How to turn an event frequency into likelihood

Repeatable events don’t have a likelihood. They have an average frequency. The occurrence of any specific number of events in a specific time does have a likelihood.

The previous post said that:

  • you can calculate the likelihood of a specific number of instances of an event type in a fixed time interval, from a known long-term frequency
  • you can infer a likelihood for the count of an event type in a future time interval, from a reliable history of such events
  • normally you care about instance counts within or outside of a range, rather than an exact number
  • similar methods can be used to calculate totals, not just counts, when events come in varying sizes, with additive effects.

The previous post gave some key terms for you to Google. This post takes you through the methods more explicitly.

All of this series assumes that the events involved do not occur in any patterns. It assumes that there is nothing to stop occurrences very close together, in the same time interval (whatever the interval might be). Neither is there anything to set a limit on the time between occurrences. The likelihood of an event tomorrow is the same regardless of whether one happened just today, or whether no event has happened for much longer than anyone expected. There is no tendency for events to cluster together, nor to space themselves apart. If either tendency occurs for your risk event, you will need much more clever advice than can be found here.

You don’t need the methods in this series if you are only trying to establish a most likely count of future event instances, or an ‘expected loss’. Expected losses are terribly mathematical: the total of each loss level multiplied by its probability, equivalent to the average rate of loss from here to eternity. The most likely instance count, the mathematically expected instance count, and the expected loss, are all very easily projected from whatever inputs you have. The most likely and expected values add almost nothing to decision-making, and they subtract the most important feature of risk management—the possibility of an outcome different from the expected outcome, or from the ‘expected loss’. In other words, they ignore risk. If you think otherwise, you’re confusing ‘risk’ with ‘cost’.

Overview of the series

The Clear Lines cover the topic as a series of four articles, of which this introduction is the first. Below each of the articles is a drill-down page that guides you through implementing the methods in Excel, and a complete Excel workbook that you can download. If you are building an Excel workbook, you should work through sequentially. Otherwise, you can jump to the part that interests you.

This series covers half of the possible ‘cases’ in this table.

Event counts Total size for events
Event size distribution known or assumed Event size distribution inferred from history
Event frequency known or assumed Likelihood of a future event count within a range, from long-term event frequency Skipped. If you want to try it, just simplify the method below. Not much point—if the size history is known, so is the frequency history
Event frequency inferred from history Likelihood of a future event count within a range, from a history of events

Likelihood of a future event size total within a range
The event size distribution is based on two ‘given’ percentile values.
For another day, and perhaps another blog

This series does not talk about the likelihood of a single event having a size within a target range. If you need to know that, you’re dealing with a non-repeatable event, probably an event with extreme consequences. If that’s where you are, you need a better understanding of the potential event size than you will find here.

The half-journey actually mapped is exhausting enough. The half-journey proves that you can calculate the likelihood of particular event instance counts and total event instance outcomes over time from event frequencies and size distributions. The methods are well-known and accessible, without specialist skills and without specialist software.

I don’t recommend using these mathematical methods in your real-world risk management practice at every opportunity. Nor should you ignore risk assessment that doesn’t involve comparable calculations. Calculations are not better than awareness, judgement, or focus on what really matters. The thing that matters in risk assessment is making decisions that you will be happy with later, even after something has gone wrong.

I do recommend knowing that these calculation methods exist.

Spreadsheet implementations of these methods are good enough for understanding the relationships between the variables, even if they are not ideal for defending real-world decisions with costs and consequences. The Clear Lines Excel workbook is limited to 4000 trials per run. This limitation means that there is a surprising amount of variation between runs. An ideal Monte Carlo system will support millions of trials and produce consistent patterns across runs.

If you do use calculations, whether in spreadsheets or in something more robust, don’t forget that within every risk assessment involving calculations, assumptions and subjectivity are also hiding. Assumptions and subjectivity create their own uncertainty. You should report the full scope of uncertainty along with every conclusion, regardless of calculations that are objectively ‘correct’ as far as they go.

This Clear Lines topic was inspired by Mukul Pareek’s 2012 ISACA Journal Article Using Scenario Analysis for Managing Technology Risk (Volume 6 of 2012), and fuelled by a lot of confused Lines during the development of the topic Worst case analysis: When, why, and how.

Map of the series

Likelihood of a future event…


How to turn an event frequency into likelihood
This article

count within a range, from a long-term event frequency

count within a range, from a history of events

size total within a range


About the Excel implementation

…in Excel.

…in Excel.

…in Excel.

Download the complete Clear Lines Excel Workbook (17 MB)

Next article for risk specialists

About the Clear Lines Excel implementation

Risk specialists Version 1.0 Beta

Next article for risk specialists

Likelihood of a future event count within a range, from long-term event frequency

Risk specialists Version 1.0 Beta

Drill-down articles

Likelihood of a future event count within a range, from long-term event frequency

Risk specialists Version 1.0 Beta

Likelihood of a future event count within a range, from a history of events

First stage: the likelihood distribution Second stage: trials Comparing the trial distributions with the simple Poisson distribution Third and final stage: likelihoods for ranges Conclusions you may draw Count ranges and risk decisions

Risk specialists Version 1.0 Beta

Likelihood of a future event size total within a range

Conceive a distribution for event sizes Find the LogNormal parameters A table for your LogNormal distribution Include sizes in trials Find the proportion of trials that will push your buttons Conclusions you may draw

Risk specialists Version 1.0 Beta

Index to the topic Risk in work unit business planning

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