Capacity planner skill

Use when an ops leader (Director of CX, Head of Support, VP Ops, Head of BizOps, Head of IT ops, Head of Finance ops) is sizing ops capacity, building a headcount plan, modeling utilization risk, planning Q3 capacity or annual support capacity, or designing CS coverage — and needs Erlang-C queueing math, P90 demand sizing, shrinkage-adjusted FTE, manager-trigger thresholds, and a quarterly hiring sequence with ramp + attrition.

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capacity-planner

Sizing tool for ops teams that handle queued work — Support, CX, Customer Success, BizOps, IT ops, Finance ops. Built on Erlang-C queueing theory, Little's Law, and the operational-leadership canon (Fournier, Larson, Cleveland, Reinertsen). Deterministic, stdlib-only, no LLM calls.

Purpose

You are an ops leader sized 15 → 35 with no idea how the 35-person org will actually behave at peak load. Or you are at 88% utilization and SLA is starting to slip. Or you have a hiring budget approved and need to sequence it across four quarters without burning out the existing team. This skill answers those questions with arithmetic, not vibes.

It produces three artifacts:

Capacity sizing at 70/80/90% utilization against P50/P90/P99 demand, with P(SLA breach) at each point and a SAFE/WATCH/AT_RISK/CRITICAL risk band.
Utilization health at the per-member traffic-light level plus a team verdict (HEALTHY/SQUEEZED/OVERLOADED/UNBALANCED).
12-month quarterly hiring plan accounting for ramp curves, attrition, QoQ demand growth, and span-of-control manager triggers.

When to use

Annual ops capacity planning (October-November for the following fiscal year).
Quarterly re-sizing if demand changed >15% or attrition spiked.
Pre-budget defense — the math that justifies the headcount ask to your CFO.
Diagnostic when an ops team is missing SLA and you need to know whether it's a sizing problem, a process problem, or a bottleneck problem.
M&A / new-segment launch modeling — sizing a new team or combined org.

Workflow

Intake demand. Pull P50/P90/P99 daily ticket/case volume from your work system (Zendesk, Intercom, JSM, ServiceNow, Salesforce). If you only have averages, stop and pull the distribution. Single- point demand estimates are the most expensive anti-pattern in ops.
Model throughput. Run capacity_modeler.py with your demand, AHT, SLA target, current FTE, and shrinkage. Use --profile for your function (support / cx / bizops / finance-ops / it-ops). Read the 80%-utilization row — that's your sizing point.
Flag utilization risk. Run utilization_analyzer.py against your current team's actual utilization data. Anyone >85% sustained is a throughput-collapse risk per Reinertsen. Spread >30 percentage points across team means UNBALANCED — fix that before hiring.
Sequence hiring. Run hiring_sequencer.py with current FTE, target EOY, ramp time, attrition, and growth. It will front-load hires (Q1 35%, Q4 15%), apply ramp curves, and trigger a manager hire when span of control crosses 7 ICs/manager.
Walk the Forcing-question library (see below). One question at a time. Do not skip ahead. Answers must be written down before you commit the plan.

Scripts

scripts/capacity_modeler.py — Erlang-C sizing with shrinkage adjustment and P50/P90/P99 breach probabilities. --profile for industry defaults.
scripts/utilization_analyzer.py — per-member traffic-light + team-level health verdict with variance detection.
scripts/hiring_sequencer.py — 12-month quarterly plan with ramp, attrition, growth, max-hires-per-quarter constraint, and manager-trigger logic.

All three accept --input <path> (JSON), --output {markdown,json}, --sample (built-in example), and --help. Stdlib only.

Quick example

# Emits an Erlang-C capacity model (required headcount + P50/P90/P99 breach probabilities) for the built-in example
cd business-operations/skills/capacity-planner && python3 scripts/capacity_modeler.py --sample

References

references/queueing_theory_canon.md — Erlang, Little, Hopp & Spearman, Reinertsen, Kingman, Cleveland, ITIL, Armony et al. (8 sources). The math.
references/ops_workforce_planning_canon.md — Fournier, Larson, Google SRE Workbook, Frei, Lawler, Bersin, Gartner, Grove (8 sources). The people factors.
references/capacity_anti_patterns.md — 11 named anti-patterns with cited sources, tool guards, and the meta-discipline that Lencioni + Goldratt + Christensen impose. (8+ named sources.)

