Enrolled ADM

Two distinct counts wear the name, they differ for every district, and the Fair School Funding Plan uses both in the same calculation. Conflating them is the single most common arithmetic error available in Ohio school finance.

What this repository computed # ↑ Contents

Not what Ohio publishes. Figures derived here from committed fixtures, each one citing the test that reproduces it.

THE GUARANTEE MAKES A DISTRICT’S AID COMPLETELY INSENSITIVE TO ITS ENROLLMENT. verified crates/project The temporary transitional aid guarantee pays a fixed dollar amount that enrollment does not enter. For the 294 districts it funds — very nearly half the state — running the FY2027 formula at FY2024, FY2025 or FY2026 enrollment produces the identical figure to the cent, and projecting their enrollment forward produces a flat line with no interval at all. What moves for them is the formula’s answer, which falls as enrollment does; the widening gap between the two is the guarantee.

REMOVING THE GUARANTEE NEARLY DOUBLES THE STATE’S EXPOSURE TO ENROLLMENT FORECAST ERROR. inference a forecast At FY2032 enrollment, total state aid under current law is $7,233M in a band of $6,958M to $7,582M (±4.3%). With the guarantee removed the same forecast error produces ±7.8%, on a band 1.8 times as wide. The guarantee is a shock absorber for the appropriation as well as for the district, and that is not usually how it is argued about. Recorded in full at guarantee phase-out.

THE AID BAND IS TIGHTER THAN THE ENROLLMENT BAND THAT DRIVES IT. verified Necessarily, and for the same reason: half the state’s aid does not respond to enrollment at all.

See MR-81 free and reduced-price lunch reports, 1998–2025.

THE METHOD IS RIGHT AND THE CONSTANT IS NOT. verified crates/project This was carried as open for want of an enrollment history longer than three points. The history arrived from a different direction than the one expected: not nces-ccd, but the F-33 panel, once it was extended past FY2022 — V33 fall membership for 602 districts across fourteen years, keyed on LEAID, which is also what answers the consolidation worry, since a district that stops being surveyed simply leaves the population rather than distorting it.

Backtested over 13,244 out-of-sample forecasts — six origins from FY2013 to FY2019, horizons of one to five years, the two pandemic years dropped as targets because no method predicts a school closure:

Damping is the right shape: at its optimum it beats a flat carry-forward by 7.1%, and an undamped trend and a least-squares straight line are both worse than either. But 0.85 damps too weakly to collect that gain, costs about a tenth of the error against the optimum, and on three of the four metrics tried is beaten by making no forecast at all. Ohio district enrollment is close enough to a random walk that a fitted growth rate is worth carrying for about a year; 0.85 carries three-quarters of it into the third.

A longer fitting window is the larger of the two available improvements and is free — the observations are already committed. verified crates/project

AND THE GUARANTEE ABSORBS MOST OF THE ERROR, WHICH BOUNDS WHAT IT COSTS. verified crates/project At the feed’s FY2036 horizon, moving the damping from 0.85 to 0.30 moves statewide ADM by +3.38% — 45,294 pupils — and realized state aid by +1.42%, or $101.0m. The enrollment error is more than twice the aid error for the reason this node already gives: the guarantee pays a fixed amount to about half the state, so state cost is far less sensitive to enrollment than the enrollment forecast is uncertain. The constant was wrong and the consequence is bounded, and both halves belong in the same sentence.

What moves most is not a dollar figure. 44 districts change guarantee status at the horizon — 356 against 312 — and that is a count the site publishes.

These figures are measured under Method::Shrunk, which is what the feed runs. The same move under the plain Method::Damped that shipped when the damping was fitted gives +4.66% and 61,297 pupils, +1.05% and $75.4m, and 47 districts against 44 — and a four-to-one ratio of enrollment to aid rather than this two-and-a-half. the_damping_nobody_fitted keeps those, because they are the evidence “The fitted damping” was decided on and a decision’s evidence has to keep reproducing; the figures above are what the same question answers today, pinned in the_trend_the_damping_discards.

THE LARGEST POPULATION OUTSIDE THE COUNT HAS NO PER-DISTRICT RECORD AT ALL. verified crates/project ADM counts children a district enrolls. The department’s own annual fact sheet counts, in one table and one year, every way an Ohio child is schooled instead — 173,156 in chartered private schools, 150,914 on vouchers, 116,973 in community schools, 79,006 on inter-district open enrollment, 49,524 in joint vocational districts, and 53,051 in home education, against a statewide enrollment of 1,665,521.

