy a target like batters faced. Same discipline: movement AND out-of-sample
improvement, paired bootstrap, clustered, cumulative-corrected. Names THEATER
the same way.
- `scripts/ingest-game-sequences.js` — per-PA batter/pitcher/hand/inning/result
plus boxscore exit lines, free from statsapi. 1,238 games cached.
- `scripts/link1-pull-timing.js`, `scripts/link2-reliever-identity.js`.
## Pre-registered, NOT run
**Link 2 — bullpen AGGREGATE instead of a named arm.** Naming the arm fails, but
a PA-weighted aggregate of the pen's contact-allowed and handedness profile may
be knowable, and the hitter×bullpen unit would have real replication where the
bullpen alone has 30. This is recorded rather than substituted in, because
running Link 3 on a swapped-in Link 2 is precisely the assumed-link failure the
order forbids. Given the premise result above, its expected value is now low.
## Parallel track — total_bases per-archetype (logged, not run)
Sample audit only: `total_bases` settled n=948 pooled; BOMBER × TB **340**,
short by 160 against the gate. No archetype slot is testable yet. Per the S88
lesson, this is a *sample-readiness* note and not a verdict — and per
`specs/per-archetype-grade-bands.md`, the grade does not yet separate within any
archetype on hits, so a TB rescale would face the same second blocker.
Counter and frozen clusters byte-identical.