An agent-based model of the route a child travels from an unmet special educational need to an Education, Health and Care plan. Around 50,000 children a year are refused support they were referred for, and most of them never come back. The model finds that the size of that population is almost completely unresponsive to assessment funding. Doubling assessment capacity changes it by one percent. The one setting that changes outcomes by half is a family's ability to appeal. Access to appeal is a mechanism the model assumes rather than one it discovers, so the result that carries weight is the asymmetry between the two levers, not the existence of the second.
IPS-England is an agent-based model of the statutory pathway a child in England travels from an unmet special educational need to an Education, Health and Care plan. That plan is a legal document obliging a council to fund and provide the support it names, and the system producing it is known in England as SEND, for special educational needs and disabilities. The model represents individual children moving through five stages across all 152 local authorities, the councils carrying the legal duty to assess and to issue plans. Families decide whether to appeal when they are refused, and each authority screens, queues and assesses at its own capacity with no central coordinator, so both sides of the gate act rather than merely queue. A parameter that makes an authority refuse more as its own backlog grows is present in the model and held at zero in every run reported here, which Section Eight sets out.
What is at stake in that pathway is time in a child's education, and for some children whether they are recognised at all. A child waiting for an assessment sits in a classroom every day without the support the law says they are owed, and the wait falls during years that do not come back. A child refused an assessment whose family cannot appeal simply leaves the system, and England records nothing about what happens to them next.
IPS-England was constructed to test the prevailing narrative that delays and shortfalls in the English system stem directly from a shortage of assessment staff. The goal was to build a working model around this explanation to evaluate various resourcing decisions. However, the model failed to replicate real-world outcomes at any staffing level, and the findings below set out what followed from that result.
Every figure the model is calibrated or tested against is published, and no number on this page is estimated where a published one exists.
| Source | Period | Used For |
|---|---|---|
| DfE, Education, health and care plans | Calendar year 2025, published January 2026 | The targets the model has to reproduce: 162,702 requests for assessment, 110,708 new plans issued, 46.1% issued within the twenty-week deadline, 43,300 requests refused progression to assessment and 7,200 assessments producing no plan |
| DfE, Special educational needs in England | Academic years 2015/16 to 2025/26 | The eleven-year trend in identification, used to set how children enter the pathway. Identification rose from 14.4% to 20.8% of pupils across that period |
| Ministry of Justice, Tribunal Statistics | Academic year 2024/25 | Roughly 25,000 SEND appeals registered across all grounds, with 99% of decided cases going in favour of families. Used to bound the appeal behaviour the model assumes |
The two DfE series count different populations and are not interchangeable. The plans release covers all ages from birth to twenty-five across every setting and reports 718,838 plans in force at January 2026. The school census covers school pupils only and reports 538,547 with plans in 2025/26. Where the two appear together on this page, the distinction is stated.
Three categories, kept separate throughout, since the difference between a value that was measured, a value that was assumed, and a value that was swept is what determines how much weight a result can carry.
| Parameter | Value | Status |
|---|---|---|
| Local authorities | 152 | Measured |
| Statutory deadline | 20 weeks | Measured, set in regulation |
| Requests for assessment | 162,702 per year | Measured |
| Refused progression to assessment | 26.6% | Measured, 43,300 of 162,700 in 2025 |
| Assessed with no plan issued | 6.0% | Measured, 7,200 of 118,800 in 2025 |
| Gross refusal before appeals | 32.4% | Derived, the rate whose post-appeal residue equals the published 26.6% |
| Share of refused families who appeal | 18% | Assumed, bounded by the roughly 25,000 appeals registered across all grounds |
| Appeal duration and success rate | 30 weeks, 99% | Assumed duration, measured success rate |
| Assessment capacity | 0.70 to 1.82 times demand | Swept |
| Statutory process duration | 10 to 26 weeks | Swept |
| Variation in process duration between cases | Gamma, coefficient of variation 0.45 | Assumed |
| Spread of family navigational capacity | Lognormal, sigma 0.80 | Assumed |
| Caseload distribution across authorities | Lognormal, sigma 0.65 | Assumed, pending the published per-authority breakdown |
| Capacity distribution across authorities | Lognormal, sigma 0.45 | Assumed, pending the same |
| Time step and horizon | Weekly, four years, final year reported | Design choice, tested in Section Seven |
| Random seeds per reported figure | 10 | Design choice. Every figure on this page is a mean across seeds |
| Authority refusal response to its own backlog | 0 | Implemented and held at zero. No result on this page uses it |
Simulation earns its place here for a reason specific to this system rather than as a general preference for modelling. The records a survey would need do not exist.
