The 2026-09-30 n=100 pooled review is underpowered: n_eff is about 39, and it can only detect a 20-point edge

[eaitbrahim]

#359 schedules the pooled forward-trades review for 2026-09-30 at a floor of n=100. That floor treats 100 pooled trades as 100 observations. They are not, because the signals fire in herds and the outcomes are correlated.

Raised after reading the Keel Quant Lab modelling note against #368 and #359 — the note supplies the power arithmetic, #359 supplies the schedule, and neither states the consequence of putting them together.

Method

Reconstructed the live rule on ONE_HOUR bars with its own parameters — entry_lookback: 40, adx_period: 14, adx_threshold: 25, atr_period: 20, atr_stop_mult: 2, target_rr: 6 — resolving each entry to win/loss by first touch, across 25 products over 5 years of cached candles.

It validates against keel's own published measurement, which is what makes the rest usable:

	reconstruction	#359
signals per asset-year	46.7	49.4
median n per rule-product	241	268

(Omitting the ADX gate gives 70.6/asset-year — the gate accounts for the difference, and its absence would have inflated everything downstream.)

Result

episodes (UTC days with >=1 signal):   1,355
size-weighted mean episode size k:      8.43
largest episode:                          24 assets firing the same day
ICC of outcomes within an episode:     0.212
design effect DEFF = 1 + (k-1)*rho:     2.58

n_eff at n = 100 pooled:                  39
detectable edge at 80% power:          20.0%    (12.4% if the trades were independent)

When a breakout triggers it triggers on about eight assets the same day, and those trades then win or lose together. A pooled sample of 100 carries roughly 39 independent observations.

What that means on 30 September

Detecting an edge at 80% power would need p ~ 21.4% + 20.0% = 41.4%. The reconstructed win rate is 14.9%.

The review is therefore near-certain to return "no edge", and that is the correct answer — but it must not be written up as "we measured no edge at n=100". The honest statement is "at n=100 pooled this test can only see an edge of 20 points or more." Those read the same to most audiences and mean very different things, and #304 / #348 have already committed keel to stating its non-results precisely.

What the floor would have to be

to detect	n_eff	pooled trades
12.4 pts	101	259
7.5 pts	275	708
5 pts	618	1,593
—	100	258 — what "n=100" is assumed to deliver

Raising the pooled floor from 100 to ~258 makes n_eff equal what everyone already believes n=100 means. That is the one-line change; min_trades already exists as a setting (keel/commands/rules.py).

Caveats, stated

1. DEFF is a lower bound. Clusters are UTC days. These are trend trades held for many hours, so correlated outcomes plausibly persist across day boundaries — the true design effect is larger and n_eff smaller.
2. ICC is from backtest outcomes, the only 5-year sample available. Forward paper outcomes may differ.
3. k scales with the pool. DEFF 2.58 reflects ~25 products. A narrower live pool clusters less and loses less; the correction is not a constant.

Prerequisite

None of this is reachable yet: keel-paperhourly.db has 0 recorded trades, and every detected setup is being vetoed (#426). The power question only becomes live once accrual starts — but the floor should be corrected before the review, not after it reports.

[eaitbrahim]

The binding constraint is rail 14, not the power calculation

The subscription is attested at Basic — $500/month of fee-free BUY notional (#426). That caps throughput, and it binds long before statistical power does.

Months to accrue the 258 pooled trades this issue asks for, at $500/month:

configuration	notional/trade	months to 258
paper-hourly as it stood ($10.5k synthetic equity)	$4,212	2,173	181 years
hourly at live-sized equity (~$450, after the #426 fix)	$190	98	8.2 years
live daily turtle (~$450 equity)	$32	17	1.4 years
live DCA (budget_usd: 25)	$25	13	1.1 years

So the #426 fix changes the number from impossible to 8 years. It does not rescue the schedule.

This inverts #359's central argument. That announcement framed the hourly clock as a 23x acceleration in evidence collection — 2.15 to 49.4 signals per asset-year — on the premise that signal frequency was the bottleneck. It is not. Under a Basic subscription the bottleneck is the monthly fee-free allowance, and generating 23x more signals does not help when the allowance funds a fixed dollar volume per month regardless of how many opportunities appear.

Worse, the two interact badly: the hourly clock shortens the stop 5.8x, which lengthens each position by the same factor (f_N = risk_pct / s), so each hourly trade consumes ~5.8x more of the allowance than a daily one at equal equity. Faster signals, proportionally fewer affordable trades.

What this means for the review

Three separate reasons the 2026-09-30 date cannot produce a properly-powered result, in increasing order of how hard they are to fix:

1. Zero accrued — every setup vetoed until today (paper-hourly has recorded zero trades: every setup is vetoed, and the sizing exceeds the exposure cap by design #426).
2. n=100 is n_eff ≈ 39 — the original finding here; the floor needs to be ~258.
3. 258 is ~8 years away at Basic, even after the paper-hourly has recorded zero trades: every setup is vetoed, and the sizing exceeds the exposure cap by design #426 fix.

(2) is a one-line change to min_trades. (3) is not a settings problem. It is a choice between a higher subscription tier (Preferred $29.99/mo → $10,000/mo; Premium $299.99/mo → uncapped), accepting a much longer horizon, or accepting that the review answers a narrower question than "does this rule have an edge".

The finding that may make the question moot

From #426: inside the fee-free allowance these rules sit within half a point of break-even (κ = 0.04R, p_be = 14.88% vs a reconstructed 14.9% win rate); outside it they are 14 points underwater (κ = 1.04R, p_be = 29.18%).

If that holds up under forward measurement, the interesting question stops being "is there an edge?" and becomes "is the fee-free allowance large enough to matter?" — which is an arithmetic question about subscription tiers, answerable today, and does not need 258 trades.

I would put that ahead of raising the pooled floor.