Elo Win Probability Expectancy
Compute stable complementary logistic Elo expected scores from explicit scale; expected score includes draws, not literal win probability unless the caller model excludes draws.
Description
Elo expected scores are complementary logistic fractions.
Elo expected scores are complementary logistic fractions. Expected score includes draws rather than describing win probability alone.1
Enter ratings bounded by absolute 1000000 and positive scale. Evaluate with a stable logistic branch and return both expected scores.
When to use Elo Win Probability Expectancy
Use Elo Win Probability Expectancy when you need to evaluate the supplied records under the calculation and evidence rules below. No rating update, federation rounding or inferred draw frequency is included.
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 Win Probability Expectancy 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 playerRating, opponentRating, callerRatingScale using the field table and calculation rules, then run the tool.
- Read eloExpectedScore, opponentExpectedScore. 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 |
|---|---|---|---|
| playerRating | Player rating | number | Required |
| opponentRating | Opponent rating | number | Required |
| callerRatingScale | Caller rating scale | number | Required |
Enter ratings bounded by absolute 1000000 and positive scale. Evaluate with a stable logistic branch and return both expected scores.
expectedA=1/(1+10^((ratingB−ratingA)/scale)); B=1−A Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| eloExpectedScore | Elo expected score | number |
| opponentExpectedScore | Opponent expected score | number |
{
"input": {
"playerRating": 1500,
"opponentRating": 1900,
"callerRatingScale": 400
},
"output": {
"eloExpectedScore": 0.09090909090909088,
"opponentExpectedScore": 0.9090909090909091
}
}Limitations and assumptions
No rating update, federation rounding or inferred draw frequency is included.
Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Elo Rating Update K-Factor Calculator: Sequential Elo updates use each newly updated rating for the next game. Batch-average opposition produces a different result. 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 Win Probability Expectancy — tool.io
Similar or alternative tools
- Elo Rating Update K-Factor Calculator
Sequential Elo updates use each newly updated rating for the next game. Batch-average opposition produces a different result.
- 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.