Choosing The Severity Observation Unit

Why the Observation Unit Matters

A severity data set is not defined only by its dollar amounts. It is also defined by what one row represents. Depending on the question and the insurer’s counting rules, a row might represent a claim record, a claimant associated with an event, or a claim under a particular coverage. Choosing the wrong row unit can duplicate losses, combine unlike records, or make severity inconsistent with the claim count used elsewhere in a ratemaking analysis.

The selection is therefore a data-design decision. Start by stating the unit counted by the frequency convention, then state the unit to which each loss amount belongs. The severity observation unit should represent that same unit, or the data must be deliberately reconciled before the two quantities are used together. The earlier material on building claim counts and frequency data construction establishes why the counting convention must be explicit.

Definition: The severity observation unit is the entity represented by one row in a severity data set. A claim-level row represents one claim under the selected claim-record convention; a claimant-level row represents one claimant within the defined event or policy scope; and a coverage-claim row represents one claim associated with one specified coverage. The amount on a row must be assigned to that same unit.

These labels are not interchangeable. A claim record may involve one claimant, multiple claimants, or more than one coverage. An occurrence can therefore generate several claim records or claimant records. Likewise, one occurrence can generate multiple coverage claims. A valid data set specifies the grouping rule that turns source records into its rows.

Define the Unit Before Grouping Records

A practical unit definition answers three questions: what entity makes one row, what records are combined into that row, and what amount is attached to it? For example, “one bodily-injury claimant per accident, with all covered payments for that claimant combined” identifies a narrower unit than “one accident, with all bodily-injury payments combined.” Both could be useful for different analyses, but the row counts and row amounts will differ.

The claim-counting convention matters because a severity observation count is meaningful only with its unit named. If the frequency convention counts one occurrence per accident, then five claimant rows from two accidents do not mean five occurrences. If frequency counts one claim per coverage, then an occurrence with two covered lines contributes two coverage claims, not one. The counting rules should be stated rather than inferred from how many rows happen to appear in a source table.

Name the counted entity.
Specify whether the relevant count is claim records, claimants, occurrences, or coverage claims, including the event and time scope.

Define one severity row.
Write a sentence that says exactly which source records are combined and which are kept separate.

Assign the amount at that level.
Use the amount belonging to the row’s entity; do not repeat an occurrence total on every claimant or coverage row.

Reconcile counts and totals.
Check that every intended record is represented once under the chosen convention and that grouping preserves the intended total amount.

Why Consistent Units Are Necessary

The consistency requirement follows from a simple accounting identity. Suppose a defined group has $N$ units, the amount assigned to unit $j$ is $Y_j$, and the total amount is $L=\sum_{j=1}^{N}Y_j$. When $N>0$, the average amount per unit is $L/N$. Thus the count multiplied by the average amount returns the total:

N\left(\frac{L}{N}\right)=L.

This identity holds only when the count and amount use the same partition. If $N$ counts occurrences but $L/N$ is calculated from coverage-claim rows, the multiplication no longer has the stated accounting meaning. This is not a technical modeling detail; it is a mismatch in what the quantities count. When there are no units, $N=0$, there is no per-unit average to calculate, although the total amount may still be recorded as zero under the specified data rules.

A second useful check is conservation of amounts. If one set of rows is regrouped into another—for example, several claim records are combined into a claimant row—the sum of the resulting row amounts should equal the sum of the source amounts, unless a documented inclusion rule intentionally excludes or changes an amount. Grouping can change the number and size of rows, but it should not silently create or discard dollars.

Worked Example: Choosing Between Claim and Claimant Rows

A hypothetical insurer reviews three auto accidents. Its frequency convention counts one occurrence per accident. The source records show: Accident A has two bodily-injury claim records for claimant Mira, for $900 and $600, and one for claimant Leo, for $500; Accident B has one record for claimant Nia, for $1,200; Accident C has one record for claimant Omar, for $700, and one for claimant Pia, for $300. The proposed severity measure is intended to describe total bodily-injury amount per accident. Select the row unit and audit the alternatives.

