Performance Rating From Score Percent
Invert explicit logistic score fraction about observed opponent mean; heuristic performance approximation, not official tournament/federation table or full unequal-opponent likelihood fit. Endpoints undefined.
Description
A logistic performance rating inverts expected-score fractions against an average opposition rating.
A logistic performance rating inverts expected-score fractions against an average opposition rating. It is a continuous model rather than a federation table.1
Enter nonempty opponent ratings bounded by absolute 1000000, positive scale and score strictly between zero and opponent count. Return mean opponent rating, score fraction and modeled performance.
When to use Performance Rating From Score Percent
Use Performance Rating From Score Percent when you need to evaluate the supplied records under the calculation and evidence rules below. Perfect or zero scores have no finite modeled rating. No official federation lookup is performed.
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 Performance Rating From Score Percent 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 opponentRatings, tournamentScorePoints, callerRatingScale using the field table and calculation rules, then run the tool.
- Read logisticPerformanceRating, observedScorePercent, opponentMeanRating. 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 |
|---|---|---|---|
| opponentRatings | Opponent ratings | list of number | Required |
| tournamentScorePoints | Tournament score points | number | Required |
| callerRatingScale | Caller rating scale | number | Required |
Enter nonempty opponent ratings bounded by absolute 1000000, positive scale and score strictly between zero and opponent count. Return mean opponent rating, score fraction and modeled performance.
performance=mean(opponents)+scale×log10(fraction/(1−fraction)) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| logisticPerformanceRating | Logistic performance rating | number |
| observedScorePercent | Observed score percent | number |
| opponentMeanRating | Opponent mean rating | number |
{
"input": {
"opponentRatings": [
1500,
1500
],
"tournamentScorePoints": 1,
"callerRatingScale": 400
},
"output": {
"logisticPerformanceRating": 1500,
"observedScorePercent": 50,
"opponentMeanRating": 1500
}
}Limitations and assumptions
Perfect or zero scores have no finite modeled rating. No official federation lookup is performed.
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 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.
References
-
Performance Rating From Score Percent — 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.
- 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.