Assets

assets/capacity_brief_template.md — 20-minute fill-out template with JSON skeletons for all three tools and an output checklist.

Assumptions

This skill assumes:

Work is queued (tickets, cases, work items) — not project-style. If your team's work isn't queued, this is the wrong skill.
Demand has a stationary-enough distribution within a quarter. Step-changes (new product launch, M&A, regulatory shift) require re-running mid-quarter.
You have at least 90 days of historical demand data to compute P50/P90/P99. If not, generate the distribution from your sales / user-base forecast first.
Service is single-class within a queue. If you have hard priority tiers (P1/P2/P3 with class-specific SLAs), model each as a separate queue and sum.
Channels are modeled coherently. Multi-channel teams use the appropriate --profile with built-in shrinkage premium.

Anti-patterns

See references/capacity_anti_patterns.md for the full taxonomy with sources. Top eight:

Plan-to-100%-utilization (Reinertsen Principle 12)
Treat-ramp-as-instant (Larson)
Ignore-attrition-in-12-month-plan (Bersin)
Hire-ICs-forever-with-no-manager-trigger (Fournier)
Size-to-P50-demand-only (Cleveland)
No-shrinkage-adjustment (Cleveland, SRE Workbook)
Single-channel-model-for-multi-channel-work (Gartner, Kingman)
No-surge-plan-for-P99-events (Hopp & Spearman, Reinertsen)

Distinct from

c-level-advisor/vpe-advisor measures engineering throughput via DORA 4 metrics, story points, deployment frequency, and cycle time bottlenecks. It is for engineering teams shipping code. This skill is for ops teams handling tickets/cases. Different unit of work, different math (Erlang-C vs. DORA), different bottleneck (queueing-blind staffing vs. WIP + lead time).
c-level-advisor/chro-advisor does strategic workforce planning (1-5 year capability portfolios, talent supply, leadership succession). This skill does operational 0-12 month capacity sizing against demand. Per Lawler: conflating them gets you hired into the wrong jobs.
project-management/* tracks delivery throughput on projects (Jira velocity, sprint capacity). This skill sizes around steady- state queued work.
Sibling process-mapper finds the bottleneck. This skill sizes the team around a known bottleneck. Order of operations: process-mapper first → capacity-planner second. Hiring around the wrong constraint wastes the hires.
business-growth/cs-coverage (if it exists) sizes Customer Success coverage by ARR/CSM ratio and segment. This skill sizes by queued work volume (tickets, cases, escalations). For a CS team that handles both relationship work AND a ticket queue, run both.

Forcing-question library (Matt Pocock grill discipline)

Discipline: walk these one at a time. Do not skip ahead. Answers must be written down. If you can't answer one, that is your next investigation.

Q1 — "What is your bottleneck, and have you confirmed it empirically?"

Recommended answer: a named, measured stage in the workflow with queue-time data showing where work waits. Not a vibe. Not "escalations take too long". An actual measured queue.

Why it's the first question: Goldratt (The Goal, 1984) — every system has exactly one binding constraint at a time. Sizing around the wrong constraint wastes hires entirely. If you do not know your bottleneck, run process-mapper BEFORE this skill.

Canon: Eli Goldratt, The Goal (1984); Reinertsen, Principles of Product Development Flow (2009).

Q2 — "What service trade-off are you accepting?"

Recommended answer: a written, explicit choice — fast vs. empathetic, broad vs. deep, low-cost vs. high-quality. Frances Frei is unambiguous: you cannot win all four. The team that tries wins zero.

Why it matters: AHT, SLA, and shrinkage inputs are the operational expression of this trade-off. If they don't agree (e.g., you set AHT for "empathy" but SLA for "speed"), the plan is internally inconsistent.

