How this calculation works
A continuous logistic Elo model compares rating differences with expected game scores, then adjusts rating when achieved scores differ from that expectation. The expected score includes the effect of draws; it is not simply a probability of winning a decisive game.
Expected score = 1/[1 + 10^((opponent rating − player rating)/400)]; period change = K × Σ(actual score − expected score)A worked example
A 2000-rated player facing two 2000-rated opponents has expected score one-half against each. A win and a draw produce 1.5 achieved points against one expected point. At K twenty, the period change is ten points and the continuous result is 2010. A win followed by a loss against those same equal opponents would leave the period change at zero.
Good to know
Uncapped continuous fixed-period model only; no official FIDE tables, caps, floors, eligibility, rounding, dynamic K or uncertainty system. Use the relevant organization’s current rules for official rating work. This is a transparent mathematical scenario and makes no claim to reproduce every federation’s calculation.
Reference: elote implementation documentation — Elo model (opens in a new tab) ↗
What this calculation answers
A continuous logistic Elo model compares rating differences with expected game scores, then adjusts rating when achieved scores differ from that expectation. The expected score includes the effect of draws; it is not simply a probability of winning a decisive game.
This page treats all games as one period with the same starting player rating and fixed K. It does not update the player’s rating sequentially after every row, which would describe a different calculation.
The Binomial probability calculator assumes repeated independent binary trials with a supplied probability. Elo expected score with possible draws is not automatically that binary win probability.
Use the right input conventions
Opponent ratings are supplied snapshots for the period, and result scores must be zero, one-half or one. The page does not fetch live ratings, validate an event or determine player eligibility.
K is an explicit sensitivity input. A larger K creates a larger change for the same score difference. It is not automatically selected from age, rating category, activity or federation rules.
Interpret the result
The model uses an uncapped base-ten logistic function with a 400-point scale. Official systems may use tables, caps, floors, special K rules and rounding conventions that differ from this smooth scenario.
The output intentionally remains continuous rather than being presented as an official rounded rating. It does not represent Glicko uncertainty, inactivity changes or a performance prediction for future games.
Work through the example
A 2000-rated player facing two 2000-rated opponents has expected score one-half against each. A win and a draw produce 1.5 achieved points against one expected point.
At K twenty, the period change is ten points and the continuous result is 2010. A win followed by a loss against those same equal opponents would leave the period change at zero.
Where the model stops
Uncapped continuous fixed-period model only; no official FIDE tables, caps, floors, eligibility, rounding, dynamic K or uncertainty system.
Use the relevant organization’s current rules for official rating work. This is a transparent mathematical scenario and makes no claim to reproduce every federation’s calculation.
A few questions, answered
Is expected score a win probability?
Not by itself when draws are possible; it is the model’s average point score.
Does the player rating change between rows?
No. Every row uses the same pre-period rating, then changes are summed.