England counts children who pass through the gates of the special educational needs system. It does not count children whose needs were never noticed; it does not record what provision a child received once a plan was written; and it does not follow the children it turns away. Two of the five stages in the pathway below produce no national statistics at all. You cannot survey what nobody writes down.
What an agent-based model offers instead is a test of sufficiency. Rather than measuring a correlation between resourcing and outcome, it asks whether a stated mechanism, run forward with individual children arriving, being screened, waiting and in some cases giving up, generates the country we observe. Interaction effects that a regression treats as noise become visible in the run: queues form, clear and re-form; some authorities absorb demand while others accumulate it; and a refusal falls very differently on two families with the same child and different capacity to fight it.
That gives a hard criterion. An explanation that cannot generate England is wrong, whatever its standing in the policy literature, and the findings below rest on that criterion rather than on a fit statistic.
A child with an unmet need travels through five stages before the state formally recognises them. Need exists. Someone notices. A request is made. An assessment is carried out. A plan is issued. Every stage can fail, and the failures differ in kind. A child can go unnoticed. A request can be refused. An assessment can run past its deadline. A plan can be written and still not change what happens in the classroom on Monday.
Step through the pathway below, and two things become apparent. The first is where children are lost: roughly 50,500 requests a year do not become plans. The second is that the earliest two stages carry no national figure at all, which is the argument for simulating rather than surveying, made in numbers rather than asserted.
The animation is made of eight transitions and two durations. They are set out below so that the picture can be checked against the numbers without opening the repository.
| From | To | Rate | Children a Year | Status |
|---|---|---|---|---|
| Outside the count | Request made | — | 162,702 | Measured. DfE, calendar year 2025 |
| Request made | Refused an assessment | 32.4% | 52,715 | Derived. The gross rate whose post-appeal residue equals the published net 26.6% |
| Refused | Appeal lodged | 18.0% | 9,489 | Assumed. Bounded by the roughly 25,000 SEND appeals registered across all grounds |
| Appeal lodged | Back into the assessment queue | 99.0% | 9,394 | Measured. Ministry of Justice, share of decided cases going in favour of families |
| Refused | Left the pathway | 82.0% | 43,321 | Residual. England publishes 43,300 |
| Request made | Assessment carried out | — | 119,381 | Residual, including appeal returns. England publishes 118,800 |
| Assessment | No plan issued | 6.0% | 7,163 | Measured rate. England publishes 7,200 |
| Assessment | Plan issued | 94.0% | 112,218 | Residual. England publishes 110,708 |
| Statutory process, average duration | 20.5 wks | — | Calibrated. The duration at which the model reproduces England’s timeliness | |
| Appeal, average duration | 30 wks | — | Assumed. A published distribution of tribunal timescales would replace it | |
England's own figures say 43,300 requests a year are refused progression to an assessment, and a further 7,200 assessments produce no plan. Together that is 50,500 children referred for support who do not receive it. What the published figures cannot say is what happens to them next, since nobody follows them.
The model places 50,081 children a year outside a plan, with a standard deviation of 207 across ten seeds. That figure is close to the published 50,500, and it should not be read as a check on the model. Applying the two published gate rates to the published request total gives roughly 50,400 before any simulation is run, so reproducing it is the inputs restated rather than a finding. It is reported here to show the accounting closes, and nothing more is claimed for it.
The interesting part is who comes back. Refusals are overturned on appeal at very high rates, so the gate cannot be filtering by need. The model represents it as filtering by whether a family can mount an appeal at all, and that representation is an assumption carried into the model rather than a result taken out of it. Under it, 8,492 children a year reach a plan only by appealing, with a standard deviation of 137, taking a median of 51.4 weeks, a year against a twenty-week deadline. None of them appear in any timeliness statistic England publishes.
