Description
Return 1 / log2(rank + 1) for a one-based positive integer rank.
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.
Return 1 / log2(rank + 1) for a one-based positive integer rank.
When to use this tool
Use Metrics: Rank Discount Position when you need one rank discount, tie block, or pairwise contribution.
How to use the tool and how it works
- Enter rank. 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.
Return 1 / log2(rank + 1) for a one-based positive integer rank.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| rank | Rank | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
| result.discount | Discount | Calculated result member: number. |
{
"input": {
"rank": 3
},
"output": {
"result": {
"discount": 0.5
}
}
}Limitations and assumptions
- This is the discount factor alone, not discounted gain, NDCG, or a complete ranking score.
- 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: Ranked Gain Tie Average Term
Multiply their mean by the sum of 1/log2(rank + 1) over the consecutive tie-block ranks.
- Rankloss One Inverted Pair Term
Return loss one when positiveScore is below negativeScore, tieCredit when equal, and zero when above.