The fitted damping

project::series::DEFAULT_DAMPING governs how much of a fitted growth rate survives into each further year of a projection. Every enrollment forecast in the published feed runs through it, out to a FY2036 horizon.

It shipped at 0.85 and said so plainly: “A convention, not an estimate. Three observations per district cannot identify a damping parameter, and there is no Ohio-specific study here to borrow one from; 0.85 is the value damped-trend forecasting commonly defaults to. It is named as a constant so that a future phase with a real enrollment history can replace it with a fitted number and see what moves.” Enrolled ADM carried the same thing as its one open question, and expected the history to come from nces-ccd.

The history arrived from a different direction. Extending the F-33 panel past FY2022 (#277) put V33 fall membership for 602 districts across fourteen years into a committed fixture, keyed on LEAID — four to five times the three points that sentence was written against. The key is also what answers the consolidation worry the open question raised: a district that stops being surveyed leaves the population rather than distorting it.

#282 backtested the parameter 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. Every forecast produced by series::project itself, so what was measured is what ships.

damping                              mean absolute log error
0.20  the fitted optimum                     0.04031
0.30                                         0.04033
0.85  what shipped                           0.04441
1.00  undamped                               0.04874
carrying the last observation forward        0.04340

0.85 cost about a tenth of the error against the optimum in all four metrics tried, and on three of the four it was beaten by making no forecast at all.

Set DEFAULT_DAMPING to 0.30.

Why 0.30 rather than the 0.20 that minimizes the headline metric. The objective is flat between them — 0.04033 against 0.04031 on the three-point window the callers actually use, 0.05%, which no honest reading distinguishes. 0.30 is the optimum on the enrollment-weighted metric, which is the one that governs a statewide total rather than a typical district, and on the fit that uses the full history rather than three points. It is also the smaller departure from the value it replaces, and the only value whose consequence for the feed was measured before the change was made.

The method is unchanged. This is a wrong constant, not a wrong shape: at its optimum the damped trend beats a flat carry-forward by 7.1%, an undamped trend is 20.9% worse, and a least-squares straight line is worse still and deteriorates with more history — it projects a district through zero, which is the failure damping exists to prevent.

The published feed moves, and it was measured first. At the FY2036 horizon, under current law, through report::forecast:

statewide ADM                1,315,656  ->  1,376,953    +4.66%   61,297 pupils
realized state aid          $7,154.7m   ->  $7,230.1m    +1.05%   $75.4m
districts on the guarantee        367   ->        320       -47

The enrollment number moves four times as far as the aid number, because the guarantee pays a fixed amount that enrollment does not enter to about half the state and absorbs most of the difference. That is the finding [the_forecast_interval_is_narrower_than_the_enrollment_interval_that_drives_it] already held; it applies here too. The largest proportional movement is not a dollar figure at all: 47 districts change guarantee status at the horizon, and that is a count the site publishes.

Projections become less confident in their own trend, which is the point. A district’s fitted growth rate is now nearly spent by the second projected year instead of the fourth. Long horizons sit closer to the last observation, which is what fourteen years of Ohio enrollment say they should do — the series is close enough to a random walk that a fitted rate is worth carrying about one year.

Two tests changed their names, which is the honest record. what_ships_is_worse_than_making_no_forecast_at_all was true of 0.85 and is not true of 0.30. It is now what_used_to_ship_was_worse_than_making_no_forecast_at_all, holding both facts: that the old value lost to the trivial baseline, and that the new one beats it. A test whose name stops being true is a finding, not a maintenance chore.

The open question on metric/enrolled-adm closes. It asked whether a damped trend is the right method; the answer is yes, at a damping the corpus had not fitted. What replaced it — the narrower question of whether to move the constant — is now answered too.

Leave it at 0.85 and record the measurement only. This is what #282 did, deliberately, because the measurement was the missing half and moving a published number is a different act from measuring it. Rejected now that both halves are on record: a constant known to be about a tenth worse than the optimum, and worse than doing nothing on three metrics, is not a defensible default to keep once it is known.

Move to 0.20, the headline optimum. Rejected on the flatness of the objective and the enrollment-weighted metric, above. The difference is 0.05% and the argument for 0.20 is that it wins a metric that weights a 300-pupil district equally with Columbus.

Fit per district rather than one constant for the feed. Rejected for now, and it is the real next question. Fourteen observations per district is enough to fit a district-level damping, and the statewide optimum being flat between 0.0 and 0.4 hints the right value differs across them. It would also mean a projection whose method varies by district, which the feed’s single damping field cannot express and the page has no way to explain.

Answered, and the answer is no. tests/the_two_questions_the_damping_left_open.rs: fitted per district it looks 15.3% better in sample and is 3.6% worse out of it, with more than two thirds of districts landing on a boundary of the grid. The hint was wrong — the flatness is the objective being insensitive, not the optimum varying. Nothing about the feed’s single damping field needs to change.

Lengthen the fitting window instead of moving the damping. Not an alternative — it is a second, larger improvement that is still available. Fitting on the full history rather than three points lowers the error at every damping tried, and the observations are already committed. HISTORY_YEARS is three because that is what the department’s model carries, so this needs the panel wired into the projection path and is a bigger change than a constant.

Answered, and the answer is yes with a caveat that makes it a decision of its own. The best form is a blend rather than a replacement: three-tenths weight on the three-point rate and seven-tenths on the district’s whole history is worth 4.6%, and beats both ends — discarding the recent rate is worse than keeping a third of it. That is larger than the 2.4% this decision bought.

The caveat is the join. The projection runs on enrolled ADM and the long rate is V33 fall membership; their FY2024 levels correlate at 0.9997 but their two-year growth rates correlate at 0.287. The disagreement is the best evidence that a two-year rate is mostly noise, and it is also why the blend cannot be dropped in mechanically — it assumes the two series share a long-run trend while differing in short-run noise, and only three years of ADM exist to test that with.