Canon: Frances Frei & Anne Morriss, Uncommon Service (HBR Press, 2012).

Q3 — "What's your demand P90, and what's the gap to your P99?"

Recommended answer: two specific numbers from the last 90 days of data, with the calendar context of each (e.g., "P90 was 480 tickets/day on normal Tuesdays; P99 was 720 on the day after the November release"). A team sized to P50 misses SLA half the time. A team sized to P99 overstaffs by 30-50%. P90 is the right operating sizing point per Cleveland.

Canon: Brad Cleveland, Call Center Management on Fast Forward (4th ed., 2019); A.K. Erlang, The Theory of Probabilities and Telephone Conversations (1909).

Q4 — "At your planned utilization, what is P(SLA breach) at P90 and at P99?"

Recommended answer: two probabilities, computed (not guessed) from Erlang-C with your specific N, AHT, and SLA target. If P(breach at P90)

10% you are understaffed at the sizing point. If P(breach at P99) > 50% you have no surge plan and the next peak event will be visible to the CEO.

Canon: Erlang (1909); Hopp & Spearman, Factory Physics (3rd ed., 2008), VUT equation.

Q5 — "Have you budgeted replacement hires for the attrition you'll see this year?"

Recommended answer: yes, with a specific number. At 30% annual attrition (Bersin BPO midpoint), a 20-FTE team loses ~6 people this year. If your "add 5 net" plan is actually a "hire 11" plan, the recruiting volume changes drastically. Anti-pattern #3.

Canon: Bersin/Deloitte talent benchmarks (2015-2023); Edward Lawler, Strategic Workforce Planning (USC CEO, 2008).

Q6 — "When does span of control trigger a manager hire, and who is the candidate?"

Recommended answer: a specific quarter (from hiring_sequencer.py) and at least one identified candidate (internal lead or external hire). Past 7 ICs/manager, 1:1s degrade, feedback cycles slip, attrition climbs. Past 10 you have a coverage crisis. Hire the manager BEFORE crossing 10, not after.

Canon: Camille Fournier, The Manager's Path (O'Reilly, 2017), ch. 5; Andy Grove, High Output Management (1983).

Q7 — "What is your surge plan for the P99 day?"

Recommended answer: an explicit, documented plan — overflow tier, BPO contracted capacity, on-call rotation, executive escalation tree, OR a written degradation contract that says "on P99 days we extend SLA to X minutes and notify customers proactively". If the answer is "we'll figure it out", the P99 day is a fire visible to the board.

Canon: Hopp & Spearman, Factory Physics (2008); Reinertsen (2009) on capacity-margin discipline.

Walk these seven in order. One at a time. Write the answers down. The plan you submit is only as defensible as your answers to these seven questions.

