A fast reply can leave the work unfinished
A customer asks why an order has not arrived. The assistant immediately drafts an elegant reply, but an operator must check shipping, terms and the promise made to the customer. The message goes out earlier; the problem returns tomorrow. A support manager needs to know whether total work to resolve a request falls while acceptable quality is maintained, rather than merely how fast AI writes. We build a verifiable calculation including review and rework, then derive when selective assistance is preferable.
The example contains one hundred invented requests split into routine and complex cases. Times, categories and rework cases are teaching inputs, not observed frequencies. We ran no model on real conversations, timed no operators and measured no customer satisfaction. This analyzes conditions for a choice; it promises no savings. Attached code reproduces every numerical result of our own, while missing conditions for a business trial remain explicit.
Choose the outcome before starting the clock
A request is a work episode, not necessarily one message. Our episode starts with examining the case and ends after resolution, including possible later intervention. For simplicity, that intervention always resolves the problem and no further reopening occurs. This is a strong assumption. Counting unresolved issues as completed artificially improves the productivity denominator. A real trial needs consistent definitions of resolution and observation windows.
Also distinguish active work from elapsed time. Ten minutes while a customer finds a document do not automatically consume ten exclusive operator minutes; another case may be handled meanwhile. Conversely, a draft generated in seconds can need minutes of attention. Our arithmetic sums assigned episode durations without modeling concurrency, queues or deadlines. A trial must separately measure staff workload, customer waiting and technical generation latency.
The minimum test a draft must pass
Let M be minutes for manual handling. Under assistance, d is assigned generation time, r initial review and w additional work when later correction is required. q is the fraction needing that intervention. Times are minutes per case; q is dimensionless between zero and one. Assisted mean A sums d and r, incurred every time, and qw, incurred only for reworked cases.
This is accounting, not an estimate of model effectiveness. It assumes the same w for reworked cases within a category and no omitted costs beyond the defined boundary. With varying durations, sum actual episodes or use mean cost conditional on rework. Do not combine one group’s frequency with another group’s duration without checking compatibility. Acceptable quality remains an external constraint, not something the formula guarantees.
For eighty routine cases choose M=4, d=0.2 and r=2 minutes. Four need eight additional minutes each: q=4/80=0.05. The draft takes twelve seconds, but the complete mean is 0.2+2+0.05×8=2.6 minutes. Group totals are 320 manual minutes and 208 assisted minutes. Most assisted time is review and later work, not generation: the first reason text speed alone cannot measure benefit.
When the same initial speed makes the outcome worse
For twenty complex cases set M=12, d=0.2 and r=10 minutes. Six require twenty extra minutes: q=6/20=0.30. Drafting is just as fast, but assisted mean becomes 16.2 minutes versus twelve manually. Group total rises from 240 to 324 minutes. We have not established real complex-case behavior: we constructed equal drafting speed with a different decision because review and rework change.
The useful threshold asks how much rework a category can tolerate before losing its time advantage. For positive w, subtract d+r from d+r+qw< M and divide by w. The threshold is q*=(M−d−r)/w. The inequality is strict: at the threshold times match. If M−d−r is negative, even zero rework cannot make assistance faster here; if the threshold exceeds one, time does not discriminate feasible fractions.
Routine threshold is 22.5%, above the assumed 5%; complex threshold is 9%, below the assumed 30%. These are neither model confidence scores nor market measurements. They depend on assigned minutes. More review may lower q, but not free of cost: both parameters may move together. Changing one while fixing the other is accounting sensitivity, not proof a product can achieve the change.
The overall average can hide where AI does not help
Together, manual work is 560 minutes. Assisting everything gives 532, a 28-minute or 5% reduction. Assisting only eighty routine cases and keeping twenty complex cases manual gives 208+240=448 minutes, 20% below baseline. All strategies face exactly the same hundred requests and assume eventual resolution. We do not change the mix to favor a strategy. Selection is known only because the author constructed the categories.