What the model does decide, rather than assume, is how far each lever moves that population. The assumption that appeal access is unequal does not fix how much it matters relative to money, and nothing in the model forces assessment funding to be inert. Testing both produces the central result.
| Change | Children Leaving | Against Baseline |
|---|---|---|
| Baseline | 50,081 | — |
| Assessment capacity increased by half | 50,397 | +0.6% |
| Assessment capacity doubled | 50,577 | +1.0% |
| Statutory process shortened to 16 weeks | 50,081 | 0.0% |
| Appeals resolved in 10 weeks rather than 30 | 50,156 | +0.2% |
| Appeal within reach of 40% of families | 39,219 | −21.7% |
| Appeal within reach of 70% of families | 24,354 | −51.4% |
One consequence is worth stating plainly. When appeal becomes reachable by seven families in ten, plans issued rise from 107,952 to 126,657 and published timeliness falls from 45.8% to 39.9%. The statistic the system is judged on gets worse at exactly the point more children receive what they are legally entitled to.
The same model answers a second question, and it points the same way. Assessment delay in England is almost always explained by a shortage of caseworkers. Requests arrive faster than they can be picked up, a queue forms, and children wait.
Sweeping assessment capacity across its full plausible range produced no setting that reproduces England. Tune capacity down until timeliness comes closest to England, at 46.4%, and the model issues 90,204 plans a year, 18.5% fewer than England issues. Tune capacity up until volume comes closest, at 109,873 plans, and timeliness climbs to 92.4%, forty-six points better than England manages. The two targets move in opposite directions, and the gap never closes.
The model comes close to England only when the statutory process itself is allowed to take longer. Holding capacity at a level where most queues stay short and letting the sequence run for an average of 20.5 weeks produces 45.8% inside the deadline against England's 46.1%, with a standard deviation of 2.0 points across ten seeds and England's figure inside the range every seed produced. Volume is the weaker half of that fit. The model issues 107,952 plans a year against England's 110,708, 2.5% short, and England sits just outside the seed range. The residual is stated here rather than tuned away, and Section Seven says where it comes from. The sequence being represented is the six-week window to decide whether to assess, the six weeks professionals are given to respond, then drafting, consultation and issue, all running one after another by regulation.
For a child, that distinction decides what happens next. Under the resourcing account a late assessment is a queueing problem that more funding eventually clears. Here the wait is produced by the rules themselves, so a child whose plan arrives four weeks late is not unlucky in a stretched authority, and the same four weeks would have been lost in a well-staffed one.
This is a claim rather than a conclusion, and it is written so that someone can kill it. Three tests, none of which needs this model or its author.
On access, compare refusal rates and appeal rates across local authorities against the socioeconomic composition of their populations. The hypothesis predicts appeal rates track family resources rather than tracking refusal rates, so that authorities refusing at similar rates lose very different numbers of children depending on who lives there.
On delay, identify local authorities that materially increased assessment staffing and compare the change in their throughput against the change in their twenty-week performance. The hypothesis predicts throughput rose and timeliness did not follow.
On the process, audit directly how long each mandated step consumes in practice. If the sequence can be executed inside twenty weeks at realistic staffing, the second finding is wrong.
It matters because the reform programme now running to 2030 rests on an account the model could not make work. Where access is governed by contestability and delay by process architecture, additional funding buys more plans and roughly the same waiting, and leaves untouched the children whose families could not appeal in the first place.
A model that only ever confirms what it was built to show is not a research instrument. Five checks run against this one. Two of them failed, and both failures are reported below along with what was changed in response.
Version 1.4 reported the model at a single random seed. Rerunning the identical specification across ten seeds showed timeliness varying by close to six percentage points between draws, and the published figure sat near the favourable end of that spread. Every quantity on this page is now the mean of ten seeds with its standard deviation stated. At the calibrated setting the model produces 45.8% inside the deadline with a standard deviation of 2.0 points, against England's 46.1%, and 107,952 plans a year with a standard deviation of 1,015, against England's 110,708. The timeliness fit holds. The volume fit is 2.5% short, and the next check explains why.
Running the same specification to longer horizons shows timeliness falling monotonically, from 47.3% at two years to 43.9% at eight. A model whose headline statistic depends on when you stop watching has not settled, so the source was located rather than left as noise. Assessment capacity is drawn per authority, and at the calibrated setting 22 of the 152 authorities hold less capacity than their own inflow. Their queues grow without bound while every other authority stays flat. Over ten years the national queue rises from 2,557 to 26,926 cases and 99% of that growth sits inside those 22 authorities.
