How ratings work · Manifold Chess Club

Short version. Each Manifold rating pool keeps a separate rating for every player who's appeared in it. New players start at 1200. After each game, both players' ratings update by K × (actual − expected). The K-factor depends on how many games you've played and how strong you are: 40 while provisional, then 32 / 24 / 16 by rating band.

The math is the same Elo formula chess has used since 1960. We keep it deliberately simple — no bonus-point or inactivity-decay layers — so the numbers are reproducible by hand or a spreadsheet.

The basic Elo idea

Before each game, the system computes each player's expected score — their probability of winning against the specific opponent in front of them, based on the rating difference.

expected = 1 / (1 + 10^((opp_rating − your_rating) / 400))

A few reference points:

Rating gap	Higher-rated's expected score
Equal	0.50
+100 points	0.64
+200 points	0.76
+400 points	0.91
+800 points	0.99

After the game, your rating moves by K × (actual − expected), where actual is 1 for a win, 0 for a loss, or 0.5 for a draw. Beating an opponent the system thought you should beat earns almost nothing; beating someone it thought would crush you earns a lot.

The K-factor

K controls how fast ratings move. A higher K means each game shifts your rating more.

Stage	K
Provisional — first 25 games in the pool	40
Post-provisional, rating below 1600	32
Post-provisional, rating 1600–1999	24
Post-provisional, rating 2000+	16

The idea: newcomers move fast (K=40) so the system can find their true level within their first few events. After 25 games, the provisional-K shuts off and the rating-band K kicks in. Lower-rated players still move faster than high-rated experts — a common pattern across rating systems.

Worked example

A 1500-rated player (40 games played) beats a 1700-rated player (60 games played).

Lower-rated player (1500, K=32)

Expected score: 1 / (1 + 10^((1700−1500)/400)) ≈ 0.24
Actual: 1.0 (won)
Delta: 32 × (1 − 0.24) ≈ +24 points
New rating: 1524

Higher-rated player (1700, K=24)

Expected score: 0.76
Actual: 0 (lost)
Delta: 24 × (0 − 0.76) ≈ −18 points
New rating: 1682

Two things to notice:

Each player uses their own K-factor. The lower-rated player moved +24; the higher-rated player moved −18. Total rating points are not conserved across the game when K's differ.
Upsets pay more. Beating a stronger player gives a big jump; beating a much weaker one gives almost nothing. Same math in reverse on the losing side.

Per-pool ratings

Every Manifold rating pool keeps its own per-player rating. If you play in two different pools, you have two separate ratings — they don't share history. Each club, series, or league tracks its own players without bleeding ratings across communities.

Your rating in a pool starts at 1200 the first time you enter that pool. Subsequent events in the same pool update from there. There's a hard floor of 100 — your rating can't drop below that no matter what happens, so a long losing streak doesn't produce a meaningless negative number.

Optional layers we don't include

Manifold's math is a deliberately compact Elo. Some rating systems layer additional rules on top; ours doesn't. So nobody is surprised:

No upset bonus points. Some rating systems award extra bonus points when a much-lower-rated player beats a much-higher-rated one. We don't add those — the K-factor differential already gives upsets a substantial swing, and the extra layer adds complexity without much practical benefit at club scale.
No inactivity decay or peak floors. Some rating systems adjust ratings after long breaks (decay, or floor at a fraction of historical peak). We don't. Your rating sits exactly where you left it, however long you've been away.

If a pool needs federation-grade ratings — for example for official tournament reports or junior-tournament qualification — we can run that pool alongside an official sanction from the relevant federation. Manifold's number remains a separate internal rating; the federation's number is the authoritative one. Get in touch via the organizer support guide.

What this means in practice

Play three or four games at a club tournament — you'll see your pool rating settle within ±50 of where you "belong" pretty quickly.
Lose to a 1900 when you're 1500? Almost no rating change (the system expected the loss).
Beat a 1900 when you're 1500? Big jump for you, big drop for them.
Provisional players' ratings will jump around dramatically in the first few events. This is the point — the system is figuring them out.