Method. Since the requested amount is per accident and the stated frequency convention counts accidents, use one occurrence-level row per accident. Combine all included bodily-injury records within each accident.

Step 1: Calculate the accident amounts. Accident A has $900+600+500=\$2{,}000$. Accident B has $\$1{,}200$. Accident C has $700+300=\$1{,}000$. The occurrence-level file therefore has 3 rows with amounts $2,000, $1,200, and $1,000.

Step 2: Reconcile the total. The occurrence-row amounts sum to $2{,}000+1{,}200+1{,}000=\$4{,}200$. The six source claim-record amounts also sum to $900+600+500+1{,}200+700+300=\$4{,}200$, so grouping has preserved the amount.

Step 3: Compare the claimant-level alternative. If the intended unit were claimant per accident, Mira’s two records would be combined to $1,500. The five claimant rows would then be Mira $1,500, Leo $500, Nia $1,200, Omar $700, and Pia $300. They also sum to $4,200, but there are 5 claimant rows rather than 3 occurrence rows.

Check and mistake avoided. The requested target and the frequency convention both use accidents, so the selected severity rows are the 3 occurrence rows. Treating the 5 claimant rows as if they were the 3 frequency units would mix two counting conventions. The claim-record and claimant alternatives are not intrinsically invalid; they answer different unit-level questions.

Coverage-Claim Rows and Coverage-Specific Questions

A coverage-claim row is appropriate when the analysis distinguishes claims by coverage and the amount is attached to that coverage. For a single occurrence with two covered lines, one row per occurrence would combine those lines, whereas a coverage-claim file would retain two rows. This distinction is essential when the frequency convention itself counts coverage claims. It is also important to ensure a coverage amount is not copied onto every row for the same event.

The following example uses a hypothetical property program. All dollar amounts are already assigned to the indicated coverage; the task is only to choose and reconcile the row unit.

Worked Example: Selecting Coverage-Claim Rows

A hypothetical insurer records two property occurrences. Occurrence R has a building amount of $8,000 and a contents amount of $2,000. Occurrence S has a building amount of $5,000 and a liability amount of $1,000. The frequency convention for a coverage-specific analysis counts one claim for each occurrence-and-coverage pair with a recorded amount. Choose the severity observation unit, count its rows, and reconcile the amounts.

Method. The stated count is per occurrence-and-coverage pair, so the severity unit must be one coverage claim. Do not collapse the two coverage amounts within an occurrence into one row.

Step 1: Create the rows. Occurrence R produces a building row of $8,000 and a contents row of $2,000. Occurrence S produces a building row of $5,000 and a liability row of $1,000. There are $2+2=4$ coverage-claim rows.

Step 2: Check coverage-level totals. The row amounts sum to $8{,}000+2{,}000+5{,}000+1{,}000=\$16{,}000$. If grouped into one occurrence row per event, R would be $10,000 and S would be $6,000; those amounts also sum to $\$10{,}000+\$6{,}000=\$16{,}000$.

Step 3: Check the counting convention. There are 2 occurrences but 4 occurrence-and-coverage pairs. The required severity file therefore has 4 rows, not 2. The aggregate total is preserved by either grouping, but the number and meaning of the observations differ.

Check and mistake avoided. The coverage-claim unit matches the stated frequency convention. A common error would be to create two occurrence rows while retaining a count of four coverage claims, or to attach the occurrence total of $10,000 to both of R’s coverage rows. Either choice breaks the intended row-to-amount match; repeating $10,000 would also inflate the total.

A Structured Data Audit

A row unit should be tested against the actual data before it is used. A useful audit follows identifiers from the source records to the proposed severity file. Check whether each source record belongs to exactly one intended row, whether multiple records are combined only when the definition says they should be, and whether distinct units remain separate. Then compare row counts with the stated claim-counting convention and compare total amounts before and after grouping.

The next example illustrates an audit where the initial extract has too many rows for the intended unit. The correct response is not to delete rows arbitrarily; it is to identify the key that defines a row and aggregate accordingly.

