Robot Payrolla hands-on lab

When does a robot actually beat a human shift?

The Depot's payroll office pays its pickers and its robots side by side. Find out what one good pick really costs each of them, what autonomy, remote operators and a learning curve do to that number, what a fleet is worth, and who keeps the saving. Every number is computed by a tested model; every assumption is on the page and yours to change. About 60 minutes of play.

0 · The payroll office: one question, two payslips

The Depot is a warehouse in Busytown. Pickers lift items out of totes into orders, and the Depot's owner is being pitched a robot that does the same. The question a COO, an investor or a founder has to answer is not "can the robot pick?" but when does it beat a human shift, and what has to be true? The payroll clerk upstairs answers it the only fair way: what does one task done right cost each of them? Every term with a wavy red underline is tappable.

The picker = a human shift
paid per hour worked, wage plus benefits
The picker robot = the robot
paid for per year, used per hour
The payroll clerk = the cost model
every line on the payslip is an assumption
A pick = one task
the unit both are judged on
The remote desk = teleoperation
a person who helps stuck robots (step 2)
A call for help = an intervention
counted per running hour (step 2)
The lesson book = training data
and the flywheel it turns (step 3)
The ledger = the deal
payback, NPV, IRR (step 4)
The spares cage = fleet reserve
and the queue at the remote desk (step 5)
The pie = the saving
and who gets a slice (step 6)

Covers unit economics of automation: cost per task · labour cost: BLS wage and benefits data

The human payslip

Start with the number the robot has to beat. The default wage is the national mean for "laborers and freight, stock, and material movers, hand" in the Bureau of Labor Statistics' May 2025 survey, $20.32 an hour. An hour of work costs the employer more than the wage: the benefits load in BLS's December 2025 employer-cost survey was $13.79 on $32.36 of wages for private industry, 42.6%. Then divide by what the hour produces.

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an hour of work, to the Depot
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per good pick
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a year, one shift (2,000 h)
Guess first!
A picker earns $20.32 an hour. What does an hour of their work cost the Depot?
$28.98: benefits add 42.6% to every hour worked (paid leave, insurance, retirement, payroll taxes). That is the BLS average for all private-industry workers; warehouse employers' own loads differ, so the slider is yours. At 300 picks an hour and 99.5% right first time, that hour buys 298.5 good picks: 9.95¢ each, including a minute of rework for each miss.
Say it out loud
A robot doesn't replace a wage; it replaces a cost per task. The picker's $28.98 hour, plus rework, buys 298.5 good picks at 9.95¢ each, and that is the number to beat.

1 · Cost per pick: the robot's payslip

A robot isn't paid by the hour, but every year of it has to be paid for. Its payslip, per scheduled hour: a capital charge that repays the price and the integration over its life at the discount rate, upkeep, power, its share of a remote operator, and rework for every miss. Then divide by the good picks it actually makes, which is where uptime, cycle time, success rate and calls for help come in. Cost per good pick = the hour's cost ÷ the hour's good picks.

Covers total cost of ownership · capital recovery vs depreciation · utilisation

Two payslips, one scale

Robot numbers are illustrative assumptions, not any company's figures. Calls for help and the remote operator are step 2; they're on the slip already.
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robot, per good pick
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human, per good pick
–
robot saves
Where a good pick's cost goes. The robot's lines, left to right: capital, upkeep (maintenance and software), power, operators, rework.

Utilisation: the same robot, more hours

The picker costs the same per hour whether the Depot runs one shift or three. The robot's capital and upkeep are fixed per year, so every extra hour it works makes each pick cheaper.

Guess first!
At two shifts the robot costs 8.23¢ a pick against the picker's 9.95¢. The Depot only runs one shift. Now?
13.91¢: the capital charge and upkeep are spread over 2,000 hours instead of 4,000, and the robot loses. Three shifts: 6.33¢. Utilisation is the first thing to ask a customer about, before the robot's price.
Guess first!
Which line on the robot's payslip is the smallest?
Power: 8¢ an hour at a 1 kW average draw and EIA's 2024 industrial price of 8.13¢/kWh. The surprise is the other end: at 97% first-time success, rework is $4.65 an hour, more than the operator's share ($3.17). Only capital, at $13.19, is bigger. Success rate is a cost line, not a quality footnote.
Say it out loud
Cost per good pick is the hour's capital charge, upkeep, power, operator share and rework, divided by good picks. Utilisation spreads the fixed costs; uptime, cycle time and success set how many good picks there are to spread them over.