1	---
2	name: capacity-planner
3	description: "Use when an ops leader (Director of CX, Head of Support, VP Ops, Head of BizOps, Head of IT ops, Head of Finance ops) is sizing ops capacity, building a headcount plan, modeling utilization risk, planning Q3 capacity or annual support capacity, or designing CS coverage — and needs Erlang-C queueing math, P90 demand sizing, shrinkage-adjusted FTE, manager-trigger thresholds, and a quarterly hiring sequence with ramp + attrition. Apply when sustained team utilization is above 80% or when the team is growing >50% in 12 months. Run before committing the headcount budget. This is NOT engineering capacity (see vpe-advisor for DORA + cycle time) and NOT strategic 3-year workforce planning (see chro-advisor)."
4	version: 2.8.0
5	author: claude-code-skills
6	license: MIT
7	tags: [bizops, capacity, headcount, utilization, queueing-theory, ops-planning, little-law, workforce]
8	compatible_tools: [claude-code, codex-cli, cursor, antigravity, opencode, gemini-cli]
9	---
10
11	# capacity-planner
12
13	Sizing tool for ops teams that handle queued work — Support, CX,
14	Customer Success, BizOps, IT ops, Finance ops. Built on Erlang-C
15	queueing theory, Little's Law, and the operational-leadership canon
16	(Fournier, Larson, Cleveland, Reinertsen). Deterministic, stdlib-only,
17	no LLM calls.
18
19	## Purpose
20
21	You are an ops leader sized 15 → 35 with no idea how the 35-person org
22	will actually behave at peak load. Or you are at 88% utilization and
23	SLA is starting to slip. Or you have a hiring budget approved and need
24	to sequence it across four quarters without burning out the existing
25	team. This skill answers those questions with arithmetic, not vibes.
26
27	It produces three artifacts:
28
29	1. Capacity sizing at 70/80/90% utilization against P50/P90/P99
30	demand, with P(SLA breach) at each point and a SAFE/WATCH/AT_RISK/CRITICAL
31	risk band.
32	2. Utilization health at the per-member traffic-light level plus a
33	team verdict (HEALTHY/SQUEEZED/OVERLOADED/UNBALANCED).
34	3. 12-month quarterly hiring plan accounting for ramp curves,
35	attrition, QoQ demand growth, and span-of-control manager triggers.
36
37	## When to use
38
39	- Annual ops capacity planning (October-November for the following
40	fiscal year).
41	- Quarterly re-sizing if demand changed >15% or attrition spiked.
42	- Pre-budget defense — the math that justifies the headcount ask
43	to your CFO.
44	- Diagnostic when an ops team is missing SLA and you need to know
45	whether it's a sizing problem, a process problem, or a bottleneck
46	problem.
47	- M&A / new-segment launch modeling — sizing a new team or
48	combined org.
49
50	## Workflow
51
52	1. Intake demand. Pull P50/P90/P99 daily ticket/case volume from
53	your work system (Zendesk, Intercom, JSM, ServiceNow, Salesforce).
54	If you only have averages, stop and pull the distribution. Single-
55	point demand estimates are the most expensive anti-pattern in ops.
56	2. Model throughput. Run `capacity_modeler.py` with your demand,
57	AHT, SLA target, current FTE, and shrinkage. Use `--profile` for
58	your function (support / cx / bizops / finance-ops / it-ops). Read
59	the 80%-utilization row — that's your sizing point.
60	3. Flag utilization risk. Run `utilization_analyzer.py` against
61	your current team's actual utilization data. Anyone >85% sustained
62	is a throughput-collapse risk per Reinertsen. Spread >30 percentage
63	points across team means UNBALANCED — fix that before hiring.
64	4. Sequence hiring. Run `hiring_sequencer.py` with current FTE,
65	target EOY, ramp time, attrition, and growth. It will front-load
66	hires (Q1 35%, Q4 15%), apply ramp curves, and trigger a manager
67	hire when span of control crosses 7 ICs/manager.
68	5. Walk the Forcing-question library (see below). One question at
69	a time. Do not skip ahead. Answers must be written down before
70	you commit the plan.
71
72	## Scripts
73
74	- `scripts/capacity_modeler.py` — Erlang-C sizing with shrinkage
75	adjustment and P50/P90/P99 breach probabilities. `--profile`
76	for industry defaults.
77	- `scripts/utilization_analyzer.py` — per-member traffic-light +
78	team-level health verdict with variance detection.
