How the DWZ is calculated

The base formula (WO 3.5.2)

For every player with an existing DWZ, after each tournament: Rn = R0 + K · (W − We). Here R0 is the previous DWZ, W is the points scored in the rated games, We is the sum of the expected scores, and K is the K-factor (development coefficient).

The result is rounded to a whole number. If it falls below 1100, it is set to 1100 — that has been the DWZ floor since the 2026 revision.

So the DWZ only changes if you score more or fewer points than your current rating predicts against these opponents. A tournament played exactly to expectation leaves the DWZ practically unchanged.

Expected score: what counts as "expected"? (WO 3.3, Appendix 2.1)

For each game, the difference D = R0 − R(opponent) is formed. The expected score is P(D) = NORMDIST(D; 0; √80000), i.e. a normal distribution with standard deviation 200·√2 ≈ 283.

• Equally strong opponent (D = 0): expected score 0.50.
• 100 points stronger than the opponent: about 0.64. 200 points: about 0.76. 400 points: about 0.92.
• 200 points weaker: about 0.24. Losing to a much stronger opponent costs almost nothing; winning brings a lot.

We is the sum of these values across all rated games. The WO explicitly allows rating software to use floating-point precision instead of the rounded table values; the differences are negligible.

Which games count?

Only games actually played against opponents with a rating count: a DWZ (R0), a newly determined initial DWZ from the tournament (R1, WO 3.4.4.2), or a foreign/converted rating such as FIDE Elo (WO 4.1.2).

• Forfeit games, byes and free rounds are not rated.
• Games against opponents without any rating drop out of the calculation; W and We are formed only over the remaining games.
• If an opponent's tournament performance rating is more than 300 points above their DWZ, they count for you with that performance rating instead (special rating, WO 3.6.3).

Example, calculated with the same engine as the forecast

A player (born 1985, so 41 years old in tournament year 2026) with a DWZ of 1650 and index 12 plays five games: 1580 (win), 1720 (draw), 1810 (loss), 1600 (win), 1690 (draw).

• Points W = 3,0; expected score We = 2,30 (sum of the five individual expectations).
• K-factor: K0 = 28 (adult under 2000, index 12), success bonus a = 0,0, brake factor b = 1,00 → K = 28,0.
• Rn = 1650 + 28,0 · (3,0 − 2,30) = 1669,6 → rounded 1670.

The calculator shows exactly these steps under "calculation steps" for your own tournament — with citations from the rating regulations.

What the forecast cannot know

• Carry-over games: players without a DWZ accumulate games across multiple tournaments until an initial DWZ becomes possible (WO 3.4.2). The calculator doesn't know these earlier games — initial DWZ estimates are therefore "conditional".
• Later corrections to tournament results made by the organiser or the rating office.
• Whether a foreign/converted rating is actually recognised as comparable by the rating office (WO 4.1.2).
• The exact evaluation timing: if a different tournament is evaluated first, your R0 there is already a different number.

Frequently asked questions