From a carried-forward number to AFE

The playing strength shown on these pages is changing. Up to and including run T-0154, each entry carried a "carried-forward figure". Newer entries will show AFEAFE Anchor-forwarded Elo: an estimate of a Coherent build’s strength on the scale of the latest anchoring, carried forward by the measured gains of the runs since. An estimate, not a measurement. in its place, the anchor-forwarded EloElo Strength difference to the opponent, estimated from the games, with a 95-percent half-width where the oracle reported one. Never an absolute rating., as a centre with a ninety percent model interval. The old entries stay exactly as they were published. This post explains what was wrong with the old number, how AFE is computed, and what it does and does not say.

The old number

The only measurement of absolute strength is the anchoring. One version of Coherent plays a set of engines from other projects whose ratings are published, at two minutes per game plus one second per move. The result is a value A, anchored to those published ratings. The last completed anchoring measured version 0.1.118 on 2026-09-29, outside the formal registration procedure: 3455 ± 52.

Every later version was carried forward from there. The old rule added the gains of all later passed versions, each measured in the long oracle stage against its own predecessor:

F = A + ΣLᵢ

For run T-0154 this gave 3455 + 261.65 ≈ 3717.

What was wrong with it

Two things, of very different size.

The conversion factor. The gains Lᵢ are measured in self-play, against the engine's own predecessor, at forty seconds per game plus four tenths of a second per move. The anchor is measured against other engines at a longer time control. Our own anchorings show that the same improvement counts for less against other opponents than in self-play. The old rule converted one into the other with a factor of one. Comparing consecutive anchorings with the self-play gains between them shows a factor of about 0.7. This is by far the larger effect: for T-0154 the difference between the two estimates is about ninety Elo, about seventy-eight of them from the factor of one and about thirteen from the stopping correction.

The stopping rule. Each Lᵢ comes from a sequential test that stopped as soon as it reached its upper bound. A test that stops on good luck reports a gain that is too large on average. A simulation of these tests puts this bias at about one to two and a half Elo for real gains, and higher when the true gain is near zero. We apply a flat two Elo per run as a simplified correction.

How AFE is computed

Let n be the number of passed runs with a long-stage gain since the last anchoring, up to and including the run shown:

centre = A + τ · (ΣLᵢ − 2n)

• A is the most recent completed anchoring of this version or one of its predecessors.
• Lᵢ are the long-stage gains of those runs, in logistic Elo.
• 2n is the flat stopping correction, two Elo per run.
• τ = 0.703 converts self-play gains into the scale of the anchor. It is estimated from five sections between anchorings that used the same set of opponents, as the sum of the unrounded anchor differences divided by the sum of the corrected gains in between. It is estimated on the same corrected sums it is later applied to, so the two match.

The uncertainty is a standard deviation SD built from four parts, treated as independent:

SD² = (h_stat / 1.96)² + (0.10 · (ΣLᵢ − 2n))² + (τ · H / 1.96)² + n · 5²

• h_stat is the inner statistical error of the anchoring, from its games and the listed ratings (±8 for 0.1.118).
• 0.10 is the assumed uncertainty of τ, applied to the whole sum, because one wrong τ affects every step in the same direction.
• H combines the half-widths of the long-stage gains, the oracle's own measurement error.
• 5 Elo per run is an assumed allowance for everything the model leaves out.

The page shows centre ± 1.645 · SD. This is a nominal ninety percent model interval for the value on the anchor scale: if the model holds, it contains that value nine times in ten. A later anchoring has its own measurement error, which has to be added when the two are compared. If a version is itself anchored, the page shows that anchoring unchanged, with its original band and status.

An example

For T-0154 the inputs are A = 3455, h_stat = 8, ΣLᵢ = 261.65, n = 9 and H = 24.72:

centre = 3455 + 0.703 · (261.65 − 18) ≈ 3626, SD ≈ 30.2, interval [3577; 3676]

This is a model calculation, not a measurement. The old number was 3717. Most of the difference comes from the factor of one.

What it does not say

AFE is an estimate, not a measurement. Four limits belong next to it:

• The scale itself. Anchoring transfers results against other engines to a value anchored to the ratings of a public rating list. That transfer carries a set reservation of plus or minus fifty-one Elo. It comes from an earlier calculation with two anchors, it is not measured, and no empirical ninety-five percent coverage is claimed for it. It is the same for every version and is stated separately rather than inside the interval.
• Coverage is not checked. Whether ninety percent of these intervals really hold can only be tested over time, against anchorings compared with forecasts frozen in advance. The page says: "Its coverage has not been checked."
• Large jumps. τ is one number for very different kinds of change. After a run that gained more than fifty Elo in the long stage, the estimate is marked as uncertain until the next anchoring. Because of run T-0153, this applies to every new entry until the next anchoring.
• A change of opponents. If an anchoring uses a different set of opponents, its value is not compared with earlier ones and is not used to re-estimate τ until a measurement bridges the old and the new set.

There is also a correction on the record. On the day the method was set, τ was first given as 0.673. That value divided by the uncorrected sums of the gains. Because τ is applied to corrected sums, it was re-estimated on the same basis before publication and became 0.703. The three independent reviews of the method, each by AI models of a different family and each tasked with refuting the method, examined the version with 0.673; the re-estimate was recalculated, not reviewed again by another model family.

What changes on the site

Each passed run from T-0155 on shows two numbers. The first is measured: the long-stage gain against the predecessor, as before, marked as coming from a stopped test. The second is estimated: AFE, with its interval and the notes above. When a new anchoring arrives, it becomes the new A and the sum starts again from zero. The parameters are re-estimated only if that anchoring used the same opponents as the one before or is bridged to it.

Earlier entries up to T-0154 keep the number they were published with. They are part of the record, and the record is not rewritten.