Beyond the Average: A Few Distributions Worth Understanding
- 6 minutes ago
- 6 min read
Averages are where most site analysis starts. They're rarely where good design decisions should end. A look at four statistical distributions that keep appearing in ecological systems.
Two sites. Both receive 600mm of rainfall annually.
In the first, rain falls steadily through the year — a little each month, reliable, even. In the second, four violent storms arrive between October and January and deliver almost everything. Then eight months of near-nothing.
Same average. Completely different systems.
And yet the number that gets written down — 600mm — is identical. It goes into the spreadsheet, the design brief, the site assessment. It looks like useful information.
This is worth sitting with for a moment. Because it means the most commonly reported figure about a site's water can be almost meaningless for design purposes. Not wrong, exactly. Incomplete in ways that matter enormously.
Which raises a question: if averages are this limited, what are we actually supposed to be looking at?
In a previous post, we explored power laws — the pattern where rare, large events dominate entire systems. Most of the rain falls in a handful of storms. Most carbon is stored in a few giant trees. The extremes write the rules, not the average day.
Power laws describe one shape of variability. Nature expresses others as well — each with its own structure, its own logic, and its own implications for design.
This isn't an attempt to cover every statistical distribution that exists. Only four that keep appearing in ecological systems. Four that are worth understanding — not as mathematics, but as patterns recognizable in the field.
The Limits of Two Numbers
Start with what the average actually is. Add all the values, divide by the number of observations. The center. A useful place to begin — and almost always insufficient on its own.
What it hides is spread. How far do values typically stray from that center? Two sites, same average temperature of 15°C. One barely deviates. The other swings between -5°C and 35°C within the same season. The mean is the same. What it's like to farm there is not.
Spread has a formal name — standard deviation — but the idea is simpler than the term suggests. It's a measure of how wide the variation is. Tight around the center, or scattered far from it.
But here's what's interesting. Even mean and spread together don't tell you the shape of a distribution. Is variation symmetric, or skewed to one side? Do extremes happen occasionally, or surprisingly often? Does the system change gradually, or in sudden jumps?
Shape is where things get interesting for design. Each of the four patterns below describes a different shape — a different way that relying on averages quietly misleads.
The Normal Distribution — When the Average Actually Works
Picture a bell curve. Most values cluster around the center. Values above the mean are just as likely as values below it. Move further from the center in either direction, and outcomes get rarer.
This pattern does show up in ecological contexts — daily temperature fluctuations within a settled season, small measurement variation in uniform terrain, or natural variation in seed size within a stable population. In these cases, the mean is genuinely meaningful. Designing around it is reasonable. Extremes are rare enough that they don't dominate.
Here's the thing: this is probably the exception in ecological systems, not the rule. And yet it tends to be the default assumption. Plan for the average year. Size infrastructure for average conditions. Expect average yields.
It's worth asking how often that assumption actually holds. Because most ecological processes seem to be skewed, lumpy, shaped by events that the bell curve would describe as nearly impossible — and that happen anyway.
The three patterns below are perhaps closer to how nature actually organizes itself.
The Poisson Distribution — How Often Does Disruption Actually Arrive?
Some events don't arrive on a schedule. They show up randomly, unpredictably, and yet — over long enough time — with a surprisingly stable average frequency.
Frost nights per winter. Pest outbreaks per season. Equipment failures per decade. Heavy rain events per year.
Any given year might bring zero of these. Or one. Occasionally three. The timing is genuinely unpredictable. But the long-run frequency is not — and that distinction turns out to matter quite a bit.
Take a region that averages two severe frost nights per winter. That doesn't mean every winter brings exactly two. Some bring none. Some bring five. What the distribution describes is the probability of each scenario — and once you start thinking in those terms, it shifts how you size things.
Not for the average year. For the distribution of years.
Water storage sized for the dry stretch that arrives once every several years, not for average rainfall. Drainage built for the storm that hits twice per decade, not typical runoff. Crop diversity arranged so that a bad year for one species doesn't take down the whole system.
There's something almost obvious about this once you see it. And yet most design still seems to be sized for the average, not the spread around it.
The Exponential Distribution — The System Has No Memory
Here's something that keeps surfacing as counterintuitive, no matter how many times it comes up.
Three quiet years don't make a fourth quiet year more likely. Five years without a major flood don't reduce the probability of one arriving this season. The waiting time between events doesn't shrink because you've been waiting a long time.
The system has no memory. It doesn't track how long it's been. It doesn't owe anyone calm.
The graph here is worth pausing on. The curve decays — high on the left, tapering right — and it can read as: the longer since the last storm, the safer you are. That's not what it's showing. Most storms historically arrive within a year or two of the previous one, hence the high left side. Long gaps occur but are less common — hence the tail. What stays constant throughout, invisible in the curve, is the underlying risk in any given year. That never changes.
Human intuition fails here in a specific way. A long run of good seasons starts to feel like evidence of stability. Buffers get drawn down. Redundancies get trimmed. The quiet stretch gets interpreted as a signal.
It isn't. It's a quiet stretch.
The real design implication might be about maintenance as much as design — buffers kept full precisely when they seem unnecessary, redundancy treated as permanent rather than precautionary.
The longer the calm, the more pressure builds to relax. That pressure is worth watching.
The Log-Normal Distribution — What Compounds, Compounds
Walk two plots of land with similar inputs, similar rainfall, similar aspect. Plant them the same way. Come back in ten years.
Sometimes the difference is startling. Not because of anything dramatic — no pest event, no flood, no intervention that would explain it. A divergence that grew quietly over time.
This is what multiplicative processes look like. Small early differences compound forward. Slightly better soil biology in year one improves water retention in year three. Better water retention improves plant survival in year five. Better survival shapes canopy structure by year eight. By year ten the gap is wide, and it got there through accumulation, not through any single event.
When many small multiplicative effects interact like this, the result is often a log-normal distribution. The graph shows this clearly — most plots cluster in that modest hump on the left, near average productivity. But the curve doesn't stop there. It stretches into a long right tail of plots that compounded so far forward they're in a different category entirely. Not because of better inputs. Because of earlier ones.
What's interesting about this for design is the timing question. In a system that adds, late correction is possible — you can always put more in. In a system that multiplies, early intervention compounds forward in ways that late intervention can't replicate.
Soil building in year one is not the same as soil building in year five, even with identical inputs. The earlier investment has been multiplying through the system for four additional years. Which might be part of why soil, structure, and diversity get treated as foundational in regenerative design — not because they're the most dramatic interventions, but because they compound.
The window for high-leverage action is often earlier than it feels.
Designing with Pattern Literacy
None of this requires statistical analysis.
It might require a habit — asking, before designing, what the shape of the system is. Not what the average is, or even how wide the spread is. What shape.
Is variation stable and symmetric? Is this a system shaped by rare events arriving randomly over time? Is the risk in the waiting — in the quiet stretch that breeds complacency? Or is the leverage early — in foundations that compound forward?
Power laws showed how systems concentrate. How rare events and dominant elements shape everything else. The patterns here describe something different — how systems fluctuate, wait, accumulate, and surprise us over time.
The average is where most analysis starts. It's probably not where most design decisions should end.
What the shape of a distribution says is something the average never quite gets around to.
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