Task Time Distribution

Understanding the graph

This graph shows the probability distribution of actual completion times, given your estimated median time (m) in the selected unit.

• The peak of the curve is the mode (most likely time), which is less than the median (mode = m * e^-σ_ln², where σ_ln=1 for the underlying normal distribution).
• The median (m) is the point where 50% of tasks finish before and 50% finish after. This is your input estimate.
• The mean (average) completion time is m * e^σ_ln²/2 (approximately 1.65 * m, where σ_ln=1 for the underlying normal distribution). The blog post often simplifies this to 1.6 * m.
• The long tail to the right shows that while finishing somewhat early is possible, finishing significantly late is much more likely than finishing significantly early.
• The red line on the graph indicates the Median (P50) completion time, which corresponds to your input estimate.

Key Percentiles & Values (based on blog post communication guidelines):

• P50 (Median):
• Mean (Average):
• P80 (m * 3):
• P90 (m * 4):
• P95 (m * 5):
• P99 (m * 7):

The P80-P99 values above use multipliers suggested by the blog post for communicating estimates with varying degrees of certainty. Choose the value that matches the required certainty for your communication. For example:

• When planning a sprint, the Mean (Average) might be most useful for averaging out over many tasks.
• When providing a date to marketing or customers where a high degree of certainty is needed, the P95 (m * 5) or P99 (m * 7) values are more appropriate, as they represent a point by which the task is very likely to be complete.

Remember the blog's distinction: your initial estimate (the median) is often a developer's best *guess*; these higher percentiles help turn that guess into a more reliable *commitment* by accounting for the inherent uncertainty and long tail of task completion times.

A Note on Hofstadter's Law

This model helps quantify the uncertainty inherent in a single task estimate, assuming the scope is understood. However, always remember Hofstadter's Law: "It always takes longer than you expect, even when you take into account Hofstadter's Law." This tool provides a statistical framework for your current understanding, but unforeseen "scope discovery" or entirely new requirements can still extend timelines beyond these projections.