Elo Rating Update K-Factor Calculator

Apply caller Elo K/scale sequentially to explicit fractional game scores, recomputing expectancy after each game; no federation defaults, rounding or batch-frozen initial rating.

Description

Sequential Elo updates use each newly updated rating for the next game.

Sequential Elo updates use each newly updated rating for the next game. Batch-average opposition produces a different result.^[1]

Enter initial/opponent ratings bounded by absolute 1000000, aligned nonempty actual scores 0–1, nonnegative K and positive scale. Recompute logistic expectation before every game; return expectations, rating history and final rating.

When to use Elo Rating Update K-Factor Calculator

Use Elo Rating Update K-Factor Calculator when you need to evaluate the supplied records under the calculation and evidence rules below. No federation caps, publication rounding, changing K or game validation is applied.

Prepare the supplied game state, observations and explicit variant settings. Follow the card, board, coordinate and state conventions in the calculation rules.

How to use Elo Rating Update K-Factor Calculator and understand its results

Prepare the supplied game state, observations and explicit variant settings. Follow the card, board, coordinate and state conventions in the calculation rules.
Enter initialRating, opponentRatings, actualScores, callerKFactor, callerRatingScale using the field table and calculation rules, then run the tool.
Read updatedRating, sequentialRatingHistory, expectedScoresBeforeEachGame. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
initialRating	Initial rating	number	Required
opponentRatings	Opponent ratings	list of number	Required
actualScores	Actual scores	list of number	Required
callerKFactor	Caller k factor	number	Required
callerRatingScale	Caller rating scale	number	Required

ratingNext=ratingCurrent+K×(actualScore−expectedScore)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
updatedRating	Updated rating	number
sequentialRatingHistory	Sequential rating history	list of number
expectedScoresBeforeEachGame	Expected scores before each game	list of number

json

{
  "input": {
    "initialRating": 1500,
    "opponentRatings": [
      1500
    ],
    "actualScores": [
      1
    ],
    "callerKFactor": 32,
    "callerRatingScale": 400
  },
  "output": {
    "updatedRating": 1516,
    "sequentialRatingHistory": [
      1516
    ],
    "expectedScoresBeforeEachGame": [
      0.5
    ]
  }
}

Limitations and assumptions

No federation caps, publication rounding, changing K or game validation is applied.

Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Numeric lists are limited to 10,000 entries; string lists to 128 strings of at most 128 characters each. The rules above may impose smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Elo Win Probability Expectancy: Elo expected scores are complementary logistic fractions. Expected score includes draws rather than describing win probability alone. For a complementary task, use Performance Rating From Score Percent: A logistic performance rating inverts expected-score fractions against an average opposition rating. It is a continuous model rather than a federation table.

References

Elo Rating Update K-Factor Calculator — tool.io

Similar or alternative tools

Elo Win Probability Expectancy
Elo expected scores are complementary logistic fractions. Expected score includes draws rather than describing win probability alone.
Performance Rating From Score Percent
A logistic performance rating inverts expected-score fractions against an average opposition rating. It is a continuous model rather than a federation table.