Show floor heat mapping that an operations lead can defend in a debrief

The heat map goes up on the screen in the debrief and the room reads it in about four seconds. Three stands glow orange. Everyone concludes those three stands had a good show and the rest of the hall did not, and the sales director starts drafting a rate card change.

Then somebody asks what the bin size was, and the analyst says five metres, and somebody else asks what happens at fifteen, and the answer is that the three orange stands disappear and a single aisle lights up instead. Same 62,000 zone pings, same day, same hall, different conclusion.

Show floor heat mapping is a spatial histogram with a colour ramp on top. The picture is a product of four choices made before any attendee walked in, and none of those choices is usually written on the slide.

What a heat map is underneath

Take every position estimate you collected, drop a regular grid over the hall, count how many fall in each cell, and colour the cells by count. That is the whole method.

The hall in question is 90 metres by 60 metres, so 5,400 square metres of floor. At five metre bins that is 18 columns by 12 rows, 216 cells, each covering 25 square metres. Spread 62,000 pings across 216 cells and the average cell holds 287.

At fifteen metre bins the same hall is 6 columns by 4 rows, 24 cells, each covering 225 square metres. The average cell now holds 62,000 divided by 24, which is 2,583.

Nothing has changed except the grid. Every ping is where it always was.

Bin size changes the answer, and it always has

Here is what the two grids report about the same busiest patch of floor.

At five metres, the hottest cell holds 1,940 pings against a mean of 287, so it is 6.8 times the mean. Two other cells sit near 1,700. Those are the three glowing stands.

At fifteen metres, the hottest cell holds 7,900 against a mean of 2,583, so it is 3.1 times the mean. The three hot spots have been absorbed into a larger cell along with a lot of ordinary floor, and the contrast has collapsed from 6.8 to 3.1. What remains visible is the aisle those three stands sit on.

Both pictures are arithmetically correct. Neither is more true than the other, and the choice between them should follow from the decision in front of you. If you are deciding where to put extra stewards, the fifteen metre picture is the useful one, because stewards work on routes. If you are answering an exhibitor asking whether their corner performed, five metres is closer to the question, though it is still four booths wide.

Openshaw set this out formally in 1984 in the Concepts and Techniques in Modern Geography series, in a monograph on what he called the modifiable areal unit problem. His examples make the size of the effect obvious. He reproduces Gehlke and Biehl's 1934 study of Cleveland, where the correlation between male juvenile delinquency and median monthly income moved from minus 0.502 across 252 census tracts to minus 0.763 when the same data were grouped into 25 units. He also reproduces Yule and Kendall's finding that the correlation between wheat and potato yields across English counties rose from 0.2189 at 48 areas to 0.9902 at 3.

Those are correlations rather than heat maps, and the mechanism is the same one operating on your hall. Aggregation smooths, and smoothing raises apparent association and lowers apparent contrast.

Moving the grid changes it too

Openshaw splits the problem into two parts, and the second one gets almost no attention in event analytics. The scale problem is what happens when you change the number of units. The aggregation problem is what happens when you change how the units are drawn while holding their number constant.

Test it on your own data in five minutes. Keep the five metre grid and shift its origin by 2.5 metres east and 2.5 metres north. On the hall above, the hottest cell drops from 1,940 to 1,180, because the busy patch that had been sitting neatly inside one cell now straddles four. The map still has 216 cells of 25 square metres each. Nothing about the show changed. The hottest cell lost 39 per cent of its count.

That is the number to keep in your head the next time a heat map is used to justify a price. A stand's apparent performance in a gridded heat map is partly a function of where the grid happened to start.

The defence is to state the grid origin on the map and to run the shift test once, reporting how much the top cells move. If they move a lot, use larger bins or move to named zones with real boundaries, which is a different object with different arithmetic and belongs to C17.

What colour scale should a show floor heat map use?

A sequential scheme, with a small number of classes, and classes chosen from the distribution of counts rather than stretched linearly from zero to the maximum.

The linear stretch is the default in most tools and it is the reason so many show floor heat maps look like a black hall with three orange dots. With a maximum cell of 1,940 and a median cell of 96, the median renders at 96 over 1,940, which is 4.9 per cent of the ramp. Half your hall is drawn in the bottom twentieth of the colour range, so half your hall is invisible, and the one exceptional cell has consumed the entire scale.

Quantile classes fix it directly. Sort the 216 cells by count, split them into seven groups of about 31, and give each group a colour. Every class now contains a readable share of the hall, and the map shows the shape of the distribution rather than the position of its maximum.

Harrower and Brewer set out the practical rules for this in The Cartographic Journal in 2003, in the paper describing ColorBrewer. Their framing is that the scheme should follow the nature of the data, sequential for ordered magnitudes, diverging for departures from a midpoint, qualitative for categories, and that the number of classes and the output medium both constrain what will actually be readable. A show floor map printed in greyscale for a debrief pack has different constraints from one on a screen in the show office, and their tool was built to answer exactly that.

If you are showing change against last edition rather than raw counts, switch to a diverging scheme with a fixed midpoint at zero. Using a sequential ramp for a quantity that goes negative is one of the most common errors in event reporting and it makes small declines look like large ones.

The time window nobody sets

The fourth choice is the one most often left at its default, which is normally all day.

An all-day heat map is dominated by the hours the hall was busiest, so it is largely a picture of the 11:00 to 13:00 period with everything else averaged into it. For most operational questions that is the wrong object. The decision about where to move stewards at 14:00 needs the 13:30 to 14:00 map, and it will look different from the day map in ways that matter.

The rule that keeps this honest is to render the same hall at three windows and put them side by side: the full open day, the busiest hour, and the hour the question is about. If they agree, say so and use the day map. If they disagree, the day map should not appear in the deck at all.

Where this stops

A heat map shows where devices were detected, and the gap between that and where people were is not small. Detection depends on carrying a device, on the device advertising, and on a receiver hearing it, and each of those varies systematically across the population and across the hall. A quiet corner on a heat map can mean a quiet corner or a receiver with a truss between it and the floor.

The deeper limit is that a heat map is a description with no denominator in it. It tells you a cell had 1,940 pings. It cannot tell you whether that is a lot for a cell of that size, in that part of the hall, at that time of day, and those are the comparisons every reader immediately tries to make. Making them properly needs counts divided by area and by open minutes, which is C17's arithmetic and the step that turns a picture into a comparison.

A heat map also flattens sequence. Two cells lit equally may be visited in a fixed order by nearly everybody or in no particular order at all, and only the ordered zone sequences behind the pings in C13 can separate those. And a cold cell is a claim that needs its own treatment, because low traffic against the hall median is a ranking exercise with a cause attached in C16, rather than something to read off a colour ramp. All three belong in the same attendee analytics pack, and they should agree on their zone definitions before any of them is printed.

Before the next debrief, take last edition's heat map and render it four times: at your current bin size, at three times that bin size, with the grid shifted by half a cell, and with quantile classes instead of a linear ramp. Put the four side by side in front of the person who used the original to make a decision. If all four support the decision, you have a defensible map. If they do not, you have learned something more valuable than the map was ever going to tell you.