Simulation

Compound Probability — Why Programme Plans Fail Like Accumulators

Set ten dependencies at 90% each and watch the overall chance of success collapse. Then couple the failures together and watch it get worse.

What this simulation shows

The genius of a football accumulator is that every individual prediction is reasonable. Nobody is backing Hartlepool United to win the Champions League. Each leg is plausible when you look at it on its own.

That is exactly why it is dangerous. Every additional match increases the potential payout because it reduces the probability of success. The bet becomes more attractive as it becomes less likely.

Most programme plans are accumulators presented in PowerPoint. The requirements are approved, the supplier delivers, recruitment fills the vacant roles, the technology performs as expected, the integration works first time. Each assumption is entirely sensible. Together they form a sophisticated fantasy, because probabilities multiply. Ten independent activities at 90% each do not give you a 90% chance of success — they give you roughly 35%.

This simulation makes that arithmetic impossible to look away from, and then adds the two things that make real programmes worse than the naive maths predicts.

How to use it

Start with Independent assumptions selected. Set Individual success probability to 90% and walk Number of dependencies up from one to fifteen, watching the overall figure. The curve is steeper than intuition expects, and the damage arrives faster than anyone plans for. Around ten dependencies the programme is closer to a coin toss than to the confident green status it is being reported at.

Now switch to Failure coupling. Real dependencies are not independent — the supplier slips because requirements changed, and recruitment fails because the budget moved. Correlated failure makes the tail heavier. Compare the two modes at the same dependency count and probability; the difference is the gap between the plan on the slide and the programme in the room.

Then use Governance level and Programme board. Governance genuinely helps, but not by improving the underlying probabilities — it helps by detecting failure earlier, which is a different benefit and a much more modest one than most programme boards believe. Compare Ambitious product launch against Public-sector mega-programme to see how dependency count dominates everything else.

Ask Jeremy and Ask Super Hans are there for the same reason the article is written in Mark Corrigan’s voice: the model is bleak enough that it needs the joke.

What to take away

If your plan has ten sequential dependencies, no amount of confident presentation changes the multiplication. The productive responses are to reduce the number of dependencies, decouple the ones that remain, or stop reporting a single date as though it were a certainty. Reducing dependency count is almost always the highest leverage move, and almost never the one that gets chosen.

Programme Governance Workbench 2009
Powered by spreadsheets, anxiety, and the illusion of control
User: M. Corrigan | Status: emotionally repressed

Mark Corrigan's Programme Planning Simulator

Build a football accumulator disguised as a transformation programme. Add dependencies, governance, optimistic assumptions and stakeholder confidence. Watch the reward rise as the probability collapses.

“There are systems for a reason...”

2. The Three-O Walcott accumulator

Overall success0%
Fantasy meter0%
Potential reward£0m
Expected value£0m
Betting slip
Monte Carlo
Dependency graph
Mark's report

The lesson

An accumulator with one match is a prediction. An accumulator with ten matches is a fantasy.

Most complex plans fail because each assumption looks reasonable in isolation. The problem is not one bad assumption. The problem is the multiplication of many plausible assumptions, especially when they are linked by schedule, budget, people, suppliers and approvals.

Reducing dependencies usually beats improving the forecast. Mark would hate this because it means the spreadsheet was not enough.

How to use this simulation

Change one input at a time, run the model, and compare the result with the starting state. Then repeat the experiment with a different constraint or strategy so you can see which relationships drive the outcome.

What to look for

Look for trade-offs, thresholds, feedback loops, and points where a locally attractive decision produces a worse system-wide result. The simulation is intended to make the article's idea observable, not to predict a real operation.

Limitations

This is a deliberately simplified model. It omits the data quality, exceptions, human judgement, and operational constraints of a live system, so treat its behaviour as an illustration of a mechanism rather than as a planning recommendation.

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