- 01.The Pass^k formula: why 90% per-step reliability gives you only 35% end-to-end over a 10-step workflow.
- 02.Why a "minor" per-step improvement from 90% to 95% nearly doubles end-to-end success -- and what this means for where you invest engineering effort.
- 03.How to measure per-step reliability independently, find the weakest link, and invest where the compounding math produces the highest return.
The 90% Trap: Why Agents Fail in the Long Tail
In 2025, a major coding agent achieved 49% on SWE-bench Verified -- solving roughly half of real-world GitHub issues. The industry celebrated. But a senior engineering director at a Fortune 100 financial services firm looked at that number differently. Her team was evaluating agent-assisted code migration -- moving 2,400 microservices from Java 11 to Java 21. Each migration involved 8 discrete steps.
She did the math. If the agent succeeded at each step with 90% reliability, the probability of completing all 8 steps without error was 0.9^8 = 43%. Less than half of migrations would complete autonomously. At 95% per step: 66%. At 99% per step: 92%. The gap between 90% and 99% is 9 percentage points per step. The gap in end-to-end outcomes is 43% to 92%.
She approved the project with a condition: measure per-step reliability independently, identify the weakest step, and invest there first. That decision saved the project. Step 5 (resolving compilation errors) had only 72% reliability. That single step dragged end-to-end to 28%. Improving step 5 to 95% lifted overall performance to 59%. One step improved. Overall success nearly doubled.
Per-Step Reliability Compounds Multiplicatively
The formula is simple. The implications are not. If each step in an agent's workflow succeeds with probability p, and the workflow has k steps, the probability that ALL steps succeed is p^k.
Agent reliability is the compound probability that every step succeeds, governed by Pass^k -- where small per-step improvements produce outsized end-to-end gains because the improvement compounds at every step.
-- The working definitionIs Almost the Whole Game.
The reliability stack. Pass^k applies not just within the agent but across the entire Agentic Stack. Context reliability at 95% across 7 layers gives 69.8%. Harness reliability at 99% across 7 steps gives 93.2%. Agent reliability at 90% across 10 steps gives 34.9%. System reliability = 0.698 x 0.932 x 0.349 = 22.7%.
Where to invest. Step 1: Measure per-step. Step 2: Find the weakest link. Step 3: Invest at the weakest step. The options, ranked by typical effectiveness: better context assembly, retry with modified approach, better tool definitions, step decomposition, and model upgrade as a last resort.
The Math Your Demo Hides From You
The 90% illusion. Sales decks quote "90% accuracy" as if it's impressive for an agent. For single-step operations, it is. For a 10-step workflow, 90% per step delivers successful results 35% of the time. Would you ship a product that fails 65% of the time?
Reliability as competitive moat. The team that achieves 95% per step first has a product that works twice as often as the competition's at 90%. That's not an incremental advantage. That's a category-defining gap.
The Trap
Measuring only end-to-end success.
Teams report "our agent succeeds 60% of the time." That number is nearly useless for improvement because it doesn't tell you WHERE failures occur. A 60% rate could mean every step is at 95% across a long chain, or one step is at 50% while the rest are at 99%.
The fix: instrument every step. Tag each step with a success/failure flag. Fix the weakest link first.Designing for End-to-End Pass Rate
A production customer service agent at a financial services firm runs a 7-step workflow. End-to-end success: 58.4%. Per-step measurement revealed Step 7 (Execute Action) at 88.6% was the bottleneck. Three targeted fixes -- auth token refresh, API timeout increase, and tool description rewrite -- projected to lift end-to-end from 58.4% to 73.2%.
Is Where the Leverage Lives.
Remember This
1. Pass^k: 90% per step x 10 steps = 35% end-to-end. 95% per step x 10 steps = 60%. That 5-point per-step improvement nearly doubles end-to-end success. Returns INCREASE as you approach perfection.
2. Always measure per-step, not just end-to-end. Find the weakest step. Invest there first. The weakest step dominates the chain's reliability.
3. Reliability compounds across the entire stack. A product "good" at every layer can still deliver poor outcomes because compound probability is merciless.
References
1. SWE-bench -- AI Coding Agent Benchmark
2. Building Effective Agents -- Anthropic Engineering Blog
3. WebArena -- CMU Research