--- title: "Median payment time and the 90th percentile: seeing beyond the average" canonical: https://www.billabex.com/en/blog/median-payment-time-90th-percentile/ lang: en alternate: https://www.billabex.com/fr/blog/delai-paiement-median-percentile.md alternates: fr: https://www.billabex.com/fr/blog/delai-paiement-median-percentile.md en: https://www.billabex.com/en/blog/median-payment-time-90th-percentile.md es: https://www.billabex.com/es/blog/plazo-de-pago-mediana-percentil-90-retrasos-que-oculta-el-promedio.md updated: 2026-10-29 index: https://www.billabex.com/llms.txt --- # Median payment time and the 90th percentile: seeing beyond the average An average payment delay of sixteen days can describe a fairly uniform customer base or a majority of quick payments alongside a few very long cases. Those situations call for different decisions. In the first, the general process deserves attention. In the second, investigate why a small group of invoices remains blocked for so much longer. The median and the 90th percentile, often called P90, help describe this spread. They can also mislead when the analysis mixes starting dates, calculation methods or paid and still-open invoices. Before adding two numbers to a dashboard, define exactly what they describe and which decision they are intended to inform. ## Define the interval before calculating it Time from issue and delay after the due date are different measures. An invoice paid forty days after issue can still be on time if its due date is later. In this article's simulations, we measure calendar days between the due date and the actual, identified full payment. We are therefore measuring observed lateness, rather than the total commercial payment period. Define “payment date” as well. The date of an identified bank credit can differ from a delayed import or the administrative completion of reconciliation. Changing that convention halfway through the series can move the indicator without any change in customer behaviour. The checks for [cash received but not yet allocated](https://www.billabex.com/en/blog/payment-received-invoice-still-open-tracing-unallocated-cash/) help establish which date the record represents. Decide how early payments are treated. They can produce negative values in a signed measure, or be grouped at zero in a metric explicitly defined as non-negative lateness. Those choices produce different results. All completed observations in our example are positive, so no such transformation is needed. State that limitation to whoever reads the report rather than leaving them to infer it. ## Examine a portfolio whose average conceals its spread Consider twenty fictional invoices, all fully paid by the analysis date. Sixteen were paid five days late, two forty days late and two eighty days late. Each invoice counts once, without weighting by its monetary value. | Observed lateness | Number of invoices | Contribution to total lateness | | ----------------- | -----------------: | -----------------------------: | | 5 days | 16 | 80 days | | 40 days | 2 | 80 days | | 80 days | 2 | 160 days | | Total | 20 | 320 days | The mean is 320 divided by twenty, or sixteen days. The median is five days because the tenth and eleventh observations in the sorted list are both five. NIST identifies the median as the 50th percentile in its explanation of ordered observations and percentiles. For P90, we choose the nearest-rank method here: sort the values, multiply their count by 0.90 and select the rank rounded upwards. With twenty observations, that is the eighteenth value, or forty days. Eighteen invoices out of twenty have lateness less than or equal to forty days, and two exceed it. With repeated values, avoid a definition promising that exactly 90% must fall strictly below the threshold. ## Distinguish a formula change from a performance change The [R statistical documentation](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/quantile.html) describes nine quantile algorithms. Our empirical percentile choice corresponds to type 1. Other methods interpolate between observations, which can produce different results, particularly in a small dataset. A shared indicator name therefore does not guarantee an identical calculation. For the same twenty invoices, the type 7 method places P90 at rank 18.1. Interpolating between forty and eighty days gives forty-four days. Moving from forty to forty-four does not mean customers paid four days later. It may simply reveal a change of formula between two reporting tools. Put the convention in the report definition and keep it stable when comparing periods. A P90 based on twenty completed payments is still a limited description for predicting thousands of future invoices. It can direct an investigation, but it is neither a guarantee of payment by that date nor a confidence estimate of 90%. Those interpretations would require a different statistical argument. ## Compare distributions with an identical mean Imagine a second portfolio of twenty invoices, each paid sixteen days late. Its mean is also sixteen days, while its median and P90 are both sixteen days. The two portfolios consequently share the same average indicator despite having very different patterns of payment. In the first portfolio, sixteen invoices out of twenty, or 80%, are paid at five days, while four take substantially longer. Examine those four cases for a shared approval route, missing documents, a different paying entity or particular contractual circumstances. In the second portfolio, a general delay may prompt a review of invoice delivery or the customer's normal supplier payment process. These are hypotheses to investigate, not causes established by the statistics. Changes in the customer mix or payment terms may explain the difference. Before comparing two teams or tools, apply the safeguards for [selecting a comparable pilot portfolio](https://www.billabex.com/en/blog/collections-automation-pilot-portfolio/). Percentiles cannot repair a poorly defined observation scope or make unlike groups comparable by themselves. ## Show still-open invoices beside completed payments Now suppose the twenty invoices in the first example belong to a group of twenty-five. The remaining five are still unpaid and each is seventy-five days past due at the reporting date. The statistics calculated from the twenty completed payments remain correct for that subset, but they do not describe the eventual payment time of all twenty-five invoices. The five open cases represent 20% of the group. Their final duration is unknown. Replacing them with zero artificially improves the result; recording them as paid at seventy-five days invents an event. NIST explains right-censored observations in reliability analysis: some events have not occurred when observation ends. We apply that concept to payment here without adopting an industrial reliability model. Report open invoice counts, amounts and current ages separately from genuinely observed payment events. Statistical analysis accounting for censoring requires suitable assumptions and methods. Adding current ages to a list of completed durations does not achieve that. Cases closed through credit notes or debt forgiveness also need a category distinct from payment, since administrative closure does not establish when money arrived. ## Connect the spread to money and next actions A percentile calculated by invoice gives a EUR 100 invoice the same weight as a EUR 100,000 invoice. That convention can help describe a process, but does not directly measure the cash tied up in receivables. The distinction between [results measured by value and by count](https://www.billabex.com/en/blog/collection-rate-value-versus-count/) helps keep both perspectives visible when deciding where to focus effort. A useful report can combine the median and P90 for observed payments, the number analysed, the chosen method and the still-open balance. Add the amounts associated with the longest delays and their verified reasons. This provides a basis for deciding who should review which cases, without attributing more precision to the percentile than the data supports. A [customer view in Billabex](https://www.billabex.com/en/product/customer-view-360/) helps you return to invoice context when the analysis identifies unusual cases. Ask how to retrieve the dates and statuses required by your calculation method, rather than assuming that identically named metrics follow the same convention everywhere. The number becomes useful when it leads to a documented examination of the case behind it. ## Sources - NIST, Percentiles, definitions and calculation methods. - [R, Sample Quantiles](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/quantile.html), types 1 to 9, particularly types 1 and 7. - NIST, Censoring, observations with an unknown final event time.