That 1,665,521 is Ohio’s public enrollment: the community schools are inside it, and home education, the chartered private schools and the voucher students at them are not. So home education is 3.2% of the public system rather than 3.2% of Ohio’s children — the second denominator is larger and nothing published states it. On the first, it is larger than the joint vocational districts, larger than every Ohio e-school together, and larger than four of the five voucher programs. It is also the only one of the thirteen channels with no per-district record anywhere. Community schools report through EMIS; vouchers are administered per student; open enrollment names both districts. A home-education notice is filed with the district of residence under R.C. 3321.042 and no statute requires anyone to forward it to the state as a count. EMIS carries withdrawal reason 43 — Transferred to Home Education, which is a flow rather than a stock: a child who begins at six and never enrolls is permanently invisible to it.

And it grew by a factor of about 1.8 in five years, in one step that never reversed. inference a secondary compilation, anchored on one verified year 33,328 in 2019-20 to 61,009 in 2024-25, with the step in 2020-21. The series is an aggregator’s and cannot be verified, but its 2023-24 member is 53,051 and the department’s sheet says 53,051, which is what identifies it as Ohio’s numbers carried forward. Against the committed F-33 panel, district enrollment fell 62,609 between FY2020 and FY2024 while home education rose about 19,700 — roughly 31% of the decline in magnitude. That is a size comparison and not a decomposition: districts also lost pupils to community schools, to vouchers, and to a falling birth cohort, and nothing here apportions between them. What it establishes is that a channel carrying no ADM, in no enrollment file, reported per district nowhere, is of the same order as a third of the enrollment loss that half the state’s guarantee status turns on. See Ohio's Education Landscape — the department's own count of every school option and Johns Hopkins Homeschool Hub — state and district home-education counts.

open Where home education is concentrated. A population spread across some 600 districts is thin almost everywhere and heavy somewhere, and the concentration is what a denominator question needs. Only the department can answer it — tracked at #257.

AND THE CONSTANT MOVED. verified crates/project It was left at 0.85 while only the measurement existed, because changing it moves every projection in the published feed, which is a decision to record rather than a number to edit. The decision is recorded at “The fitted damping” and the value is now 0.30 — chosen over the 0.20 that minimizes the headline metric because the objective is flat between them (0.04033 against 0.04031, which no honest reading distinguishes) and 0.30 is the optimum on the enrollment-weighted metric, the one that governs a statewide total rather than a typical district.

So a district’s fitted growth rate is now nearly spent by the second projected year instead of the fourth, and a long horizon sits closer to the last observation — which is what fourteen years of Ohio enrollment say it should do.

AND THE TWO QUESTIONS THAT DECISION LEFT OPEN ARE ANSWERED — ONE NO, ONE YES. verified crates/project

A damping per district is noise. Fitted on each district’s own history it looks 15.3% better than the single constant and is 3.6% worse out of sample. More than two thirds of districts fit a boundary of the grid — 316 of 602 at zero, 101 at one — which is what an unidentified parameter looks like when it is fitted anyway. Fifteen forecasts cannot locate a decay rate. The feed keeps one damping, now for a reason rather than for want of trying.

A longer fitting window is worth more than the damping was, and blending beats replacing. Weighting the three-point rate against the district’s whole-history rate:

Discarding the recent rate is worse than keeping about a third of it, so three points carry real information about where a district is now and not enough to stand alone. At 0.3 the gain is 4.6%, larger than the 2.4% that moving the damping bought. Re-tuning the damping on top moves the optimum to 0.40 and buys a further 0.18%, which is not worth a second change to a published constant.

AND THE BLEND IS NOW WHAT THE PROJECTIONS USE. verified crates/project Recorded at “The shrunk rate”. Every district’s rate is three-tenths its own FY2024-FY2026 history and seven-tenths its fourteen-year rate in the F-33 panel. Statewide ADM at FY2032 moves from 1,376,970 to 1,384,245 and the count on the guarantee from 320 to 312; aid moves $3M, because the guarantee absorbs most of it.

It rests on one assumption, and the assumption is why this took a decision rather than a patch. The projection runs on enrolled ADM and the long rate is V33 fall membership. The two count nearly the same children — their FY2024 levels correlate at 0.9997 across 608 districts — but their two-year growth rates correlate at only 0.287. The shrink assumes they share a long-run trend while differing in short-run noise, and only three years of ADM exist, so nothing here can test it. The disagreement is at once the best evidence that a two-year rate is mostly noise and the reason the substitution could not be made mechanically.

AND THE THING NEITHER FITTING DECISION COULD SEE IS THAT THE PROJECTIONS RUN HIGH. verified crates/project Both were scored on mean absolute log error, which is blind to sign. The five-year backtest bias falls monotonically as the damping rises — +0.033 at a damping of zero, +0.030 at the shipped 0.30, +0.002 undamped — so the damping causes it, and the undamped trend pays for its lack of bias with 41% more dispersion. It is a bias-variance trade priced on one side.