In the table M means manual, A assistance for all and S0 ideal selection without routing cost.
| Mode | Routine (min) | Complex (min) | Total (min) |
|---|---|---|---|
| M | 320 | 240 | 560 |
| A | 208 | 324 | 532 |
| S0 | 208 | 240 | 448 |
Bars show total minutes per hundred episodes, not model speed or hours actually freed in a company. Selective assistance is lower because it avoids the complex group’s 84 additional minutes relative to manual handling. If identifying categories costs time or makes mistakes, add that cost. Our selective strategy is an ideal comparison with free, correct classification, not a deployment-ready solution.
Read percentages with the right denominator. Going from 560 to 448 minutes reduces time for the same work by 20%; it does not mean capacity rises by 20%. With fixed available time the theoretical ratio is 560/448=1.25, or 25% more, only if workload and constraints remain identical. Code checks both. Neither percentage describes customer waits, wages, staffing or real capacity, which depend on unmodeled factors.
Deciding who handles a case also costs time
Make selection less ideal with another calculation, without inventing a tested classifier. c is routing minutes per request; f is the fraction of twenty complex cases wrongly assigned AI, with routine assignments still correct. Total time becomes 448+100c+84f. The 84f term is the complex group’s extra assisted work, 324−240, applied to the wrong fraction. Errors are assumed uniform within the category; if the most costly cases are misrouted, rebuild the calculation by episode.
With half the complex cases misrouted, thirty seconds routing per request gives 540 minutes; forty-eight seconds gives 570. The latter exceeds 560 manual minutes: selection’s advantage can disappear without changing drafting time. Code checks both, measuring no real system. A trial therefore needs both execution and routing, instead of presenting an ideal comparison as if case distinction were already free and available.
What published research adds
Brynjolfsson, Li and Raymond’s Generative AI at Work (QJE, 2025) studies staggered introduction among 5,172 agents using differences in differences: roughly +15% hourly resolutions, with heterogeneous effects. This is the authors’ context-specific evidence, not our replication or an automatically transferable benefit.
A company before/after comparison may confuse tool effects with changing requests or operator experience. Our exercise therefore does not imitate a causal study with invented data. Arithmetic establishes consequences of assumptions, not consequences that adoption will cause. Even an observed mean across people cannot predict every request category. A transferable decision needs measurement of the local process, separating mix from effect.
A useful trial retains the work that comes back
Before a trial define correctness: current information, case-compatible instructions and no unauthorized promise. Set the window for recognizing reopenings and later interventions. A non-AI alternative, such as approved text linked to a verified procedure, should be eligible. If only wording changes while the operator still searches for every fact, the intervention assists writing, not automatic diagnosis.
We propose, without claiming execution, comparing authorized or synthetic cases stratified by difficulty defined before use. Assignment should prevent AI receiving only easy requests. If an operator sees a problem twice, memory can benefit the second attempt: control order and learning. Retain review times, necessary edits, outcomes and reopenings to reconstruct the difference. One final average without that trail cannot explain what to change.
Counting accepted drafts alone creates selection: rejected outputs, failed attempts and manual fallbacks disappear. Include these in assisted-mode analysis under a predefined rule. Quality assessment should use repeatable criteria and, where possible, hide which mode produced the text. We claim no human reviewers or reader tests here; these are missing checks between an accounting example and operational evidence.
Where a simple solution can win
For repetitive questions with stable answers, approved templates and document search can reduce work without free-form generation. For order- or permission-dependent cases, information access may matter more than wording. A domain-adapted vertical model is a hypothesis to compare, not a proven requirement. Assess it against the same cases, criteria and review costs. Technological complexity wins no automatic prize.
Startup cost is excluded to keep the mechanism readable. Real decisions include integration, procedure updates, training, licenses and service oversight. Freed time does not necessarily save cash; it may reduce backlogs or improve neglected cases. We have no data to quantify this. State both included work and the business outcome of interest, avoiding double counting benefits describing the same phenomenon.