Two things follow. The four-year reporting point is a stated convention rather than a converged value, and every figure on this page should be read as the state of the system four years into that divergence. The 2.5% volume shortfall is the same phenomenon, since plans still queued in those authorities are not issued inside the reporting year. A national average is not a stable property of this system, which is a result about English SEND rather than an inconvenience in the code, and it is the reason the per-authority data named in Section Eight is the first thing this model needs.
The same configuration run at 26, 52, 104 and 208 steps per year gives 44.8%, 45.1%, 45.4% and 45.2% timeliness, and plans issued within 0.4% across all four. Nothing reported here is an artefact of the weekly time step.
Version 1.4 drew process duration from the same generator as every queueing decision, so changing the duration parameter silently changed which children were refused and when. The duration curve in Figure 2 appeared to move volume, which duration cannot do. Duration now draws from its own stream. The curve is vertical as a result, and that is the correct behaviour: how long the statutory process takes changes when plans are issued and not how many.
The second finding hinges on how long the statutory process takes, so that dependence is reported rather than buried. Holding capacity adequate and varying only the process duration gives the following.
| Process Duration | Issued Within 20 Weeks | Reading |
|---|---|---|
| 10 weeks | 85.0% | Far better than England |
| 14 weeks | 72.3% | Far better than England |
| 18 weeks | 55.6% | Still better than England |
| 20 weeks | 47.6% | Closer, still too good |
| 20.5 weeks, with variation | 45.8% | England reports 46.1% |
No short-process configuration reaches England, which is why the finding is stated as a claim about process duration and not about staffing levels.
Four results were taken out of this model before publication, and none of them appears anywhere on this page. A claimed ratio between high-issuing and low-issuing authorities was Monte Carlo noise at the agent counts then in use. Per-authority monthly capacity was floored to a whole number each month rather than carrying its remainder forward, which stalled queues that should have moved. Appeal returns were added on top of the published refusal rate rather than inside it, which overstated plans issued by 17%. A single-seed timeliness figure was reported as though it were the model's central value. Each was found by a check listed above, and the checks are in the repository alongside the model so that they run against any future version.
Every number on this page is computed in Python and written to a data file that the page reads. The page recomputes nothing, so the published figures and the model cannot drift apart. The model, the source data, and the script that generates the figures are in the repository linked below, and running one command reproduces the whole set. The same files are deposited in Harvard Dataverse under doi:10.7910/DVN/NAFBST, so a version of record exists independently of this page and of the repository.
Navigational capacity is a single modelled quantity standing in for everything that makes an appeal reachable or unreachable for a family. It is not measured, and nothing on this page identifies which families hold more or less of it. The first finding says that identification is sorted by that quantity. It does not say which children are on the wrong side of it, and the published data cannot currently answer that.
The share of refused families who appeal is assumed at 18% rather than measured. Published tribunal statistics count appeals across all grounds together, so the share brought against these two refusal decisions specifically is not separable from the published total. The counterfactuals in Section Four vary that share deliberately, which is why they are stated as counterfactuals rather than forecasts.
How long an appeal takes is assumed to be 30 weeks. A published distribution of tribunal timescales would replace it.
Authority-level caseload and capacity dispersion are modelled as lognormal distributions rather than the published per-authority breakdown. Until that is replaced, no claim should be drawn from this model about variation between individual authorities.
The variation in process duration between cases is assumed rather than measured. A published distribution of actual step durations would replace it, and the audit proposed in Section Six would produce exactly that.
The stage that brings children into the pathway is calibrated to the national trend in identification and its absolute level remains an assumption. Nothing on this page should be read as a claim about how many children are never noticed at all.
Authorities do not adapt. The model implements a parameter by which an authority raises its refusal rate as its own backlog grows, and that parameter is set to zero in every run reported here, so no published figure depends on it. Switching it on changes the first statutory gate and would require recalibrating against the published 26.6%, which is work this version has not done. The agent claim in this version rests on heterogeneous authorities queueing independently, on the individual appeal decision, and on the divergence between authorities reported in Section Seven, not on adaptive refusal.
Finally, this model addresses access and delay rather than outcome. A plan issued within twenty weeks is recorded here as a success, and whether the provision that followed helped the child is a separate question no national dataset currently answers.