Estimate the token bill for a 4 agent supervisor team over 6 hops

Predict output·Medium·4.0 · 0·~2 min·Asked atFlipkart Glean Sambanova

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A supervisor and workers team has 1 supervisor plus 4 workers. The workflow runs 6 hops (one worker call per hop). The supervisor consumes 3K tokens of context per routing call and outputs 0.5K tokens. Each worker consumes 4K tokens of context and outputs 1K tokens. Compute the rough total tokens for one full task. Express in thousands of tokens (K).

**Break the cost into two terms.** - Supervisor cost: the supervisor runs once per hop. 6 hops times (3K context plus 0.5K output) equals 6 times 3.5K equals 21K tokens. - Worker cost: one worker runs per hop. 6 hops times (4K context plus 1K output) equals 6 times 5K equals 30K tokens. - Total: 21K plus 30K equals 51K tokens. **The teaching point.** The supervisor is responsible for 21K out of 51K, which is roughly 40 percent of the bill. The supervisor never does real work; it just routes. Paying 40 percent of the bill for routing decisions is the canonical waste pattern. **The fix.** Move the supervisor to a cheaper, faster model (Claude Haiku 4.5, GPT-5.5-mini, Gemini 3.1 Flash). The work the supervisor does is closer to classification than to open-ended reasoning, which is exactly the workload small models handle well. Per-token cost drops 5 to 10 times with minimal quality impact on routing. This is the highest-leverage single change you can make on a supervisor and workers cost shape.

**The arithmetic.** Two-term formula: supervisor cost plus worker cost. - Supervisor: 6 hops times (3K context plus 0.5K output) equals 6 times 3.5K equals **21K tokens**. - Workers: 6 hops times (4K context plus 1K output) equals 6 times 5K equals **30K tokens**. - Total: 21K plus 30K equals **51K tokens**. **The structural insight.** The supervisor contributes 41 percent of the total bill (21K of 51K) even though its job is just to read the latest message and pick a worker. The supervisor never reasons over the full task, never calls a tool, never produces substantive output beyond a routing decision. Yet it costs nearly as much per hop as a worker doing real work. This is not unusual; it is the typical shape of a chatty supervisor workflow. Supervisor share lands in the 30 to 60 percent range across most production multi-agent systems with default sizing (everyone on the flagship model). **The cost lever.** Move the supervisor to a fast small model (Claude Haiku 4.5, GPT-5.5-mini, Gemini 3.1 Flash, Llama 4 8B). The routing decision is classification-shaped, which small models handle well. Per-token cost drops 5 to 10 times. After the change, supervisor cost would be roughly 2K to 4K instead of 21K, dropping total from 51K-equivalent to about 32K-34K-equivalent. That is a 30 to 35 percent total cost reduction from one config change. Add prompt caching on the supervisor's stable prefix (system prompt plus agent roster) and the supervisor's effective cost drops another 70 to 80 percent on top. Combined, the supervisor goes from 41 percent of the bill to roughly 5 percent.

TL;DR

Supervisor contributes 6 times 3.5K equals 21K; workers contribute 6 times 5K equals 30K; total 51K with the supervisor responsible for roughly 40 percent of the bill even though it only routes.

Memory aid

Easy to grasp

Imagine a small restaurant where every order goes through a host who reads the order and picks a chef, then a chef cooks. Six orders in a shift. The host spends 3.5 minutes per order reading and assigning; the chef spends 5 minutes cooking. Total host time: 21 minutes. Total chef time: 30 minutes. Total: 51 minutes. Notice the host spent 40 percent of the shift's labor just reading orders. If the host's labor cost the same as a chef's, you would be paying chef rates for a job a faster assistant could do. The same lesson holds for multi-agent supervisors: 40 percent of the bill on routing is exactly the cue to downsize the supervisor model.

Key concepts

Multi-Agent Systems

Concept explanation~2 min read

Everything you need to truly understand this topic: intuition, mechanics, step by step explanation, code, formulas, and worked example. Click to expand.

Predict-output questions in multi-agent are useful because they force the cost intuition to become quantitative. It is easy to say 'the supervisor is expensive' in the abstract; it is harder to say '21K of 51K tokens, 41 percent of the bill, on routing.' The second statement is the one that drives the right config change.

This walkthrough walks the arithmetic, breaks down where the cost lives (input versus output, supervisor versus worker), and shows how the two main optimization levers (downsize plus cache) compound on this exact shape.

Mental model: the two-term formula has the supervisor on one side and the workers on the other. Both terms scale with hop count. The supervisor term is the one most teams under-attribute because routing 'feels cheap' until you do the math.

Walking the arithmetic

Setup

1 supervisor, 4 workers.
6 hops total (one worker call per hop).
Supervisor per call: 3K input context + 0.5K output = 3.5K tokens.
Worker per call: 4K input context + 1K output = 5K tokens.

Supervisor total

Supervisor runs once per hop. Over 6 hops:

6 \times 3.5\text{K} = 21\text{K tokens}

Worker total

One worker runs per hop. Over 6 hops:

6 \times 5\text{K} = 30\text{K tokens}

Grand total

21\text{K} + 30\text{K} = 51\text{K tokens}

Per-role share

Supervisor: 21K of 51K = 41 percent.
Workers: 30K of 51K = 59 percent.

The supervisor is responsible for 41 percent of the bill despite doing only routing. That is the headline number.

Input vs output decomposition

The downsize-supervisor lever

Compounding with caching

Situations where this technique stops working.

2–4 min · Everything important, quickly.

Real products, models, and research that use this idea.

LangGraph's cost dashboards (when paired with Langfuse or LangSmith) surface per-agent token spend, making the supervisor-share calculation a one-query lookup.
Claude Haiku 4.5 and GPT-5.5-mini are the canonical 2026 fast-tier models teams move supervisors to, while keeping workers on Claude Opus 4.7 or GPT-5.5.

What an interviewer would ask next. Try answering before peeking at the approach.

QHow does the bill change if you double the worker count from 4 to 8 while keeping hops at 6?

Worker count does not enter the formula because each hop only invokes one worker. Doubling workers without changing hop count leaves the bill unchanged at 51K. This is a common misconception: more workers means more cost. It does not; more hops or larger per-call context means more cost.

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Red flags & common mistakes

The phrases that signal junior thinking. Click to expand.

Most common mistake

Counting the supervisor cost only once instead of once per hop, undercounting the total by 5/6 of the supervisor contribution and missing that supervisor share is the optimization lever.

60 second bullets to scan on the way to the call.

The two-term cost formula: hops times supervisor cost plus hops times worker cost
Per-hop arithmetic on the given numbers (6 * 3.5K + 6 * 5K = 51K)

Primary sources. Browse if you want the original framing.