𝐅𝐢𝐯𝐞 𝐒𝐭𝐚𝐠𝐞𝐬 𝐚𝐭 𝟗𝟓 𝐏𝐞𝐫𝐜𝐞𝐧𝐭 𝐈𝐬 𝐍𝐨𝐭 𝟕𝟕 𝐏𝐞𝐫𝐜𝐞𝐧𝐭

You've seen it happen in design review - someone pulls out a calculator, multiplies 0.95^5, gets 0.77, and suddenly the entire pipeline architecture is dead. Three months of work pivots to agents based on eleven seconds of arithmetic.

That math is correct. But the compounding-error argument has a fatal flaw: it's computed for the option you're rejecting, never for the option you're authorizing.

Here's what actually matters:

• 𝐋𝐮𝐬𝐬𝐞𝐫'𝐬 𝐋𝐚𝐰 𝐡𝐚𝐬 𝐚 𝐩𝐫𝐞𝐜𝐨𝐧𝐝𝐢𝐭𝐢𝐨𝐧. The product rule for reliability only holds if stage failures are statistically independent. Nobody checks that precondition anymore. Real pipelines share inputs, models, prompts, and retry logic - stages fail together, not independently.

• 𝐓𝐡𝐞 𝐜𝐚𝐥𝐜𝐮𝐥𝐚𝐭𝐢𝐨𝐧 𝐢𝐬 𝐚𝐬𝐲𝐦𝐦𝐞𝐭𝐫𝐢𝐜. 0.95^5 = 0.77 gets computed exactly once, to kill the pipeline option. Nobody runs the same math on agent reliability, error recovery loops, or hallucination rates under dynamic execution. You're comparing a measured number against an unmeasured one.

• 𝐓𝐡𝐞 𝐟𝐨𝐫𝐦𝐮𝐥𝐚 𝐝𝐞𝐦𝐚𝐧𝐝𝐬 𝐢𝐧𝐟𝐨𝐫𝐦𝐚𝐭𝐢𝐨𝐧 𝐢𝐭 𝐧𝐞𝐯𝐞𝐫 𝐚𝐬𝐤𝐬 𝐟𝐨𝐫. Does the pipeline succeed when all stages work, or when any one works? Can later stages undo earlier mistakes? Do shared inputs create correlated failures? The calculator takes none of this as input and returns a number anyway.

• 𝐃𝐞𝐩𝐞𝐧𝐝𝐞𝐧𝐜𝐞 𝐜𝐮𝐭𝐬 𝐛𝐨𝐭𝐡 𝐰𝐚𝐲𝐬. When stages fail together because they share an input, the correlation can actually improve reliability - a bad input fails fast instead of cascading. But you'll never know, because the arithmetic stops at 0.77.

The real decision isn't pipeline vs. agent. It's whether you've measured the actual reliability of your system under your conditions. The compounding-error argument lets you skip that work by converting an unexamined assumption into a number that looks like evidence.

Read the full analysis here:

https://ranjankumar.in/genai-architectures-level-3-compounding-error-arithmetic

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