Empirical vs. Conservative Values
Source of truth:
calculations/docs/conservative_u_comparison.md and the generated outputs/u_probabilities.md. The values below are copied from those files as of repository commit 0b50516. They change if the tool is re-run, so check the repository for current values.
The ratio in the last column is the specification's conservative value divided by the tool's estimate. It is not a measure of how over-cautious a value is for every row. Rows marked as a floor, proxy, or closed form do not measure what the specification's value is meant to cover. Read the notes under the table before drawing any conclusion.
Two kinds of numbers
- Conservative u (input, from the specification). The hand-picked assumptions in the specification's Table 3. The tool does not produce them. They are the values being checked against.
- Empirical u (calculated by the tool). Derived from public data, or from a closed form for SSN and ITIN. See u-Probability Calculations.
Fields the tool computes
| Field | Variant | Conservative u (spec) | Empirical u (tool) | Ratio |
|---|---|---|---|---|
| Last name | exact | 0.005 | 0.0006779 | 7.38x |
| Last name | fuzzy | 0.01 | 0.0008325 | 12.01x |
| First name | exact | 0.02 | 0.001793 | 11.16x |
| First name | fuzzy | 0.03 | 0.002257 | 13.29x |
| Middle name | exact | 0.01 | 0.001793 (proxy) | 5.58x |
| Year of birth | exact | 0.015 | 0.01178 | 1.27x |
| Date of birth (full) | exact | 0.0001 | 3.226e-05 | 3.10x |
| ZIP code (5-digit) | exact | 0.0003 | 9.698e-05 | 3.09x |
| State | exact | 0.06 | 0.04455 | 1.35x |
| City | exact | 0.01 | 0.003121 (bound a) | 3.20x |
| Street line | exact / fuzzy | 0.00003 / 0.00006 | see note | see note |
| Phone number | exact | 0.000001 | 1.31e-09 (co-resident landline floor) | see note |
| SSN last 4 | exact | 0.0001 | 0.0001 (1/9999, closed form) | 1.00x |
| ITIN last 4 | exact | 0.0001 | 0.0001 (1/9999, assumed by analogy) | 1.00x |
| MBI | exact | 0.000001 | 1.471e-08 (1/N, N = 2024 Medicare enrollment) | 67.99x |
Notes on specific rows
- Year of birth (1.27x). The tightest margin of any computed field. The tool's documentation says it is worth revisiting whether 0.015 is the right conservative value. Note that the specification's Table 3 marks year of birth as dismissed ("due to observed low adoption and low selectivity") and section IV.D says it was eliminated from the combination analysis, so it is not used in Table 2 combinations.
- City (3.20x). The headline is bound (a), which covers only the 63.1% of the population living in a Census place or Census Designated Place. Bound (b), which treats everyone else as unique, gives 1.243e-03, so the coverage-adjusted ratio against 0.01 is closer to 8x.
- Street line. The specification's value is conditional on the ZIP already matching. The tool's closest quantity is
street_line_given_zip(6.527e-05), which is higher than the specification's 0.00003. The tool's other quantity,street_line_with_zip(6.33e-09), is the joint probability of street line and ZIP and answers a different question, so its ratio (4739x) should not be read as over-conservatism. Both are co-resident floors that ignore unrelated households on the same street name. The tool also reports a second method (average household size) alongside the household-size-distribution method; the values here are the headlineu_unbiasedfigures. - Phone. The 763x ratio against 0.000001 is not evidence that the specification's value is overly cautious. The tool's number covers only landline sharing among co-resident household members. It excludes shared "family contact" numbers and mobile number reassignment, which the tool names but does not quantify.
- SSN and ITIN last 4 (1.00x). This is not an independent check: the specification's value and the tool's closed form are the same calculation. The closed form holds only for SSNs issued on or after 2011-06-25. Earlier SSNs were assigned sequentially, so the population-wide value is likely higher. The tool does not estimate that cohort. For ITIN, the IRS has not published a randomization policy, so the closed form is an unverified assumption.
- Middle name (5.58x). Based on a proxy (the first-name distribution), not a direct measurement. Indicative only. The specification's Table 3 marks middle name as dismissed as well, so it is not used in Table 2 combinations.
- MBI (67.99x). A namespace-size floor assuming every MBI is issued to exactly one person. The specification's value is set well above it deliberately, to cover duplicate issuance, reissuance, and transcription errors.
- Fuzzy name values were revised after two bug fixes recorded in the tool's documentation. The values in the table are the corrected ones.
Fields the tool does not compute
For these, only the specification's value exists. They are not discrepancies.
| Field | Conservative u (spec) | Why the tool cannot compute it |
|---|---|---|
| Suffix | 0.2 | Dismissed in the specification; no public suffix frequency table |
| Year of birth (as listed in the specification's Table 3) | 0.015 | The calculations project's comparison document lists this row separately from the computed row above. The specification's Table 3 has a single year-of-birth row at 0.015, marked as dismissed. |
| Email address | 0.000001 | Same shape as phone; no public sharing-rate survey is used |
| Legal ID | 0.000001 | Namespace-specific per issuing authority; no single public count |
| Namespace-bound unique identifiers (EMPI, FHIR Patient Identifier, CSP UUID) | ≈0 | Namespace size is an organization's own patient count, which is internal data |
| Insurance Member ID | 0.000001 | Payer-specific enrollment; no single public figure |
| Insurance Subscriber ID | 0.0001 | Same as Member ID; the roughly 40% dependent-sharing assumption is not validated against public data |
| Relationship Linkage, clinical source | 0.01 | An error-rate question that needs an internal accuracy study |
| Relationship Linkage, self-reported or intake | 0.05 | Same as above |
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