Aligning booking windows when one edition opened registration eleven weeks late

The 2023 edition of the show opened registration 77 days later than it should have. A platform migration ran long, the marketing calendar was rebuilt around it, and the campaign that normally has 210 days had 133.

Two years later that edition is one of five in the pacing baseline, and nobody looking at the baseline can see it. The snapshot table has counts at day 90 for all five editions and the 2023 number is much lower than the others, which reads as a bad year rather than as a short runway.

Aligning booking windows is the correction, and there are two ways to do it that assume different things about how campaigns work.

Two editions with different runways have no common day 90

Say it precisely, because the imprecise version is what lets the mistake through.

At 90 days before doors, an edition with a 210 day window has had its registration system open for 120 days. An edition with a 133 day window has had it open for 43. The first has had nearly three times as long to accumulate, and the difference is a property of the calendar rather than of demand.

Putting both on a days to open axis, which is O9's subject and the right first move, lines up their endpoints and does nothing about their starting points. The shorter campaign has structural zeros stretching back from day 133 to day 210, and a smoother running over that range will read those zeros as extremely weak early demand.

So the days to open axis is necessary and it is not enough. The second alignment decision is about what to do with the mismatched runway.

Should you rescale the axis or truncate it?

Rescaling maps each edition onto the fraction of its own window that has elapsed. Day 90 out on a 210 day window becomes 120 over 210, or 0.571 of the way through. Day 90 out on a 133 day window becomes 43 over 133, or 0.323. Comparisons then happen at matching fractions.

Truncating cuts every edition back to the shortest window and throws away the earlier part of the longer campaigns. All five editions are then compared over the last 133 days only, and the counts accumulated before day 133 by the four normal editions are treated as a starting level rather than as part of the curve being modelled.

The two carry different assumptions and both assumptions are testable.

Rescaling assumes the campaign stretches to fill whatever runway it is given. Announce registration eleven weeks late and the audience compresses its whole booking behaviour into the shorter period, so the curve has the same shape drawn on a shorter axis.

Truncating assumes the campaign shape is anchored to the show date. The audience registers when it always registers, mostly in the last two months, and the missing eleven weeks at the start cost you only the trickle that would have arrived then.

Which assumption does your show satisfy?

Check where each edition crossed half of its final registration total.

On this show the four normal editions crossed half at 84, 82, 86 and 85 days before doors. Converted to fraction of window elapsed those are 0.600, 0.610, 0.590 and 0.595. The 2023 edition crossed half at 53 days before doors, which on its 133 day window is 80 over 133, or 0.602.

Read both columns. In days to open, 2023's halfway point is 31 days adrift of the others, well outside their spread of four days. As a fraction of window elapsed it is 0.602, which sits comfortably inside the range 0.590 to 0.610 that the other four occupy.

That is the signature of a campaign that stretched. The fraction-of-window coordinate is the stable one on this show, so rescaling is the correct alignment and truncation would be throwing away information for nothing.

The opposite result is just as easy to read. Had 2023 crossed half at 85 days before doors, matching the others in days to open and sitting at 0.361 of its own window, the shape would have been anchored to the show date and truncation would be right. Run the check on your own editions. It is five numbers and a division.

What the alignment choice is worth, in registrations

Current edition, 210 day window, 90 days before doors, 3,550 registrations in the file.

Take the four normal editions first. Their shares of final at 0.571 of window elapsed, which for them is day 90 out, are 0.44, 0.46, 0.45 and 0.47. The mean is 0.455 and the forecast from those four alone is 3,550 over 0.455, which is 7,802.

Now bring 2023 in, rescaled. At 0.571 of its 133 day window, which is 57 days before doors, it held 0.46 of its final. The five shares average 0.456 and the forecast becomes 3,550 over 0.456, or 7,785. Seventeen registrations from the four edition answer, and you have recovered a fifth observation.

Now bring 2023 in without adjusting it, which is what happens by default when the snapshot table is queried by days to open. At day 90 out the 2023 edition held 0.22 of its final, because its campaign was only a third of the way through. The five shares now average 0.408 and the forecast is 3,550 over 0.408, which is 8,701.

The naive inclusion is 916 registrations above the aligned answer, or 12 per cent, and nothing in the calculation flags it. The rescaled and dropped versions differ by 17. That ordering is the practical lesson: the expensive error is including a mismatched edition unadjusted, and the choice between rescaling and dropping is comparatively cheap. Rescale anyway, because on a five edition history the fifth observation is worth having.

Warping, and the constraint that keeps it honest

Rescaling by a constant factor is the simplest possible alignment. The general version lets the mapping between two time axes vary along their length.

Sakoe and Chiba gave the formalism in the IEEE Transactions on Acoustics, Speech, and Signal Processing in 1978, working on spoken word recognition, where the same word spoken at different speeds needs matching. Their dynamic programming algorithm finds the warping function between two sequences that minimises the distance between them, and they derive both a symmetric and an asymmetric form of the normalised distance.

The part worth importing is their slope constraint. Without one, the warping function can map a long stretch of one sequence onto a single point of the other, which produces a beautiful match and destroys the meaning of the alignment. Constraining the slope of the warp keeps the mapping sensible, and for registration curves it is the difference between an alignment that says the 2023 campaign ran 1.6 times faster and an alignment that says 60 days of it happened in an afternoon.

Whether you need warping at all is a question of scale. For two editions and one known disruption, rescaling by the window ratio is enough and it is explainable in a meeting. For a portfolio of forty event instances with irregular launch dates, an automated alignment step is worth building, and the slope constraint is the guardrail that stops it producing nonsense at volume.

The statistical framing for all of this is the separation of phase from amplitude. Marron, Ramsay, Sangalli and Srivastava set it out in Statistical Science in 2015: phase variation is lateral displacement in curves, distinct from variation in their height, and leaving it unremoved "inflates data variance, blurs underlying data structures, and distorts principal components". That last consequence is concrete for anyone planning to run a component decomposition across editions, which is O7's subject and which will faithfully model your misalignment as though it were structure.

Where this stops

Alignment repairs the axis and leaves the reason for the disruption unexamined.

An edition that opened registration eleven weeks late probably differed in other ways too. The marketing budget was spent over a shorter period, the early bird tier may have been dropped, and the audience got less notice. Rescaling the axis makes the curve comparable in shape and does not make the edition comparable in kind, and if the late launch also cost the show 8 per cent of its final registrations, no coordinate change recovers that.

There is also a limit on how far the stretch assumption travels. A campaign compressed from 210 days to 133 plausibly stretches. A campaign compressed to 40 days does not, because the audience has hard constraints, and travel approval and budget cycles do not compress below a certain point. Somewhere between those two the rescaling assumption fails, and with five editions you have no way of locating it.

The last one is a data problem rather than a modelling one. Rescaling needs the registration open date for every edition, recorded accurately, and in most systems that date is either absent or is the date the record was created in the new platform. Reconstruct it from the first non-zero snapshot if you have to, and record it explicitly from now on, since any curve fitted to those editions in the way O4 describes inherits whatever the open date got wrong.

Pull the registration open date and the show open date for your last five editions and compute the window length of each. If they differ by more than a fortnight, run the halfway test before you use those editions for anything, and record the result next to the baseline so the next person does not have to rediscover it. The alignment decision belongs in the same place as the rest of your forecasting methods conventions.