The Half-Life Tax

An interactive model of AI agent economics. Agent cost per successful outcome scales exponentially with task length, while human cost scales linearly. Adjust the parameters below to explore why the half-life of agent reliability is the only variable that truly matters. Based on Ord's half-life analysis and METR's empirical data.

Parameters

Model Inputs

Adjust these to match your scenario. The model recomputes instantly.

$0.22
Average cost of one model call including context. $0.02 for cheap models, $0.50+ for frontier with long context.
80
Agent actions per hour of equivalent human work. 50 for complex reasoning, 120+ for routine tasks.
5h
Task length at which the agent succeeds 50% of the time. METR data: ~2.5-5h for frontier models (2025).
$150
Salary + benefits + overhead. $100-200 typical for skilled knowledge workers.
// Key relationship
P(success) = 0.5 ^ (task_hours / half_life)
E[attempts] = 1 / P(success) = 2 ^ (task_hours / half_life)
Agent cost = steps × $/step × 2 ^ (task_hours / half_life)
Human cost = hourly_rate × task_hours  // linear
Results

Agent vs Human Cost by Task Length

The highlighted row marks where agent cost per success overtakes human cost. Note the exponential blowup beyond this point.

Logarithmic scale. The divergence after the crossover is the exponential at work.
Task length Steps $/attempt P(success) E[attempts] Agent cost Human cost Ratio
Ratio = agent cost / human cost. Values below 1 favour the agent; above 1 favour the human.
Sensitivity analysis

Half-life vs Cost per Step

For a fixed task length, how does the agent-to-human cost ratio change as you vary half-life and cost per step? The half-life dominates because it acts on the exponent.

8h
Values are agent cost / human cost. Green: agent cheaper. Red: human cheaper. Each cell uses the current steps/hr and human rate settings.
Task decomposition

Can You Break It Up?

Splitting a long task into shorter chunks keeps each chunk in the high-success zone. But each handoff costs coordination overhead and loses context.

24h
1
10%
Shows total agent cost as you vary the number of chunks. The minimum is the sweet spot balancing reliability gains against coordination overhead.