Description
Multiply their mean by the sum of 1/log2(rank + 1) over the consecutive tie-block ranks.
Ranking metrics compare order or discount relevance by position. Ties, one-based ranks, and normalization choices change the contribution of an individual pair or rank.
Multiply their mean by the sum of 1/log2(rank + 1) over the consecutive tie-block ranks.
When to use this tool
Use Metrics: Ranked Gain Tie Average Term when you need one rank discount, tie block, or pairwise contribution.
How to use the tool and how it works
- Enter gains, firstRank. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Require nonempty nonnegative gains and positive firstRank. Multiply their mean by the sum of 1/log2(rank + 1) over the consecutive tie-block ranks.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| gains | Gains | Required. Array of finite number. Implementation limit: 128 items. |
| firstRank | First Rank | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
| result.meanGain | Mean Gain | Calculated result member: number. |
| result.discountedTieBlockGain | Discounted Tie Block Gain | Calculated result member: number. |
{
"input": {
"gains": [
1,
3
],
"firstRank": 1
},
"output": {
"result": {
"meanGain": 2,
"discountedTieBlockGain": 3.261859507142915
}
}
}Limitations and assumptions
- This averages supplied gains within a tie block; it does not transform relevance labels or normalize by an ideal ranking.
- Outputs are nested inside result. 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
Evaluate the full ranked set with a documented gain transformation, tie convention, and normalization.
References
Similar or alternative tools
- Metrics: Rank Discount Position
Return 1 / log2(rank + 1) for a one-based positive integer rank.
- Rankloss One Inverted Pair Term
Return loss one when positiveScore is below negativeScore, tieCredit when equal, and zero when above.