Worked Example: Auditing a Commercial Liability Extract

A hypothetical commercial insurer counts one liability occurrence per incident. One incident involves two injured people. The source extract has three records: person J, legal-cost component $400; person J, covered compensation component $2,100; person K, covered compensation component $1,500. The severity target is total amount per occurrence. Determine the correct row, calculate it, and explain why the raw record count is unsuitable.

Method. The target and frequency convention both define a unit as an incident. Aggregate the included records by incident, not by source line or person.

Step 1: Count the source rows. There are 3 source records: two for J and one for K. This is a count of records, not a count of incidents.

Step 2: Aggregate to the target unit. The incident amount is $400+2{,}100+1{,}500=\$4{,}000$. The severity file has one incident row with amount $4,000.

Step 3: Reconcile with the frequency convention. The incident count is 1, and the severity file contains 1 row. The source-record total is also $4,000, so aggregation preserves the amount.

Check and mistake avoided. Using three raw records as three frequency units would contradict the stated one-occurrence convention. Alternatively, a claimant-level file would have two rows—J at $2,500 and K at $1,500—but that would describe amount per injured person, not amount per incident. The correct choice is one occurrence row because that is the defined target.

Common Traps and Practical Choices

The most frequent errors arise from assuming that a familiar label has a universal meaning. “Claim” may refer to a source-system record, an occurrence-level claim, or a coverage claim depending on the documented convention. Before using the word in a data specification, define what is counted.

Common exam trap: Suppose a file has 4 coverage-claim rows totaling $16,000, while the frequency convention counts 2 occurrences. The coverage-row average is $$16{,}000/4=\$4{,}000$. Multiplying that amount by the occurrence count gives $2\times\$4{,}000=\$8{,}000$, not the $16,000 total. The error is pairing a per-coverage-claim amount with an occurrence count. For occurrence rows, the amounts are $10,000 and $6,000, so the occurrence-level average is $$16{,}000/2=\$8{,}000$; multiplying by 2 returns $16,000. Alternatively, retain coverage-claim rows and the matching count of 4.

This arithmetic is a consistency check, not a rule that one row unit is always preferable. Choose the unit that fits the intended loss target and count convention, then keep the choice consistent throughout construction and validation. A practical specification should document:

the entity represented by one row and its identifying key;
the scope in which claimants or coverages are distinguished;
which records are combined into a row and which remain separate;
the amount assigned to each row; and
the frequency convention against which row counts are reconciled.

When a question does not specify the unit, state a defensible assumption and show how the data would be grouped under it. If two units could be appropriate, explain what question each answers and avoid comparing their counts as though they were the same. This discipline makes a severity file interpretable and helps prevent accidental duplication before later steps define and analyze the loss amounts themselves.

Check Your Understanding

For each hypothetical situation, identify the suitable observation unit and complete the requested count or amount check.

A fleet frequency convention counts one accident per event. One accident has two source records for the same driver, $250 and $750, and one record for another driver, $1,000. What is the severity unit and the row amount? (Answer: One occurrence row; $2,000.)
A contractor’s frequency convention counts each claimant per incident. One incident has claimant A with records of $300 and $500, and claimant B with $900. How many severity rows are needed, and what are their amounts? (Answer: 2 claimant rows; $800 and $900.)
A hypothetical property event has a dwelling amount of $6,000, a contents amount of $1,500, and a separate liability amount of $500. The specified count is one occurrence-and-coverage pair per recorded coverage. State the row count and total amount. (Answer: 3 coverage-claim rows; $8,000 total.)
A data extract contains 4 coverage rows for two incidents, with amounts $2,000 and $1,000 for the first incident and $4,000 and $3,000 for the second. The frequency convention counts incidents and the target is amount per incident. Give the correct row amounts and verify their total. (Answer: 2 occurrence rows of $3,000 and $7,000; total $10,000.)
A hypothetical liability file counts one occurrence per event. Event M has two claimant rows of $1,200 and $800; Event N has one claimant row of $2,500. The target is per occurrence. How many target rows are required, what are their amounts, and what raw claimant-row count should not be mistaken for the occurrence count? (Answer: 2 occurrence rows of $2,000 and $2,500; the 3 claimant rows are not the occurrence count.)

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