A probabilistic view of grading

[Bellsprout]

This is the probability of electrons around a proton. What it shows is that an electron is not distributed like a particle with a defined position orbiting the proton. It behaves like a wave, to express this function we need to use a probabilistic view.

Like an electron, a card has no true grade. Or otherly said it has a true grade, but it is not accessible through observation, because the observation brings it out of it’s superposed state, due to decoherence. The card is in a quantum or fuzzy state, before grading, which is the act of observation from the experimentator.

This is confusing so let’s do a thought experiment. Take one card and apraise it. To you it may seem like a 9, for another person it will be a 10.
Now let’s send it for grading, at PSA usa for example. It doesn’t matter for this experiment.
It comes back a 9. Now you crack the slab and you submit the card again. It comes back a 10. This gets unrealistic now but you do that 1000 times.

If you toss a coin 1000 times, it is very unlikely you get 500 heads and 500 tails. What will happen however, is that the ratio of heads to tail will be distributed like a bell curve around 0.5

Imagine a card that returns a 10, 900 times out of 1000. this would be quite a strong 10
Imagine a card that come back a 10, 300 times out of 1000, 600 times a 9 and 90 times an 8 and 10 times a 7. This would be a weak 10.

Dont get focused on the numbers these are just to illustrate. Actually, there is a non zero chance for all possible outcomes, from ungradeable to 1 through 10. but it will always look like a gaussian curve centered around the true grade.
The true grade is unknown, and it cannot be known. It is only possible to get a close approximation with this theoretical experiment.

When you say a card is 10 and someone else says 9, this is only a sample of 2 so the significance is not reached (the sample size must be increased). In practice this of course does not happen, and people are left debating what is the grade of a card, like in the infamous pikachu illustrator case.

Someone, grab a paper and draw what he thinks the illustrator grade distribution would look like

[Will]

[anyon]

A grade is a number that appears on a grading label.

A card does not “have a grade” until after it is graded - it does not have a label, and a grade is a number that appears on the label.

Grading is a complex process, involving the actions of many people, that begins with a card in your possession, and ends with a card inside a sealed case alongside a grading label, with a grade on it. (Assuming the card is not lost/stolen/misdirected along the way.)

Probability is a philosophically tricky thing, but I would say that this process is “qualitatively as random” as flipping a coin, shuffling a deck, rolling dice, etc. Not going to comment here on quantum physics.

On the other hand…

• The probability distribution over the 10 possible outcome numbers is not fixed to any particular functional form, e.g. Gaussian. Still, it does have a mean (unlike certain continuous distributions, like Cauchy). Should the “true grade” of a card be an arbitrary real number, e.g. 7.842351?
• The people involved in the grading process change over time. Any probabilistic model of the grading outcome therefore also has to be time-dependent. Is the “true grade” of a card something that should change with time?
• Statements people make are usually very imprecise. Saying a card is “a strong 9” could mean “this card is in better condition than most other examples of that card I’ve seen that got a 9”, or “ if I had that card I would break it out of its case and regrade in hopes of getting a 10” or “I like the way this card looks and I just feel it really ought to have been a 10 and those PSA graders are all idiots” etc. Is the “true grade” of a card something that should be determined by a community of such people?

The only “true grade” a card has, I contend, is the number that appears on the label in the case it is in.

Whether such numbers are meaningful, predictable before grading, etc. is an interesting question.

[pfm]

A pokemon card is both a wave and a particle

[magikarpflail]

My cards are in storage, does that make them waves?

[Will]

[Cerulean]

This is why I was thrilled when I had the option not to take math during my senior year of high school.

[Bellsprout]

A random thought I was having today

A slab is either in a personal collection and unmoving state, or it is moving in the open market exchanging hands. Sometimes a slab will fluctuate from one state to another, but as time goes by, more and more slabs goes into PCs (an energy well)

If the card is a true PSA10 (satisfying the collector), its chances of going into a PC and staying there are higher
If the card is labeled PSA10 but presents obvious defects to the naked eye, it has a higher probability of being put in the market. Also, because a lot of people are grading to make profit, there are also more likely to try to get 10s out of cards they know have small defects.

When as a buyer, we are therefore more exposed, in proportion, to these low quality PSA10, skewing our view, because the unquestionable ones are more likely to be kept in PCs