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CDA·267 Computing, Data & AI 6 MIN · 8 STATIONS

Why the average recovery time lies

A Socratic walk-through of why the average recovery time lies — reasoned out one step at a time, not lectured.

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a

The question we started with

THE QUESTION #

Why is the mean time to recover almost never the time it takes to recover?

A team reports a mean time to recover of fifty-two minutes. It goes into the quarterly review, it is compared against last quarter's forty-eight, and someone concludes that recovery is getting worse.

Before accepting that, ask a smaller question. Of the incidents behind that number, how many actually took about fifty-two minutes?

Very often the answer is none. Most were resolved in under ten minutes, one ran for eleven hours, and fifty-two is a number that describes no incident that ever happened. So what exactly is it describing — and is it entitled to be compared quarter to quarter at all?

b

Reasoning it through

REASONING #

Start with what a mean is for. It is a balance point: the value at which deviations above and below cancel. When values cluster symmetrically around a centre — adult heights, say — that balance point sits where the data sits, and the mean is a fair summary of a typical case.

So: do incident durations cluster symmetrically? Think about what bounds them at each end. Below, there is a hard floor — an incident cannot take negative time, and realistically not less than the minutes needed to detect and act. Above, there is no bound at all. An incident can run for hours when the cause is unfamiliar, the expert is asleep, or the failure is in a vendor you can only email.

That asymmetry is structural, not incidental. A duration bounded below and unbounded above cannot be symmetric, so the distribution is right-skewed: a dense pile of short incidents and a long thin tail. Empirical studies of repair times generally find something of this shape, often described as approximately log-normal or heavy-tailed — though the precise family varies by organisation, and I would claim no more than the skew itself, which is robust.

Now put the mean back onto that shape. Where does the balance point of a right-skewed pile sit? Pulled right, toward the tail. It lands in the sparse region between the ordinary incidents and the exceptional one — describing neither. That is the first sense in which the average lies: it is not a typical value, and on this shape it structurally cannot be.

Then the second problem, which is worse. How stable is that number?

Because the tail is unbounded, one long incident can move the mean by more than every short incident combined. Fifteen incidents at eight minutes and one at eleven hours produce a mean near fifty; remove that one incident and the mean falls to eight. So a quarter-to-quarter comparison of MTTR is largely a comparison of whether a bad one happened, close to a coin flip on small counts. Most teams have few enough incidents that the sampling noise exceeds any real change in capability.

A third problem hides beneath both. What is being averaged together? A certificate expiry, a bad config push, a corrupted replica, and an upstream provider's outage are not draws from one process — they are different populations with different recovery mechanics. Averaging across them produces a number whose movement can be entirely explained by a change in the mix of incident types. A team that got faster at everything can report a worse MTTR simply by having had more of the hard kind.

And a fourth, quieter one. The measurement itself is discretionary: recovery time is the gap between two human-recorded timestamps, and both ends are soft. When did it start — when the alert fired, when the first user was affected, or when the deploy went out? When did it end — when the error rate recovered, or when the last customer was made whole? Those choices can change a number by a factor of two without anyone acting dishonestly.

So what should be reported instead? The distribution, not a point. The median tells you what a typical recovery looks like and is barely moved by the one eleven-hour incident. A high percentile tells you about the bad case, which is usually what leadership is actually worried about. And plotting the durations themselves communicates more than any summary, because it shows the shape a single number was hiding. Where a summary is unavoidable, the honest form is a median with a percentile beside it and the incident count stated, so the reader can see how little the number is standing on.

c

The analogy

THE ANALOGY #
THE FIGURE

Think of describing a town's typical commute by averaging journey times. Nearly everyone walks for ten minutes. One person flies in from another continent every fortnight. The mean commute comes out at ninety minutes — a figure that describes no one's morning, and one that swings wildly depending on whether the traveller happened to come this week.

The average is not wrong as arithmetic. It is answering "what would each journey be if the total were shared equally", which is simply not the question anyone asked.

