Collation – What’s in the box?

I’ve rambled on about collation – calculating odds, looking at all possible outcomes, and doing simulations to predict probabilities.  Now it is time to see how some of my own box openings have held up to my predictions.  I’ll look at four boxes.

This is an experiment.  The predicted outcomes are determined by the computer.  I’m assuming they are truly random (or at least pretty close).  The box results are the actual experiment.  The question is how well do they match (i.e., are the contents of the boxes random?).

1998 Pinnacle

Set: 200 base cards
Box: 200 cards -> 195 base cards & 5 inserts
Base cards: 191 different with 4 duplicates

Prediction (1,000,000 simulated box openings)
Average number of different cards: 124
Minimum number of different cards: 105
Maximum number of different cards: 144

Here is an example in which Pinnacle has taken great care to make sure a box contains as many different cards as possible.  As a set collector, I appreciate it, but the contents in 1998 Pinnacle are far from random.

1992 Triple Play

Set: 264 base cards
Box: 540 cards -> 537 base cards & 3 inserts
Base cards: 199 different with 338 duplicates

Prediction (1,000,000 simulated box openings)
Average number of different cards: 229
Minimum number of different cards: 207
Maximum number of different cards: 252

In 1998 Pinnacle went out of its way to make sure collectors got as many different cards as possible, but 1992 Triple Play did the opposite.  In a million openings, the computer never got less than 207 different cards, and this box gave up just 199.  Terrible.  There’s nothing random about this box. Then again, I did get 7 Chuck Knoblauch cards, so what am I complaining about?

1994 Stadium Club 3

Set: 180 base cards
Box: 288 cards -> 263 base cards & 25 inserts
Base cards: 178 different with 85 duplicates

Prediction (1,000,000 simulated box openings)
Average number of different cards: 138
Minimum number of different cards: 118
Maximum number of different cards: 158

Here is another box stacked in favor of the set collector.  To get 178 different cards in this box is beyond improbable.  The cards in this box were intentionally placed to give as many different cards as possible.

1994 Select 1

Set: 210 base cards
Box: 288 cards -> 286 base cards & 2 inserts
Base cards: 145 different with 141 duplicates

Prediction (1,000,000 simulated box openings)
Average number of different cards: 156
Minimum number of different cards: 132
Maximum number of different cards: 178

The results from this box are not far out of line from what the program predicted.  When I opened this box, I complained quite a bit about the collation.  I wanted more different cards, and I was bummed at the number of cards that I got three and four copies of.

Conclusion

How can a box of cards ever be random?  Organized (not random) sheets of cards are cut.  Ideally cards going into packs would be shuffled.  Baseball cards are not playing cards.  They can’t be shuffled.  How they get mixed (without being damaged) before being wrapped in packs determines the seeming randomness of the cards.

Some companies apparently do a lousy job of mixing cards so multiple cards abound.  Other companies work to minimize duplicates.  Neither of these are random outcomes.  The fact is that no boxes are random.

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