The mechanism is arithmetic rather than anything about Ohio. Damping applies the fitted rate for (1 - d^h)/(1 - d) year-equivalents whatever the horizon — 1.43 years at 0.30, for every horizon past about six — so a projection misses h - 1.43 years of trend, and in a shrinking population that miss is upward. Sorted by their own fifteen-year rate, the fastest-declining quarter of districts are forecast 8.0% high at five years and the flattest quarter 2.0% low; the sign flips exactly where the growth rate does.

The districts forecast high are disproportionately the ones the guarantee protects, though not by a clean gradient: at observed enrollment 57.2% of the fastest-declining quarter are on the guarantee against 34.2% of the flattest, the two middle quarters sitting at 48.7% and 53.3%. The over-forecast therefore lands hardest where the guarantee is what pays, and the error runs toward under-stating guarantee reliance.

AND AT THE PUBLISHED HORIZON THE TREND IS SIMPLY GONE. verified crates/project Statewide ADM projected by the shipped method falls 12,500 in the first year, 3,654 in the second, 127 in the seventh, and 12 pupils in total between FY2032 and FY2036 — the two years this repository publishes — across 609 districts, in a state whose F-33 panel records a fall of 208,918 over fifteen years. The undamped trend reaches 1,290,680 at FY2036 against the shipped 1,384,232, so the damping holds 93,553 pupils above it.

This is not a defect in series::advance, which does what damping means. It is that a ten-year panel drawn this way carries about four years of demographic content and six years of the same number relabeled, and nothing said so. Measured in the_trend_the_damping_discards.

AND IT CANNOT BE DE-BIASED BY CHOOSING A DIFFERENT DAMPING. verified crates/project That was left open and the answer is no. The damping that zeroes the bias rises with the horizon — there is no crossing at all at one or two years, then 0.32 at three, 0.64 at four, 0.79 at five — so any single value is over-damped for the near years and under-damped for the far ones. Choosing 0.79 to zero the five-year bias puts −0.010 on the second. At one year the parameter is not connected to the outcome at all: series::advance decays the rate from the second step, so the one-year bias is −0.00492104 at every damping to the last digit, a floor the constant cannot reach and negative where the long-horizon bias is positive.

The fair worry — that a criterion blind to sign also chose badly — does not hold either. Root mean squared log error prices bias and variance together and puts the optimum at 0.45 against absolute error’s 0.40. At the shipped 0.30 the squared bias is 0.0000190 against a variance of 0.0029624, six-tenths of one percent of the mean squared error. Scored on four- and five-year forecasts alone the optimum is 0.55 and 0.30 costs 1.4% — the strongest case for moving the constant, and not a strong one, since the feed publishes every year from FY2027 to FY2036 and the surface is flat from about 0.30 to 0.55.

A remedy would have to be a horizon-dependent damping: a change to the shape of Method::Damped and its TypeScript mirror, resting on a five-year backtest extrapolated to a ten-year horizon. Measured in the_bias_no_single_damping_can_remove.

AND THE BIAS BELONGS TO THE YEARS, NOT TO THE DISTRICTS. verified crates/project The backtest reaches thirteen years, and at the feed’s ten the mean district’s log error is +0.056 while the statewide total’s is +0.032: the two figures the feed publishes from the same projections carry different biases, and before the closure the total’s was within 0.7% at every horizon to seven years with a sign that changed from origin to origin. The mean district’s pre-closure drift is stable — a third of a point a year past the 1.43 years the damping carries, within a fifth of itself across five independent origins — and it is shared: sorted on the rate a forecast could see at its origin, or on the district’s size, the quarters neither order nor spread, and every one is forecast high. The gradient reported above, from +8.0% to −2.0% across the quarters, sorts on the fifteen-year rate, which includes the target years.

The reason no rate-side correction reaches it is one number. A district’s long-run rate to an origin predicts its rate over the next three, five, seven or nine years at 0.30, 0.29, 0.29 and 0.27 — the same three tenths as year on year — and relative to the state’s rate it is no more persistent. Decaying the rate toward a share of the long-run rate rather than toward zero over-corrects at every share above five hundredths, because the statewide decline of 1.7% a year to FY2013 had become 0.3% a year by FY2015–FY2020; five hundredths is worth a third of a percent, and the share that zeroes the bias rises with the horizon as the damping’s did. A drift fitted on the pre-closure mean district removes half of what crosses the closure and puts the total a point low before it. An asymmetric band is that correction drawn as a band and holds less. Neither the center nor the band moves; the bias is to be published beside the projection, two figures per horizon, which is a feed field and a decision of its own. Measured in the_bias_that_belongs_to_the_years.