79	- `scripts/hiring_sequencer.py` — 12-month quarterly plan with ramp,
80	attrition, growth, max-hires-per-quarter constraint, and
81	manager-trigger logic.
82
83	All three accept `--input <path>` (JSON), `--output {markdown,json}`,
84	`--sample` (built-in example), and `--help`. Stdlib only.
85
86	## Quick example
87
88	```bash
89	# Emits an Erlang-C capacity model (required headcount + P50/P90/P99 breach probabilities) for the built-in example
90	cd business-operations/skills/capacity-planner && python3 scripts/capacity_modeler.py --sample
91	```
92
93	## References
94
95	- `references/queueing_theory_canon.md` — Erlang, Little, Hopp &
96	Spearman, Reinertsen, Kingman, Cleveland, ITIL, Armony et al. (8
97	sources). The math.
98	- `references/ops_workforce_planning_canon.md` — Fournier, Larson,
99	Google SRE Workbook, Frei, Lawler, Bersin, Gartner, Grove (8
100	sources). The people factors.
101	- `references/capacity_anti_patterns.md` — 11 named anti-patterns
102	with cited sources, tool guards, and the meta-discipline that
103	Lencioni + Goldratt + Christensen impose. (8+ named sources.)
104
105	## Assets
106
107	- `assets/capacity_brief_template.md` — 20-minute fill-out template
108	with JSON skeletons for all three tools and an output checklist.
109
110	## Assumptions
111
112	This skill assumes:
113
114	- Work is queued (tickets, cases, work items) — not project-style.
115	If your team's work isn't queued, this is the wrong skill.
116	- Demand has a stationary-enough distribution within a quarter.
117	Step-changes (new product launch, M&A, regulatory shift) require
118	re-running mid-quarter.
119	- You have at least 90 days of historical demand data to compute
120	P50/P90/P99. If not, generate the distribution from your sales /
121	user-base forecast first.
122	- Service is single-class within a queue. If you have hard
123	priority tiers (P1/P2/P3 with class-specific SLAs), model each as
124	a separate queue and sum.
125	- Channels are modeled coherently. Multi-channel teams use the
126	appropriate `--profile` with built-in shrinkage premium.
127
128	## Anti-patterns
129
130	See `references/capacity_anti_patterns.md` for the full taxonomy with
131	sources. Top eight:
132
133	1. Plan-to-100%-utilization (Reinertsen Principle 12)
134	2. Treat-ramp-as-instant (Larson)
135	3. Ignore-attrition-in-12-month-plan (Bersin)
136	4. Hire-ICs-forever-with-no-manager-trigger (Fournier)
137	5. Size-to-P50-demand-only (Cleveland)
138	6. No-shrinkage-adjustment (Cleveland, SRE Workbook)
139	7. Single-channel-model-for-multi-channel-work (Gartner, Kingman)
140	8. No-surge-plan-for-P99-events (Hopp & Spearman, Reinertsen)
141
142	## Distinct from
143
144	- `c-level-advisor/vpe-advisor` measures engineering throughput
145	via DORA 4 metrics, story points, deployment frequency, and cycle
146	time bottlenecks. It is for engineering teams shipping code. This
147	skill is for ops teams handling tickets/cases. Different unit of
148	work, different math (Erlang-C vs. DORA), different bottleneck
149	(queueing-blind staffing vs. WIP + lead time).
150	- `c-level-advisor/chro-advisor` does strategic workforce
151	planning (1-5 year capability portfolios, talent supply, leadership
152	succession). This skill does operational 0-12 month capacity
153	sizing against demand. Per Lawler: conflating them gets you hired
154	into the wrong jobs.
155	- *`project-management/`** tracks delivery throughput on projects
156	(Jira velocity, sprint capacity). This skill sizes around steady-
157	state queued work.
158	- Sibling `process-mapper` finds the bottleneck. This skill
159	sizes the team around a known bottleneck. Order of operations:
160	process-mapper first → capacity-planner second. Hiring around the
161	wrong constraint wastes the hires.
162	- `business-growth/cs-coverage` (if it exists) sizes Customer
163	Success coverage by ARR/CSM ratio and segment. This skill sizes by
164	queued work volume (tickets, cases, escalations). For a CS team
165	that handles both relationship work AND a ticket queue, run both.
166
167	## Forcing-question library (Matt Pocock grill discipline)
168
169	Discipline: walk these one at a time. Do not skip ahead. Answers must
