Continuing with our little test of 1966 Topps Mickey Mantle, from the other post we started showing the relationship between grade and price from a data perspective.
Let’s take it further.
We’d like to find out if the change in price when grade is factored is linear, exponential, etc. Let’s take a collection of sales prices and normalize them. We will make the lowest price we observe for each card in the dataset 0 and the highest 1. We will remove outliers. So for the 1966 Topps 50 Mickey Mantle card, let’s look at its prices:
## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 28.0 95.0 159.9 647.3 362.5 14711.0
Ok, so lowest is 28, highest is 14,711. We’ll map the prices linearly onto this 0-1 scale.
So far so good.
Let’s expand this to more cards. Let’s pick 10 highly traded cards, shown here:
So, 15 cards. Several Mickey Mantle Cards, a 1986 Fleer Michael Jordan Sticker, Charles Barkley, John Elway, Nolan Ryan, Willie Mays. Just random Hall of Fame players and random cards. Each traded more than 1000 times, publicly (the number on the right column).
Ok, so clearly some price normalization needs to happen.
Ok, that is more how we want this data to look. Also, because it looks like PSA started collecting much more data after September, 2016, we’ll just use data after that.
Here’s the point!
This box plot tells the story of how grade affects price.
With prices normalized, we can see much more clearly the relationship between price and grade. AND, it does look like there is an exponential relationship. In other words, as grade increases, price increases at an increasing rate.
Interestingly, below a PSA 6, the prices don’t vary that much. At PSA 7 the change in price really starts to jump. AND, you can see at PSA 9 and 10 there’s an exponential jump in the relationship between price and grade.
The next article will have a tactical application.