Read a threshold probability when measurements tie

Define the task

Before summarizing a benchmark, write the exact event in words. “Finishes within five seconds” includes runs that end at exactly five. “Finishes before five seconds” excludes them. Record the measurement resolution because rounding a clock to seconds can create a substantial pile at the boundary.

Carry out the check

Sort the observed durations, keep repeated values, and count the records below, equal to and above the threshold. Divide each count by the number of eligible observed runs. Report the omitted or missing count separately. A step in an empirical cumulative distribution describes the observed sample. Generalizing to future runs requires a representative sampling design.

Worked hypothetical example

For hypothetical durations of 2, 5, 5 and 8 seconds, one run finishes before five and three finish within five. The empirical cumulative probability at five is 3/4. Its jump at five is 2/4. If your report gives 25% instead of 75%, compare its inequality sign and its treatment of ties before investigating the software.

Method checked 10 November 2026 against R documentation: Empirical Cumulative Distribution Function.

Open the empirical threshold mass calculator.

Download the threshold event definition card.