The decision the arithmetic actually supports
In our constructed workload, universal assistance cuts time by 5% while worsening complex cases; ideal selective use cuts 20%. These figures motivate category-specific checks including review and rework. They authorize no promise of those percentages to customers. Insufficient quality cannot be offset by favorable minutes. If categories cannot be recognized at sustainable cost, the selective strategy has not been implemented.
Complete code uses decimal arithmetic and assertions for totals and thresholds. Summation is linear in category count; it generates no answers and fits no neural network. Results retain assumptions and limits. This is AI-assisted editorial analysis, not an EL-AI customer or staff experiment. We attribute no new products, results or installations to the company: value comes from reproducible comparison and a better question for a trial.
Brynjolfsson, Li & Raymond (2025) — QJE, doi:10.1093/qje/qjae044.
from decimal import Decimal as D
from pathlib import Path
import json,sys
# Hypothetical workload only: no customers, operators, models or timings measured.
groups=[dict(key='routine',count=80,manual=D(4),draft=D('.2'),review=D(2),reworkCases=4,reworkMinutes=D(8)),dict(key='complex',count=20,manual=D(12),draft=D('.2'),review=D(10),reworkCases=6,reworkMinutes=D(20))]
rows=[]
for g in groups:
q=D(g['reworkCases'])/g['count'];mean=g['draft']+g['review']+q*g['reworkMinutes'];limit=(g['manual']-g['draft']-g['review'])/g['reworkMinutes']
rows.append(dict(group=g['key'],count=g['count'],hypotheticalReworkFraction=str(q),manualMinutes=str(g['manual']),assistedMeanMinutes=str(mean),breakEvenReworkFraction=str(limit),manualTotalMinutes=str(g['count']*g['manual']),assistedTotalMinutes=str(g['count']*(g['draft']+g['review'])+g['reworkCases']*g['reworkMinutes'])))
manual=sum(D(x['manualTotalMinutes']) for x in rows);allAI=sum(D(x['assistedTotalMinutes']) for x in rows);selective=D(rows[0]['assistedTotalMinutes'])+D(rows[1]['manualTotalMinutes'])
assert (manual,allAI,selective)==(D(560),D(532),D(448))
assert D(rows[0]['breakEvenReworkFraction'])==D('.225') and D(rows[1]['breakEvenReworkFraction'])==D('.09')
assert D(rows[0]['assistedMeanMinutes'])==D('2.6') and D(rows[1]['assistedMeanMinutes'])==D('16.2')
assert D('.2')*60==12 and manual-allAI==28 and D(rows[1]['assistedTotalMinutes'])-D(rows[1]['manualTotalMinutes'])==84
assert manual/selective==D('1.25')
routeLow=selective+100*D('.5')+84*D('.5')
routeHigh=selective+100*D('.8')+84*D('.5')
assert routeLow==540 and routeHigh==570
result=dict(routingSensitivity=dict(complexMisrouteFraction='.5',halfMinuteRoutingTotal=str(routeLow),pointEightMinuteRoutingTotal=str(routeHigh)),python=sys.version.split()[0],seed=None,scope='Synthetic deterministic workload arithmetic. No model, staff, customer, causal trial, rework frequency or quality measured. Assumes every episode becomes resolved after one specified rework; no queue or service-level model.',rows=rows,totalsMinutes=dict(manual=str(manual),allAssisted=str(allAI),routineOnlyAssisted=str(selective)),timeReductionFractions=dict(allAssisted=str((manual-allAI)/manual),routineOnlyAssisted=str((manual-selective)/manual)),warning='Time reduction differs from throughput increase; cannot infer observed savings or wage reductions. Draft latency and active staff time must be separated in real measurement.')
Path(__file__).with_name('results.json').write_text(json.dumps(result,indent=2),encoding='utf8')
print(json.dumps(result))
Code, data, and instructions · JSON. Educational calculations executed with Python 3.14.0; figures with Matplotlib 3.11.2. AI-assisted analysis, without claiming peer review or human review. Original illustrative ImageGen cover: it does not document EL-AI people, premises, or installations. Sources accessed 3 November 2026.