[fix] Event Strength of Schedule crash and Simulation EPA column

[chondl]

Track 1 · standalone bug fix. Off master (a2cea55). No dependencies; order-independent relative to the other bug fixes. Recommended slot: 3 of 5 in Track 1 (#5 → #12 → #8 → #6 → #1). No companion tests. Conflict-free against every other open PR.

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Two fixes to the event page's live-simulation feature, both surfaced by
rigorously testing the Strength of Schedule and Simulation tabs against
several 2026 events. Both bugs are pre-existing: worker.ts and simulation.tsx
are unchanged on every branch relative to master.

1. Strength of Schedule renders blank (or NaN) when pre-event EPAs are identical

Symptom. On the Strength of Schedule tab the RP/Rank/EPA/Composite score
columns fail to populate. Two observed manifestations across events:

• score columns entirely blank;
• NaN in EPA Score and Composite Score (RP/Rank Score present).

Root cause. strengthOfSchedule() calls _strengthOfSchedule(data, simCount, false) (the "Before Event" pass) first. That pass computes epaSd, the standard
deviation of every team's pre-event start EPA, and builds a Gaussian to score
EPA-based schedule strength:

const distrib = Gaussian(0, (epaSd * epaSd * 5) / N);

Early in a season — before ratings diverge — every team at an event shares the
same cold-start EPA, so epaSd is 0, the variance is 0, and gaussian
throws Error('Variance must be > 0'). Because the worker's message handler
calls strengthOfSchedule(...) without await/catch, the throw becomes a
silent unhandled promise rejection inside the worker: no message is posted and
the table stays blank. A floating-point variant produces the NaN symptom —
with all EPAs equal, Math.sqrt(sum(x^2)/n - avg^2) occasionally takes the root
of a tiny negative rounding residue, so epaSd is NaN, gaussian does not
throw (NaN <= 0 is false), and every EPA percentile is NaN. Both are the same
degeneracy: EPA carries no schedule signal when all ratings are identical.

Fix. Floor the variance with || 1e-9, which treats both 0 and NaN as
falsy and substitutes a negligible positive variance; with deltaEPA == 0 the
CDF at the mean is 0.5, so every team gets a neutral 0.5 EPA percentile — the
correct answer when EPA is non-informative. Any real positive variance passes
through untouched, so events with diverged ratings are unaffected. Matches the
|| 0 fallback idiom already used throughout this worker.

2. Simulation tab shows EPA 0 for every team

Symptom. On the Simulation tab the EPA column reads 0 for all teams
(the predicted ranks, RP means, and percentiles are correct).

Root cause. simulation.tsx reads the team EPA as
teamEvent.epa.total_points.mean. That matches the APITeamEvent TypeScript
type, but not the runtime shape: the backend serves epa.total_points as a plain
number, so .mean is undefined and ?? 0 renders 0.

Fix. Read epa.breakdown.total_points — the same field the SOS tab and the
simulation worker already use — which is present at runtime.

Verification

Reproduced and confirmed fixed against completed 2026 events:

• epaSd == 0 event: before — Gaussian throws, SOS blank; after — all score columns populate (EPA Score 0.5).
• epaSd == NaN (float rounding) event: before — EPA/Composite NaN; after — populate (EPA Score 0.5).
• event with a genuinely non-zero EPA spread: EPA percentile 0.387 before and after — unchanged (fix is inert on the non-degenerate path).
• Simulation EPA column: 0 before, real per-team EPA after; predicted-rank distributions unchanged and still vary run-to-run.

[chondl]

Superseded — both fixes (SOS variance floor, Simulation EPA field) relocated to #5. Branch kept.