The books: every assumption

Every number the lab uses, where it comes from, and a slider. Changes here carry through every step. BLS EIA are cited public data (see SOURCES.md); illustrative numbers are assumptions to change; toy marks the teaching model in step 3.

2 · The remote desk: autonomy is not a yes or no

No robot in a real warehouse is fully autonomous. Some of the time it gets stuck (an item it can't grip, a tote out of place) and calls for help: an intervention. A remote operator fixes it by teleoperation. Two numbers describe this: interventions per running hour λ (or its inverse, the MTBI), and the operator time each one takes, τ (minutes per call, written as a share of an hour). Together they set the operator ratio: one operator can keep up with at most occupancy ÷ (λτ) robots.

Covers autonomy as a rate · teleoperation economics · the last 5% problem

Calls per hour, minutes per call

Minutes between calls (MTBI) illustrative–
Operator ratio
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calls per running hour
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autonomous, per pick attempt
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robots per operator
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operator busy
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operator cost per pick
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robot per good pick
Log scale: from a call every minute to one every 100 hours. The dot is where you are.

The last 5%

Autonomy quoted as a percentage hides the rate. At 10 seconds a pick, the robot attempts 360 picks a running hour, so every point of autonomy below 100% is 3.6 calls an hour.

Guess first!
The default robot calls for help twice an hour and each call takes the operator 2 minutes. That's 99.44% autonomous per pick. How many robots can one operator look after, staying 75% busy?
11.25. Each robot needs 2 × 2 = 4 operator-minutes per running hour, and 45 busy minutes an hour ÷ 4 = 11.25. "Over 99% autonomous" and "one person per eleven robots" are the same robot.
Guess first!
At 95% autonomy per pick the robot costs 23.8¢ a pick, with 1.25 robots per operator. At 99.9%?
7.13¢. Almost the whole gain is in the last five points: 99% is still 9.42¢, barely under the picker. Past 99.9% the curve goes flat (99.99%: 7.07¢): the operator line has shrunk to a sliver, one person is capped at watching 50.0 robots, so the rest of the payslip is all that's left. The last 5% of autonomy is where a robot company's economics are made.
Say it out loud
Autonomy is a rate: calls per hour times minutes per call. That product sets how many robots one person can watch, and over the last few percent of autonomy the operator line collapses from a cost that sinks the robot to almost nothing.

3 · The flywheel: interventions are training data

Every intervention is a labelled example of something the robot couldn't do, recorded exactly where it went wrong. Feed them back into training (the idea behind DAgger and human-in-the-loop learning) and the next software release calls for help less. The more robots deployed, the more hours, the more lessons: a flywheel. How fast it spins is not something this lab can measure, so it is modelled as a transparent toy: interventions per hour fall by a fixed share each time the vendor's cumulative fleet hours double, a learning curve borrowed by analogy from Wright's 1936 study of airframe labour (about 20% per doubling). No robotics company's curve is used or implied.

Covers learning curves · data network effects · one line of DAgger / HIL

Calls per hour, as the fleet's hours double

A toy, labelled. λ(H) = λ₀ · (H / H₀)^log₂(1 − drop), never below the floor. H₀ is the vendor's fleet hours so far, growing by the hours per year. Change any of it.
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calls an hour, year 1
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year 3
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year 5
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robot beats the picker from
Left scale: cents per good pick. Right scale, in brick red: calls per running hour. The dashed green line marks the month the robot gets cheaper than the picker, if it does.
Guess first!
A younger robot calls for help 6 times an hour and loses to the picker today. With 20% fewer calls per doubling, starting at 200,000 fleet hours and adding 400,000 a year, when does it start beating the picker?
Month 12 (set calls to 6 and read the tile). The early doublings come fast: 200,000 hours becomes 600,000 in the first year. The later ones are slow: by year 3 the default robot has had 2.81 doublings and calls 1.07 times an hour, not zero. A curve per doubling rewards whoever has the most deployed hours.
Guess first!
For the Depot's fleet of 20, what does the learning curve add to the deal's NPV (step 4, 5 years at 10%)?
NPV goes from $1.63M to $2.20M when the software updates bring the calls down (toggle "learning" in step 4). Fewer calls means fewer operators, because the ratio follows the workload. That's why buyers ask whether updates are included, and investors ask for the curve: by cohort, by site, with the definition of an intervention fixed.
Say it out loud
Every intervention is a training example. If the vendor learns from them, calls fall with doublings of fleet hours, so deployed hours are the moat, and the curve is an assumption to ask for, not a fact to assume.