The department’s own series now checks the damping, and a splice would have failed it # ↑ Contents

DEFAULT_DAMPING is the share of a district’s growth rate a projection carries into each further year, and it was fitted out of sample on the F-33 panel’s fall membership — a different survey over a different population — because Ohio’s own enrolled ADM had three observations and three observations give one growth rate. Four give three, and three give two estimates of exactly the quantity the constant is: the correlation between a district’s growth rate and its next one, each year demeaned.

They are 0.328 and 0.341, over 609 districts. The fitted value is 0.30. A different measure, a different population and a different method, landing within five hundredths. verified crates/project

The check only works on one of the two FY2023 columns. Splice the growth supplement’s M1B FY23 onto the base cost window’s FY2024, FY2025 and FY2026 — which is what the 162-column panel invites, carrying it as enrolled_adm_fy23 beside _fy24, _fy25 and _fy26 — and the earlier correlation comes out -0.049: same districts, same years, one column swapped, and the sign reversed. The later window pairs the growth into FY2025 with the growth into FY2026 and so touches no FY2023 at all, which is why 0.341 stands whichever column a reader picks. verified crates/project

What the two columns measure differently is not established. M1B is right for the supplement it belongs to and the supplement reproduces from it; whether the difference is a different pupil basis, a different collection, or a restatement the ADM Data sheet never received is not something either workbook says. open

AND THE PROJECTION IS LINEAR IN A COUNT THAT TWO PER-PUPIL TERMS ARE NOT. verified crates/project A forecast substitutes a projected enrollment into the formula by scaling the department’s published base cost state share by the ratio of the two counts. That holds base cost per pupil and local capacity per pupil at their FY2027 values, and neither is constant in the count: R.C. 3317.011’s staffing floors are a max that does not follow a roll down, and R.C. 3317.017’s wealth blend is a dollar amount over a shrinking denominator. Base cost aid is the difference of those two, so the errors compete rather than cancel.

Recomputed from their own inputs at the projected count, at FY2032 and current law, the two terms are $11,254,806 the state’s way and $40,995,631 the district’s. The net is $31,675,951 of aid the linear projection pays that the recomputed one does not — 0.44% of the level, and 65.9% of the enrollment effect the forecast exists to report. The capacity term is three and a half times the base cost term and carries the sign; the issue that opened this named the base cost one, on the strength of the staffing-minimum wedge having just been measured, and it is the smaller of the two and points the other way.

The interval moves further than the point does. Both terms are convex in the count, so the correction is largest at the low end of the enrollment band and smallest at the high end: the FY2032 band goes from $6,958M–$7,582M to $6,853M to $7,740M, and the ±4.3% stated above becomes ±6.2%. A forecast that scales a curved function from its center understates its own interval.

The exposed population is exactly the formula population. The guarantee is a max, so a guaranteed district is inert. At FY2032 the linear path leaves 297 districts on formula and every one of them moves, against one of the 312 it pays. 120 move by more than 1% of their aid; 233 are overstated and 65 understated, and the sign is the difference of the two per-pupil terms for every district those terms can reach, with no exceptions. The correction then sends 15 districts the other way onto the guarantee, which is the same absorption the staffing floors show, arriving from a second direction.

Neither run is a forecast of a tax base, which is why the published one is unchanged. The linear path holds a district’s wealth per pupil fixed — the arithmetic of a tax base that shrinks exactly as fast as its children leave. The recomputed path holds its wealth fixed in nominal dollars for the whole horizon. Sixty per cent of the capacity blend is assessed valuation and this repository cannot project valuation, so the figure above is the width of an interval a projected local share sits inside rather than a correction waiting to be applied. Measured in what_a_linear_projection_holds_per_pupil, and recorded at what a projection holds per pupil.

AND THE THREE-YEAR COUNT IS A CUSHION THE PROJECTION SPENDS. verified crates/project Base cost enrolled ADM is the greater of the three-year average and the current year, so a district in decline is funded on more pupils than it teaches — statewide, 1.65% more in the FY2027 model. By FY2032 the shipped projection has that at nothing: the damping flattens the series, and a flat series has no average to sit above. So base cost enrolled ADM falls 2.86% over the horizon against enrolled ADM’s 1.26%, and more than half of the correction above is the cushion closing rather than children leaving.

It is the same fact as at the published horizon the trend is simply gone, read through the statute rather than through the count, and it cuts both ways: a district really would lose the cushion if its decline really did flatten. What cannot be said is that the averaging absorbs the error. At this horizon it more than doubles it.