170	be written down. If you can't answer one, that is your next investigation.
171
172	### Q1 — "What is your bottleneck, and have you confirmed it empirically?"
173
174	Recommended answer: a named, measured stage in the workflow with
175	queue-time data showing where work waits. Not a vibe. Not "escalations
176	take too long". An actual measured queue.
177
178	Why it's the first question: Goldratt (The Goal, 1984) — every
179	system has exactly one binding constraint at a time. Sizing around the
180	wrong constraint wastes hires entirely. If you do not know your
181	bottleneck, run `process-mapper` BEFORE this skill.
182
183	Canon: Eli Goldratt, The Goal (1984); Reinertsen, *Principles of
184	Product Development Flow* (2009).
185
186	### Q2 — "What service trade-off are you accepting?"
187
188	Recommended answer: a written, explicit choice — fast vs. empathetic,
189	broad vs. deep, low-cost vs. high-quality. Frances Frei is unambiguous:
190	you cannot win all four. The team that tries wins zero.
191
192	Why it matters: AHT, SLA, and shrinkage inputs are the operational
193	expression of this trade-off. If they don't agree (e.g., you set AHT for
194	"empathy" but SLA for "speed"), the plan is internally inconsistent.
195
196	Canon: Frances Frei & Anne Morriss, Uncommon Service (HBR Press,
197	2012).
198
199	### Q3 — "What's your demand P90, and what's the gap to your P99?"
200
201	Recommended answer: two specific numbers from the last 90 days of
202	data, with the calendar context of each (e.g., "P90 was 480 tickets/day
203	on normal Tuesdays; P99 was 720 on the day after the November release").
204	A team sized to P50 misses SLA half the time. A team sized to P99
205	overstaffs by 30-50%. P90 is the right operating sizing point per
206	Cleveland.
207
208	Canon: Brad Cleveland, Call Center Management on Fast Forward (4th
209	ed., 2019); A.K. Erlang, *The Theory of Probabilities and Telephone
210	Conversations* (1909).
211
212	### Q4 — "At your planned utilization, what is P(SLA breach) at P90 and at P99?"
213
214	Recommended answer: two probabilities, computed (not guessed) from
215	Erlang-C with your specific N, AHT, and SLA target. If P(breach at P90)
216	> 10% you are understaffed at the sizing point. If P(breach at P99) >
217	50% you have no surge plan and the next peak event will be visible to
218	the CEO.
219
220	Canon: Erlang (1909); Hopp & Spearman, Factory Physics (3rd ed.,
221	2008), VUT equation.
222
223	### Q5 — "Have you budgeted replacement hires for the attrition you'll see this year?"
224
225	Recommended answer: yes, with a specific number. At 30% annual
226	attrition (Bersin BPO midpoint), a 20-FTE team loses ~6 people this year.
227	If your "add 5 net" plan is actually a "hire 11" plan, the recruiting
228	volume changes drastically. Anti-pattern #3.
229
230	Canon: Bersin/Deloitte talent benchmarks (2015-2023); Edward Lawler,
231	Strategic Workforce Planning (USC CEO, 2008).
232
233	### Q6 — "When does span of control trigger a manager hire, and who is the candidate?"
234
235	Recommended answer: a specific quarter (from `hiring_sequencer.py`)
236	and at least one identified candidate (internal lead or external hire).
237	Past 7 ICs/manager, 1:1s degrade, feedback cycles slip, attrition
238	climbs. Past 10 you have a coverage crisis. Hire the manager BEFORE
239	crossing 10, not after.
240
241	Canon: Camille Fournier, The Manager's Path (O'Reilly, 2017),
242	ch. 5; Andy Grove, High Output Management (1983).
243
244	### Q7 — "What is your surge plan for the P99 day?"
245
246	Recommended answer: an explicit, documented plan — overflow tier,
247	BPO contracted capacity, on-call rotation, executive escalation tree,
248	OR a written degradation contract that says "on P99 days we extend SLA
249	to X minutes and notify customers proactively". If the answer is "we'll
250	figure it out", the P99 day is a fire visible to the board.
251
252	Canon: Hopp & Spearman, Factory Physics (2008); Reinertsen (2009)
253	on capacity-margin discipline.
254
255	---
256
257	**Walk these seven in order. One at a time. Write the answers down. The
258	plan you submit is only as defensible as your answers to these seven
259	questions.**
260