Delayed dispute cohort

Figure 01 / 12

The evaluated population

The cohort contains 18,000 captured purchases, of which 450 have the defined synthetic outcome: Synthetic final dispute loss. The outcome is known by construction here. In production, label uncertainty and selection must be recorded separately.

Figure data and text version

Outcome	Count
Synthetic final dispute loss	450
Other labeled outcomes	17,550

The analyst measures disputes by original purchase cohort. Some outcomes arrive well after the merchant has received proceeds.

The reference case starts with the stated population and a functioning evidence path. The owner is risk operations.

All amounts, rates, capacity limits, and outcomes in this case are synthetic. The three conditions are separate assumptions for comparison. A better result in the response condition is not measured proof that the proposed control causes that improvement. The figures expose the calculation and its limits; a real deployment needs its own evidence.

Read the result

The rule flags 623 of 18,000 captured purchases. Of those flags, 360 meet the synthetic target, giving 57.78% precision. It misses 90 target events. Under the stated cost assumptions, residual loss and operating friction total $15,230. The important result is the connection between the population, action, capacity, and outcome—not one isolated score.

Figure 02 / 12

Four outcomes of the rule

The rule flags 360 synthetic positives and 263 negatives. It misses 90 positives. A flagged item is a decision to intervene; it is not proof of fraud, a legal prohibition, or any other real-world conclusion.

Figure data and text version

Known outcome	Flagged	Not flagged
Synthetic final dispute loss	360	90
Other outcome	263	17,287

Figure 03 / 12

Three rates with different denominators

Precision is 57.78%, recall is 80%, and the false-positive rate is 1.5%. Changing the denominator changes the meaning. This record keeps each numerator attached to the population from which it came.

Figure data and text version

Metric	Numerator	Denominator	Result
Precision	360	623	57.78%
Recall	360	450	80%
False-positive rate	263	17,550	1.5%

Figure 04 / 12

Precision changes with prevalence

This sensitivity plot holds recall at 80% and false-positive rate at 1.5%, then changes prevalence. It is an algebraic comparison, not a forecast. Even unchanged detection quality can produce a very different review queue when the base rate changes. Horizontal positions are the labeled observations or scenarios; equal spacing does not imply equal numerical increments.

Figure data and text version

Assumed prevalence	Precision %
0.1%	5.07
0.5%	21.14
1%	35.01
2%	52.12
5%	73.73
10%	85.56

Figure 05 / 12

The threshold trade-off

Six illustrative score bands use a stated pair of detection rates. Lower sensitivity can reduce false alarms but miss more target events. These points do not come from a trained model and do not establish the best operating threshold. Horizontal positions are the labeled observations or scenarios; equal spacing does not imply equal numerical increments.

Figure data and text version

Score band	True positives	False positives
Band 1	441	2,632
Band 2	423	1,404
Band 3	387	614
Band 4	324	211
Band 5	225	70
Band 6	112	18

Figure 06 / 12

A transparent loss-and-friction calculation

At $120 severity per missed synthetic positive, residual loss is $10,800. Review costs $3,115; lost contribution on false alarms is $1,315. The calculation assumes intervention prevents all flagged-positive loss and each false alarm loses the stated contribution. Relax those assumptions before applying it to a real policy.

Figure data and text version

Cost component	USD
Missed-positive loss	10,800
Review cost	3,115
False-alarm contribution	1,315

Figure 07 / 12

Observed outcomes mature over time

The final synthetic positive count is 450. Earlier observations reveal only a stated fraction. Comparing a day-1 cohort with a day-30 cohort would confuse label age with control quality. This curve models observation delay only; it does not change the final outcome. Horizontal positions are the labeled observations or scenarios; equal spacing does not imply equal numerical increments.

Figure data and text version

Days after event	Observed positives
1	81
3	158
7	270
14	369
30	450

Figure 08 / 12

Review demand and available capacity

The flag count is 623. The comparison capacity is an illustrative 720 reviews per cohort window. A mathematical rule can be coherent while its resulting workload exceeds the operating team’s capacity. Capacity is not permission to ignore an applicable mandatory control.

Figure data and text version

Queue measure	Items
Flagged for review	623
Available capacity	720
Excess demand	0

Figure 09 / 12

A feature is an observation with provenance

This evidence contract supports disputes create delayed labels. A value needs its event time, arrival time, scope, and source. Keeping unavailable evidence distinct from a measured zero prevents an outage from becoming a falsely reassuring feature.

Figure data and text version

Field	Example	Meaning
entity_ref	Delayed dispute cohort	Subject of this case
event_time	2026-09-18T09:00:00Z	When the event occurred
received_time	2026-09-18T09:00:02Z	When the system learned it
signal_status	available	Evidence quality, not an outcome
label_definition	Synthetic final dispute loss	The target used in these calculations

Figure 10 / 12

Missing evidence changes the observed population

The cells show an explicitly constructed completeness profile for three signal groups. The stress condition removes more history and device evidence. Missingness does not prove the target outcome; it changes what the decision process knows.

Figure data and text version

Signal group	Available	Missing
Identity evidence	17,820	180
Activity history	17,640	360
Context signal	17,100	900

Figure 11 / 12

Evidence, score, and action remain separate

The policy can use disputes create delayed labels only within its approved scope. The action record must retain which evidence was available, which model or rule ran, and which action was actually applied. The final action can differ from the score recommendation when a separate constraint applies.

Figure data and text version

Stage	Record
Observe	Delayed dispute cohort: evidence as of the decision time
Evaluate	Rule flags 623 of 18,000 captured purchases
Apply	Record action, reason, owner, and expiry
Reconcile	Join the action to later outcomes without overwriting history

Figure 12 / 12

What the result cannot establish

Observed classifications do not reveal every counterfactual. The synthetic labels make arithmetic possible, but production decline data is selected by prior policy. Keep measured outcomes, assumed prevention, and unknown alternatives separate when reporting impact.

Figure data and text version

Claim	Evidence in this case	Limit
Detected target	360 known synthetic positives flagged	Production labels may be delayed or wrong
Prevented loss	Assumed 43,200 USD	Requires an intervention-effect assumption
Customer impact	263 synthetic negatives flagged	Not every flag causes abandonment
Unobserved alternative	Outcome without the action	Needs a valid evaluation design

Connect the result to the system

Keep purchase time, dispute arrival, final reason, and label maturity separate.

Check the population, evidence, permitted action, and actual effect together. A balanced calculation can still use the wrong population; a successful response can still leave an unknown financial outcome. The case’s numerical result applies only to its stated assumptions.