WHERE IT BREAKS DOWN

the commuter and the traveller are visibly different people, so the mixing is obvious, whereas incidents arrive under one label and their differences are only apparent after diagnosis — which is exactly why the mix keeps changing underneath a metric that is reported as though it were measuring one thing.

d

Clarifying the model

THE MODEL #

Three refinements.

The first is that the mean is not defective; it is being asked the wrong question. A mean is exactly right for a total: mean duration times incident count gives total downtime, a genuinely useful quantity for reliability targets. What it cannot do is stand for a typical case on a skewed distribution. Use it for aggregation, not description.

The second corrects a tempting fix. Removing the eleven-hour incident as an outlier makes the number stable and meaningless — on a heavy-tailed distribution the extremes are not contamination, they are the phenomenon. Those are the incidents that produced the customer harm. Trimming them yields a comfortable metric that no longer tracks what anyone cares about.

The third is about what the metric is for. MTTR is generally used as a proxy for organisational capability, yet recovery duration is dominated by factors that vary independently of capability: how novel the failure was, what time of night it started, whether the fix needed a third party. The underlying components move more honestly — time to detect, acknowledge, and mitigate — because each is shorter, more frequent, and less contaminated by the rare hard case. Improving detection shows up there long before it shows up in the average.

e

A picture of it

THE PICTURE #
Why the average recovery time lies
Why the average recovery time lies Read the bars left to right as a histogram of one quarter's incidents. The mass sits in the first two buckets -- the median incident recovers inside about fifteen minutes. Now find the mean of roughly fifty-two minutes: it falls in the fourth bucket, where one incident sits, in the empty region between the pile and the tail. The single incident in the rightmost bucket pulled it there, and removing that one bar would move the reported average by more than every other bar combined. {"generator":"[email protected]","source":"../Socrates/.diagram-cache/_src/why-the-average-recovery-time-lies.md","sourceIndex":1,"sourceLine":4,"sourceHash":"87135f1155eab962832bd86b3c2934685adbf18e2441b01eb8d5b5d84877fb85","diagramType":"xychart","layoutVariant":"source","repairedDuplicateIds":[],"motion":"entrance-with-reduced-motion-fallback","presentation":"editorial","attempt":1,"viewBox":{"x":0,"y":0,"width":791,"height":668},"qa":{"passed":true,"findings":[]}} 0 to 10 10 to 20 20 to 30 30 to 60 60 to 120 120 to 240 240 plus Recovery time bucket in minutes 8 7 6 5 4 3 2 1 0 Number of incidents

How to readRead the bars left to right as a histogram of one quarter's incidents. The mass sits in the first two buckets — the median incident recovers inside about fifteen minutes. Now find the mean of roughly fifty-two minutes: it falls in the fourth bucket, where one incident sits, in the empty region between the pile and the tail. The single incident in the rightmost bucket pulled it there, and removing that one bar would move the reported average by more than every other bar combined.

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What became clearer

WHAT CLEARED #
WHAT CLEARED

The mean is a balance point, and on a distribution with a floor and no ceiling the balance point sits away from where the data lives. So MTTR reports neither the typical incident nor a stable trend — it reports, mostly, whether one bad incident happened to land in the window. Seeing that is really seeing that a single number cannot summarise a shape, and that the shape was the informative part.

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Where to go next

ONWARD #
  • Log-normal and heavy-tailed distributions, and how to recognise one from a sample.
  • Time to detect, acknowledge, and mitigate as separate, better-behaved measures.
  • Why the same argument applies to mean latency, and what percentiles fix and do not fix.
h

Key terms

TERMS #
TermWhat it means
Mean time to recover (MTTR)the arithmetic average of incident recovery durations over a period.
Right-skewed distributionone with a floor, a dense low region, and a long tail of large values, in which the mean exceeds the median.
Heavy taila distribution whose extreme values are frequent enough to dominate the mean rather than being negligible.

Every term the collection defines is gathered in the glossary.

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