Equitable Threat Score ETS

Compute observed binary ETS after marginal random-hit correction, retaining possible negative skill; unlike raw CSI or HSS, correct negatives change chance hits but not event union directly.

Description

Equitable Threat Score subtracts the hits expected from contingency-table margins.

Equitable Threat Score subtracts the hits expected from contingency-table margins. Correct negatives affect those expected hits even though they are absent from the event-union count.^{[1, 2]}

Compute observed binary ETS after marginal random-hit correction, retaining possible negative skill; unlike raw CSI or HSS, correct negatives change chance hits but not event union directly.

When to use Equitable Threat Score ETS

Use this tool to compute observed binary ETS after marginal random-hit correction, retaining possible negative skill; unlike raw CSI or HSS, correct negatives change chance hits but not event union directly.

Prepare the observed sounding, cloud records or forecast verification data. Check pressure and height coordinates, wind conventions and the stated units.

How to use Equitable Threat Score ETS and understand its results

Prepare the observed sounding, cloud records or forecast verification data. Check pressure and height coordinates, wind conventions and the stated units.
Enter hits, misses, falseAlarms, correctNegatives using the field table and calculation rules, then run the tool.
Read equitableThreatScore, chanceExpectedHits. 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
hits	Hits	integer	Required
misses	Misses	integer	Required
falseAlarms	False alarms	integer	Required
correctNegatives	Correct negatives	integer	Required

Supply four nonnegative integer counts with positive total. Compute chance hits and require the corrected event-union denominator positive; return ETS, retaining negative values, and the expected-hit count.

chance hits = (hits+misses)(hits+false alarms)/total; ETS = (hits−chance hits)/(hits+misses+false alarms−chance hits)

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

Output field	Meaning	Value type
equitableThreatScore	Equitable threat score	number
chanceExpectedHits	Chance expected hits	number

json

{
  "input": {
    "hits": 30,
    "misses": 10,
    "falseAlarms": 20,
    "correctNegatives": 40
  },
  "output": {
    "equitableThreatScore": 0.25,
    "chanceExpectedHits": 20
  }
}

Limitations and assumptions

Degenerate tables are rejected. No confidence interval or operational calibration judgment is inferred.

Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Forecast Skill Heidke Score: Compute binary Heidke skill against marginal chance agreement on explicit observed contingency counts; undefined degenerate chance is rejected, no independence confidence interval or operational forecast quality certification. For a complementary task, use False Alarm Ratio Precip Verification: Compute observed false alarms/(hits+false alarms), not false-positive rate over observed nonevents; no-event forecasts leave ratio undefined.

Further background: Equitable Threat Score.

References

Equitable Threat Score ETS — tool.io
Equitable Threat Score — ECMWF

Similar or alternative tools

Forecast Skill Heidke Score
Compute binary Heidke skill against marginal chance agreement on explicit observed contingency counts; undefined degenerate chance is rejected, no independence confidence interval or operational forecast quality certification.
False Alarm Ratio Precip Verification
Compute observed false alarms/(hits+false alarms), not false-positive rate over observed nonevents; no-event forecasts leave ratio undefined.