Why Projects Always Go Over Budget: The Nonlinearity Problem

Everyone knows: projects always go over budget.

Software projects, construction projects, government projects — they arrive late and over-cost. The pattern is so consistent that it's been studied extensively.

The reason isn't bad planning or incompetent managers. The reason is nonlinearity.

Cost overruns are nonlinear. They have a heavily right-skewed distribution.

The Distribution

Here's what actually happens with project costs:

Notice the distribution. There's a long tail on the right. Projects can go way over budget. But they almost never come in way under budget.

This is a concave system. The distribution of outcomes is skewed toward larger-than-expected costs.

Why the Estimates Are Wrong

When someone estimates a project will cost $1M, they're usually not malicious. They've done their analysis, identified the tasks, added some contingency. The estimate is the expected value.

But the expected value of a right-skewed distribution is higher than the median. The average (mean) is pulled toward the extreme right tail.

By the time you account for Murphy's Law, unforeseen complexities, and the discovery of problems mid-project, the actual costs are distributed with a long right tail.

An estimate of $1M as the "expected value" actually means: somewhere between $1M and $2M is most likely. A 30% chance it goes 2x-3x over.

The Kerviel Example

Jerome Kerviel accumulated €50 billion in unauthorized positions at Société Générale.

When discovered, the bank had to rapidly unwind the position — a fire sale of €50 billion into a thin market.

The fire sale itself cost approximately €6 billion in losses. The actual trading loss on the €50 billion position was modest. But the unwinding costs were catastrophic.

Here's the key: if the same €50 billion exposure had been divided among 10 traders at 10 smaller banks, each unwinding €5 billion, the total market impact would have been near zero.

The cost is nonlinear in size. A single €50B position costs far more to unwind than 10 € 5B positions.

This is the project cost problem: the costs aren't linear in the size of the project.

The Same Nonlinearity in a Bankroll

The concentration problem shows up directly in how bettors deploy capital.

Put your entire bankroll behind one large straight position and the outcome distribution is brutally right-skewed. Most nights it works. Then the tail arrives: in the 2023 playoffs the Chargers led the Jaguars 27-0 and lost 31-30. A bettor fully loaded on one side was wiped out in a single quarter. The loss wasn't linear in the size of the bet — one oversized position blew up the whole account, exactly as a single €50B block costs far more to unwind than ten €5B ones.

The Ungambled structure attacks this the way good project management attacks overruns. Spread capital across eight to twelve books so any one account limiting or closing costs only a fraction of the whole. And on each game, collapse the variance to near zero by hedging both sides across two books, locking the spread before kickoff. The right tail that destroys the concentrated bettor is engineered out before it can form.

Why It Matters

Because of this nonlinearity, any model using average expected costs will systematically underestimate actual costs.

If you observe that projects average 50% overruns, and you estimate $1M, you should expect $1.5M.

But most organizations estimate $1M and then act surprised when it comes in at $1.5M. They attribute it to poor planning rather than to nonlinearity.

Then, they plan the next project at $1.5M... and it comes in at $2.25M. Because the nonlinearity wasn't addressed, just the average adjusted.

The Solution

Three approaches:

1. Add contingency based on the distribution, not the average

If overruns follow a right-skewed distribution, add more contingency than the simple average suggests.

If the expected value is $1M but the distribution is 50-100% overrun for 30% of projects, add 50-75% contingency upfront.

2. Break the project into smaller pieces

Nonlinearity in costs means large projects have worse outcomes than small ones on average.

Instead of one $1M project, break it into 4 $250K projects. The total might be higher (due to overhead), but the distribution of outcomes is less skewed. You reduce tail risk.

3. Build in staged gates with renegotiation

Don't commit to a final cost upfront. Commit to completing Phase 1 at $X cost. Then, after Phase 1, estimate Phase 2. This allows you to handle discoveries as they emerge rather than pretending you knew everything upfront.

The Business Implication

Companies that understand nonlinearity manage projects differently:

Bad approach: Estimate the project cost. Commit to the estimate. Blame the team when it overruns.

Good approach: Estimate a base case. Add contingency based on the distribution of historical overruns. Plan for phased delivery. Be transparent about tail risk.

The "good approach" costs more upfront (because of the larger contingency) but avoids the disaster of a project that overruns by 200% and kills the company.

The Philosophical Point

Here's why Taleb keeps coming back to convexity and nonlinearity:

Most of reality is nonlinear. Cost overruns, project failures, financial losses, health outcomes — they're all right-skewed.

But our planning and prediction is linear. We estimate averages. We expect outcomes to cluster around the average.

The gap between our linear planning and the nonlinear reality is where disasters live.

Acknowledging the nonlinearity — recognizing that the distribution is right-skewed, that tail risks dominate, that the average is misleading — is the first step to managing better.

Projects will always go over budget. But the extent to which they go over is a choice. Acknowledge the nonlinearity. Add contingency. Plan in phases. Build in optionality.

Or keep being surprised.

The Ungambled method applies the same three moves to money at risk on games: break exposure into smaller pieces across many books instead of one concentrated position, and remove the right tail entirely by hedging both sides and locking the spread before the game starts. The bettor who ignores nonlinearity keeps getting surprised by the blowup; the one who respects it never leaves the tail open.