What a projection holds per pupil

policy::apply takes a substituted enrollment and computes base cost aid as the department’s published state share times the ratio of the two counts. Its own note says what that is worth: “the defensible approximation: it is exact at modeled enrollment, which is where every deterministic result in this crate is computed.”

report::forecast is the one caller for which that sentence is false. It substitutes a count no other input in the model was computed at, out to a FY2036 horizon, and every band the site draws comes through it.

Two per-pupil quantities are frozen by that scaling and neither is constant in the count:

• Base cost per pupil. R.C. 3317.011’s staffing floors are a max and do not follow a roll down, so a shrinking district’s base cost per pupil rises. FSFP Base Cost Calculation carries the measurement: a marginal pupil is worth 0.642 of the average one in the smallest ADM sextile, and 313 of 608 districts are below 0.95.
• Local capacity per pupil. R.C. 3317.017 blends valuation, income and a median-income term and divides all three by base cost enrolled ADM, so what the section charges is a dollar amount set by wealth alone — which FSFP Local Capacity Measure establishes and capacity_denominator proves against the department’s own intermediates. Over a shrinking denominator it rises too.

Base cost aid is the difference of the two, so the errors compete rather than cancel. #407 opened the question and named the first term; it is the smaller.

Measure both terms, publish the width, and leave report::forecast computing what it computes.

project::projected_base_cost recomputes each from its own inputs at the projected count — aggregate base cost from foundation on the enrollment scaled to it, and capacity from the published wealth charge over the projected denominator — and runs the correction through report::forecast_with, which is report::forecast with a restatement hook rather than a second copy of the loop. Terms::NEITHER reproduces the committed path exactly, and that is asserted rather than assumed.

Why not correct it. The linear path holds a district’s wealth per pupil fixed, which is 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 ten years. Neither is a forecast of an Ohio tax base, and this repository does not have one: 60% of the capacity blend is assessed valuation, and crates/project’s own note records that valuation cannot be projected from the committed data — one observation per district, stepping on a county reappraisal cycle.

So the $31.7m is the width of an interval a projected local share sits inside, not a correction waiting to be applied. Applying it would move every band in the published feed on the strength of an assumption about Ohio property values that nothing here has measured, and the direction of that assumption is the whole of the answer.

Why not correct the base cost half alone, which is not in that condition — R.C. 3317.011 says what aggregate base cost is at any enrollment and foundation computes it. Because it is the smaller of the two terms and points the opposite way: correcting it alone moves the published figure up by $11.3m, in the direction the larger term says is wrong. A partial correction that moves a number the wrong way is worse than no correction, and it would look like a more careful answer.

The size of what is now on the record. At FY2032, current law, the shipped method:

projected realized aid, linear — what the feed publishes     $7,233.1m
  base cost per pupil recomputed alone                       $7,244.4m   +$11.3m
  local capacity per pupil recomputed alone                  $7,192.1m   -$41.0m
  both                                                       $7,201.5m   -$31.7m

$31.7m is 0.44% of the level and 65.9% of the -$48.1m enrollment effect the forecast exists to report. Against the level it looks negligible; against the movement it is reporting it is two thirds. The second comparison is the one that decides.

The interval moves further than the point. 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 — the ±4.3% this corpus publishes becomes ±6.2%. A forecast that scales a curved function from its center understates its own interval, and that is the part of this a wider band would not have absorbed.

The exposed population is exactly the formula population. 297 districts are off the guarantee at FY2032 and every one of them moves; one of the 312 the guarantee pays does. 233 are overstated and 65 understated, and the sign of each is the difference of the two per-pupil terms with no exceptions. The correction then sends 15 districts onto the guarantee, which is the same absorption R.C. 3317.011’s floors show from the other side.

And a second finding came out of carrying the count forward. Base cost enrolled ADM is max(three-year mean, current year), so a district in decline is funded on 1.65% more pupils than it teaches statewide. The shipped projection has that at nothing by FY2032, because the damping flattens the series and a flat series has no average to sit above — so the funded count falls 2.86% against the taught count’s 1.26%, and more than half the correction above is that cushion closing. It is “The fitted damping”’s horizon behavior showing up inside the statute.

report::forecast gained a seam and no behavior. forecast_with takes a restatement hook and forecast passes an inert one that allocates nothing. The published numbers are unchanged to the cent, which the figure manifest’s pins hold.

Correct report::forecast and move the feed. Rejected on the reasoning above: it would substitute one unmeasured assumption about Ohio property values for another and publish the result as an improvement. This is the alternative to revisit if a valuation projection ever exists — regime_diff::recognized_valuation holds the Department of Taxation’s reappraisal calendar and the abstract now carries four tax years, so the reason recorded for not having one is no longer the reason.

Correct policy::apply instead. Rejected. It is deliberately a one-year function, and the three-year average in DistrictRecord::base_cost_adm means a district’s loss reaches base cost over three years. That is the forecast’s clock, not apply’s, and R.C. 3317.017(B) genuinely multiplies a per-pupil residual by current-year enrolled ADM — so margin’s one-year prices are right where they are, and nothing about the deterministic half of this crate is affected.

Widen the published interval instead of reporting the correction. Rejected as the wrong shape. The correction is not symmetric noise: it has a sign per district that is exactly predictable from the two terms, and burying that in a wider band would report a measured systematic movement as uncertainty.

Carry the base cost count forward one-for-one with enrolled ADM rather than re-applying R.C. 3317.011’s three-year rule to the projected series. Rejected because it is wrong about the statute, and measuring it is what found the cushion: it gives $13.3m rather than $31.7m, and the $18.4m difference is the averaged count catching up rather than anything about pupils.