Description
Divide (actual - predicted)^2 by (actual - reference)^2 and require a strictly positive denominator.
A skill comparison expresses performance relative to a reference loss or scale. Zero baselines and orientation choices can make a nominal score undefined or reverse its interpretation.
Divide (actual - predicted)^2 by (actual - reference)^2 and require a strictly positive denominator.
When to use this tool
Use Relative Squared Error One Pair Term when you need an explicit baseline-relative error or equality term.
How to use the tool and how it works
- Enter actual, predicted, reference. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read ratio. Use the output convention below.
Divide (actual - predicted)^2 by (actual - reference)^2 and require a strictly positive denominator.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| actual | Observed value on the same scale and unit as its prediction. | Required. Finite number. |
| predicted | Predicted value on the same scale and unit as actual. | Required. Finite number. |
| reference | Reference | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| ratio | Dimensionless ratio when numerator and denominator use compatible units. | Required. Finite number. |
{
"input": {
"actual": 10,
"predicted": 8,
"reference": 6
},
"output": {
"ratio": 0.25
}
}Limitations and assumptions
- A reference equal to actual is rejected; this is one pair's ratio rather than a ratio of dataset-level error sums.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Check baseline suitability and aggregate losses on comparable observations before interpreting relative performance.
References
Similar or alternative tools
- Skill Score Sign Reference Choice
Return modelLoss / referenceLoss - 1 when higherIsBetter, otherwise 1 - modelLoss / referenceLoss.
- Relative Skill Zero Baseline Policy
For nonnegative loss and positive baseline return 1 - loss / baseline.