4 · The ledger: payback, NPV, IRR, and rent or buy

Now the Depot considers a fleet. Year 0: it pays for the robots and their integration. Every year after: it saves the payroll for the picks the robots make, minus what the robots cost to run. The clerk reports three numbers: payback (when cash in covers cash out), NPV at the discount rate, and IRR. Then two questions a board asks: rent or buy, and which assumption matters most (the tornado).

Covers capital budgeting: payback, NPV, IRR · RaaS vs buy · sensitivity analysis · break-even wage

A fleet deployment

RaaS here: a monthly fee per robot that includes the hardware, maintenance and software; the Depot still pays for integration, power, operators and rework. Contracts vary; this one is illustrative.
Undiscounted running total of cash: the year-0 outlay, then each year's saving. Where a line crosses zero is its simple payback.
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break-even wage: robot = human per pick
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wage at which NPV = 0

Which assumption matters most?

Each bar moves one assumption to a low and a high value (labelled), everything else at the books, and shows the fleet's NPV. Widest first.

the pessimistic end of each range · the optimistic end · the solid line is the books' NPV
Guess first!
Of these, which swings the fleet's NPV the most across its range?
Shifts (the tornado's top bar: Shifts a day). One shift and the deal loses money; three and NPV more than triples. A deck that quotes payback "on a 24/7 operation" to a one-shift customer is quoting a different deal. Useful life is next: robots that last 3 years rather than 5 turn the NPV negative.
Guess first!
The fleet pays back in 32 months with an NPV of $1.63M and an IRR of 24.9%. Below what wage does the robot stop beating the picker?
$16.18, only 20% under the national mean. And the wage at which NPV hits zero is the same, $16.18: the capital line on the payslip is the level payment that repays the robot at the discount rate, so "cheaper per pick" and "positive NPV" are one test. Renting at $5,000 a robot-month gives an NPV of $1.44M: less, but with a quarter of the cash up front and the vendor carrying the hardware risk.
Say it out loud
Payback ignores the cost of money and every year after it; NPV and IRR don't. The deal turns on utilisation and useful life before the robot's price, and the break-even wage says which labour markets it works in.

5 · The fleet: shared operators, queues and spares

With twenty robots sharing a remote desk, two of them sometimes get stuck at once, and one waits. A waiting robot isn't picking. This is a queue: calls arrive at random, operators serve them, and the Erlang C formula from the M/M/c queue gives the chance a call waits and how long. The arrival rate depends on how many robots are running, which depends on how long they wait, so the model solves for both together. Then the other fleet question: how many spares.

Covers queueing: M/M/c, Erlang C, the finite-population check · pooling · spares (binomial)

The remote desk as a queue

Robots sharing the desk–
Operators on shift–
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offered load (erlangs)
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each operator busy
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calls that wait (Erlang C)
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average wait per call
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of a robot's time spent waiting
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robot per good pick

Pooling: the same ratio, bigger desks

Spares

Chance the full fleet is working–
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chance all are up, no spares
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spares needed
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extra robot capital
Guess first!
Twenty robots share two operators, each operator busy about 60% of the time. How long does a stuck robot wait, on average, before someone picks up?
60 seconds on top of the 2-minute fix: 42% of calls find both operators busy, because calls arrive in clumps. One operator for twenty robots: 12.2 minutes, and the robot loses to the picker. Three: 9 seconds. The cheapest desk here has 2 operators: fewer and robots idle, more and operators idle.
Guess first!
Keep the ratio at one operator per ten robots. Ten robots with one operator, or a hundred robots with ten: who waits longer?
Ten robots, one operator: 147 seconds a call. A hundred robots, ten operators: 3 seconds. That's pooling: a busy moment at one robot is a quiet one at another. An operator ratio from a small pilot understates what a big fleet can run; a ratio quoted for a big fleet overstates what a small customer gets.
Say it out loud
When robots share operators, calls queue, and waiting robots don't pick. Erlang C prices the wait; pooling operators across a bigger fleet makes the same ratio wait far less, so scale is an economy of the remote desk. Spares are a binomial: with 95% uptime, twenty robots are all up only about a third of the time.

6 · Who gets the saving: the investor's lens

A robot replaces payroll. That payroll is a pie, and the customer is the last to be served: the robot maker takes its hardware and service price, the integrator its fee, the money tied up its interest, the operators their wages, and rework and power their share. This is a one-step illustrative split of one robot-year at the books' numbers, with margins you can change. It shows the mechanics, not any company's economics.

