132 Divided by 55 Is Not a Whole Number

Three of the sets this index tracks have 55 cards. Two have 44. Five have 66. Those are not arbitrary numbers, and the difference between them decided which cards are common sixty years later.

The explanation is a printing press, and it is duller and more powerful than any story about what children did with the cards afterwards.

The sheet

From 1957 until 1995, every standard-size Topps card was printed the same way. Baseball, football, hockey, and non-sport alike: a press sheet carrying two large blocks, each one eleven cards across and twelve cards down.

Eleven times twelve is 132. Two blocks to a sheet, separated by a white gutter down the middle, sliced apart before cutting.

That single number explains a great deal of the hobby's furniture. Set sizes of 132, 264, 396, 528, 660 and 792 are all multiples of it. And a great many non-sport sets ran to exactly 66 cards, which is half a block.

Nobody chose 66 because it was the right number of pictures. They chose it because it divided.

The arithmetic, set by set

Take the sets on this index and do the division.

1977 Star Wars, 66 cards per series. 132 divided by 66 is exactly 2. Every card in every series printed the same number of times. No double prints, no short prints, nothing.

1966 Batman Red Bat and Blue Bat, 44 cards each. 132 divided by 44 is exactly 3. Again perfectly even.

1962 Mars Attacks, 55 cards. 132 divided by 55 is 2.4.

And there the problem starts.

What a remainder does

You cannot print 2.4 copies of a card.

Print each of the 55 twice and you have filled 110 of the 132 positions in a block. Twenty-two positions remain. They have to be filled with something, and the something is twenty-two of the cards printed a third time.

So in a 55-card Topps set, some cards were printed half again as often as the others. Not because anybody decided those cards mattered more. Because 132 does not divide by 55.

The same applies to 1966 Batman Black Bat and Bat Laffs, both 55-card sets, and to Riddler Back at 38 cards, where the remainder is even more awkward.

Three of the sets this index tracks have a built-in inequality that the Star Wars series and two of the Batman series simply do not have.

Is it still visible?

This is where we can stop citing other people and look at what we track.

Across the Mars Attacks cards currently listed, the availability is genuinely uneven. The most-listed card has several times the number of live listings of the least-listed one, and that gap is much wider than you would expect from a set where every card was printed equally.

But the shape is not what a simple twenty-two-and-thirty-three split would produce. If twenty-two cards had been printed 50 per cent more often, the sorted listing counts should show a visible cliff between the twenty-second card and the twenty-third. They do not. The distribution slopes smoothly from top to bottom.

So something is uneven, and it is not the neat split the arithmetic alone would suggest.

The row-shaped pattern

There is one grouping where a pattern does appear, and it is worth reporting carefully.

Fifty-five cards is five rows of eleven. Group the set that way, by card number, and four of the five groups behave alike while one does not. Cards 12 to 22 average about a third fewer live listings than the other four groups.

That is the shape you would expect if one row of the sheet had been printed less often than the other four, which is exactly what researchers who reconstruct Topps press arrays describe happening on 55-card series.

And here is why we are not going to claim it as proof. It assumes Topps laid the cards out on the sheet in numerical order, row by row, and there is no reason to assume that. The people who reconstruct these arrays do so precisely because the layouts are not sequential and have to be worked out card by card from surviving sheets.

So: a row-shaped pattern exists in our data, it matches a documented mechanism, and it may be a coincidence of which subjects people happen to be selling. We would need an actual Mars Attacks press sheet to say more, and we do not have one.

Where the sheet shows up elsewhere

Sheet position explains more than double printing, and we have run into it twice before without naming it.

The 1940 Superman set was printed by Gum Inc rather than Topps, on 24-card sheets. PSA's account of the set notes that card 72 sat on the bottom right edge of one, a position that made it vulnerable to flaws, and that card 66 sat on an edge too. Cards on the outside of a sheet take the cutting and the handling. We wrote about that set's grades separately, and found the high numbers grade better than the low ones for an unrelated reason.

And the first card in any set takes its damage after the sheet is cut, not on it. Card number one grades worse in all four franchises we checked, because it sat on the outside of every child's stack. That is a different mechanism with a similar result, and the two compound: a card can be short-printed and then handled badly.

What to take from it

Three things.

Check the set size before assuming anything about scarcity. A 66-card or 44-card Topps set from this era has no structural short prints at all. Any scarcity in those sets came from what happened after they left the factory, not from the press.

In a 55-card set, treat availability differences as real. Something made some of those cards commoner, and while we cannot say which from listings alone, the unevenness is not imaginary.

And be wary of anybody who tells you exactly which cards were double-printed without showing you a sheet. The arrays are reconstructed from surviving press sheets by people doing painstaking work, and a confident list without that evidence behind it is a guess wearing a lab coat.

The thing worth sitting with

A set of cards has a certain number of cards in it because a printing press had a certain number of positions on it.

Not because 66 was the right number of Star Wars scenes, or because 55 was how many Martian atrocities anyone could think of. Because the sheet was eleven across and twelve down, and the arithmetic had to come out.

When it did not come out, somebody had to decide what to do with the remainder, and sixty-odd years later that decision is still sitting in what you can and cannot find.

This index tracks every set it follows card by card and grade by grade, so the availability differences described here can be checked directly. You can read how we work the numbers out.

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