Covers value capture · price ceilings · robotics diligence

One robot-year of replaced payroll, sliced

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payroll replaced a robot-year
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the Depot keeps
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price ceiling for the robot
Guess first!
A robot replaces $123,780 of picker payroll a year. How much of it does the Depot keep?
17%. The robot maker's gross profit is $21,000 a robot-year at these margins, about as much as the customer keeps. The robot's price ceiling is $212,360: above it the Depot is better off with pickers. Every point of uptime, success or autonomy raises that ceiling, which is why a robot company's pricing power lives in its operating metrics, not its bill of materials.

The diligence checklist

A robotics startup's deck quotes an MTBI, an operator ratio and an autonomy rate. Put its claims here; the checklist tests them against each other and the books, and lists what to ask for. The 95% range on MTBI is the exact Poisson interval for the number of interventions behind it.

Claimed MTBI–
Robot-hours behind the claim–
Claimed robots per operator–
Claimed autonomy per pick–
Guess first!
A deck says "MTBI of 8 hours", from 120 robot-hours of pilot data. What range is that consistent with?
120 hours at 8 hours each is 15 interventions, and the exact 95% interval for 15 random events turns into an MTBI between 4.9 and 14.3 hours. Ask for the hours behind every rate, by site and by month, and for the definition of an intervention.
Say it out loud
The saving is the payroll replaced minus everyone else's slice; the customer eats last, and the robot's price ceiling is set by the payroll. Diligence asks for the numbers that size the pie: calls per hour, minutes per call, uptime, success, operator ratio, and the hours behind each.

★ Investor review board

Three pitch decks from three fictional robot companies, each with one flawed line in its spreadsheet. For each: run the deck's own sheet through the model (it reproduces the claim), pick the fix, re-run it, and name what the deck got wrong. The tempting fixes are on the list; they move the number the wrong way, or not at all. Each deck is scored on the re-run and the diagnosis.

☆☆☆

✓ Field test

Ten questions. Answer each by operating the widget in the step named, at the books' default assumptions (reset them in step 1 if you've changed any). Eight or more earns the check.

What's exact here, what's sourced, and what's a model

  • Exact arithmetic: the capital recovery factor, NPV, IRR (bisection), payback, break-even wages (bisection), Erlang C (from Erlang B by the standard recursion), the M/M/c wait, the finite-population "machine-repair" queue used as a cross-check, binomial spares, and the exact (Garwood) Poisson interval. node tests/check.js checks each against hand-computed cases and prints every number this page quotes.
  • Sourced defaults: the picker's wage ($20.32, BLS Occupational Employment and Wage Statistics, May 2025, SOC 53-7062, national mean); the benefits load (42.6%, BLS Employer Costs for Employee Compensation, December 2025, private industry, $13.79 of benefits on $32.36 of wages per hour worked); electricity (8.13¢/kWh, EIA's 2024 US average industrial price). Dated, with links, in SOURCES.md.
  • Illustrative assumptions, labelled on every slider: every robot number (price, integration, life, maintenance, software, power draw, uptime, cycle time, success, interventions, minutes per intervention), the human's picks per hour and accuracy, rework minutes, the operator's wage and ratio limits, the discount rate, the RaaS fee, and the margins in step 6. Publicly listed robot prices are quoted in SOURCES.md only as anchors (a $24,950 mobile manipulator for research, a $74,500 quadruped in 2020); a warehouse picking cell is a different product. No company's private numbers are used, and the three decks are fictional.
  • Teaching models: the learning curve is a toy (a Wright-style curve by analogy, not a measurement). The queue assumes random arrivals and service times and uses the infinite-population Erlang C with a fixed point for the call rate; the exact finite-population model is shown beside it and waits less for small fleets. Cash flows are yearly, pre-tax, with no residual value, no ramp-up and no inflation. Humans are assumed to be paid only for hours worked; real staffing has minimum shifts, overtime, hiring and turnover costs this model leaves out.

Sources (dated, with what each supports, in SOURCES.md): BLS OEWS, 53-7062 · BLS Employer Costs for Employee Compensation · EIA Electric Power Annual · IFR World Robotics 2025 · Wright (1936), "Factors Affecting the Cost of Airplanes" · Erlang (1917) · Ross, Gordon & Bagnell (2011), DAgger.

Part of a series of hands-on labs: Inference Kitchen (serving economics) · Compute Deal Desk (compute deals) · Arm Playground (kinematics and control) · Demos to Deployment (imitation learning) · Robot Payroll (the business of deploying robots)