**I. Player Indexes**

Each player in Card Ladder has an index. These indexes are total market indexes. They contain

every card of the player in Card Ladder’s database.

Card Ladder’s player indexes serve two primary purposes. First, they seek to represent

fluctuations in a player’s sports card market over time. Second, they aim to establish a baseline

that can be used to project plausible price movements of individual cards of that player.

*(A) Basic Methodology*

A player’s index is calculated as follows. Every card of a player is multiplied by its “last sold”

value. “Last sold” means the average value for which the card sold on the most recent day that it

sold. The resulting sum is divided by the total number of cards the player has. This produces the

index value. This value is calculated once per night after each day’s sales have been approved.

The mathematical representation of this formula is below.

*Example*: Suppose Kobe Bryant has 500 cards in Card Ladder’s database. Each card is

multiplied by its “last sold” value. The resulting sum is $5,000,000. This sum is divided

by 500 (the number of Kobe cards in the index) to produce an index value of $10,000.

Each night, a new index value is created, and a new data point is added to the player’s index.

*(B) Exclusions*

A card must have at least 2 sales in the last year, and at least one in the last 6 months, in order to

be included in a player index.

*(C) Retroactivity*

Because Card Ladder houses the all-time online sales histories for every card in its database,

player indexes are retroactively calculated going as far back in time as the very first online sale

of any card of a player.

Furthermore, any time a new card is added to Card Ladder’s database, the index is retroactively

updated to include that card’s all-time sales history.

**II. Divisor Adjustments in Player Indexes**

*(A) Problem with Player Index Methodology*

A problem facing player indexes is that most cards have recorded their first sale on a different

date. This means that the index value will jump each time a card in the index records its first

sale, effectively rendering index values from the period prior to that sale irrelevant for the

purposes of understanding fluctuations in the player’s market over time.

*Example*: Suppose that a Kobe Bryant 1/1 card in Card Ladder’s database recorded its

first sale – for $1,000,000 – on April 1st, 2021. Suppose further that Kobe’s index value

was $10,000 on March 31st, and then, because of the $1,000,000 sale, jumped to $15,000

on April 1st, while the prices of the other cards in Kobe’s index remained constant. The

index thus registered a 50% increase in value although none of the cards in Kobe’s index

changed in value. This portrays a non-representative fluctuation in Kobe’s market, thus

defeating the purpose of the Kobe index.

*(B) Solution: Divisor Adjustments*

Stock market indexes face a similar problem that player indexes face. From time to time, stocks

are added to or removed from an index. To prevent an index’s value from changing when stocks

are added or removed, a “divisor” is used. (Read more about the methodology of stock market

index construction at this link:

https://www.spglobal.com/spdji/en/documents/methodologies/methodology-index-math.pdf)

A divisor is a number used to divide the value of an index. Card Ladder’s player indexes use a

divisor.

*Example*: Suppose that Kobe’s index value is $10,000. A divisor of 10 is then applied.

The new index value is $1,000.

The formula, including divisor, for calculating player index values is:

A divisor is useful in player indexes because it can be adjusted to offset fluctuations that are

caused by a card selling for the first time. When a card in a player index records its first sale,

then (1) the net change in the index’s value due to that card’s first sale is determined and (2) this

is used to create a new divisor.

The formula for adjusting the divisor follows:

For the purposes of the following illustration, assume that each player index in Card Ladder

begins with a divisor value of “1.” When the second card in the index records its first sale, the divisor is adjusted. The same happens when the third card in the index records its first sale, and

the fourth, and so on.

*Example*: Suppose that the first Kobe card in Card Ladder’s database to record a public online sale is the 1996 Topps Chrome #138 Base PSA 10. Its first sale is $455 on January 11th, 2004. Kobe’s index’s value on January 11th, 2004, is $455.

*Example: Index Value Calculation*

- Suppose that the second card in Kobe’s index to record its first public online sale is the

1996 Flair Showcase #31 PSA 10 for $126 on May 9th, 2004. No other Kobe cards have

sold, except for the $455 sale of the 1996 Topps Chrome #138 PSA 10. Because a card

in the index has recorded its first sale, this triggers a divisor adjustment.

*Example: Divisor Adjustment Calculation*

*Example: Index Value Comparison With and Without Divisor Adjustment*

*Without Divisor Adjustment:*

*With Divisor Adjustment:*

Thus, the divisor adjustment preserves the index’s $455 value as a new card records its first sale.

The index does not experience a value fluctuation merely because one of its constituent cards

sold for the first time.

*Example: Index Fluctuations*

Going forward, of course, if the value of the constituent cards fluctuates, the index will, too. For

example, the 1996 Flair Showcase #31 PSA 10 sold for $177.50 on May 17th, 2004, marking an

increase in value of the card from its $126 sale on May 9th, 2004. The index will adjust as

follows:

The index increases in value to reflect the fact that the one of its constituent cards increased in

value while the other remained constant in value. Thus, the divisor-adjusted index has captured

a market fluctuation in Kobe’s index.

*(C) Methodology for Calculating "Old" and "New" Index Values*

For the purposes of adjusting the divisor, the definitions of the “old” and “new” index values are

important. The event that the divisor adjustment seeks to offset is the first sale of a card in a

player index. In an index with hundreds of cards, for example, some of them can experience

value fluctuations on the same day that a different card in the index sells for the first time. Those

fluctuation should show up in the index.

To ensure that only the first sale is offset, the following order of processes is followed:

- A card that records its first sale on Date Z is temporarily set aside.
- All sales of cards in the index that are not first sales that occur on Date Z are used to

calculate Date Z’s index value. This is the “old” Index Value. - Then, any first sales on Date Z are included into the Index Value calculation. This is the

“new” Index Value.

*(D) Normalization*

Each player index is normalized so that its initial value is $1,000. This is accomplished by

modifying the divisor’s initial value in relation to the index’s unnormalized value on its first day.

Once the initial divisor is derived, it is then applied to the index’s unnormalized value on its first

day, resulting in an index value of $1,000.

*Example*

- Suppose that Kobe’s player index’s value on its first day is $455. The following

calculation is performed to generate an initial divisor.

- The initial divisor is then applied to the index’s unnormalized value on its first day in

order to normalize its value to $1,000.

**III. Index-Suggested Price Modeling**

Beyond the insights that can be gleaned from observing total market player indexes for players in

Card Ladder’s database, these indexes present a unique opportunity for price modeling.

*(A) Ratios*

A numerical relationship exists between the price history of a player index and the price history

of each of its constituent cards. Any time a card records a sale, that sale can be understood as

one side of a ratio. The other side of the ratio is the value of the player index to which the card

belongs on that date.

*Example*: Suppose the Kobe index is worth $10,000 on March 31st, 2021. On that date,

the “last sold” value of the 1996 Metal #181 Kobe Bryant PSA 10 was $3,333. Thus, the

card’s value in relation to the index’s value is $3,333/$10,000, or 0.33.

Because Card Ladder’s player indexes are retroactively calculated going back to the first sale of

any card in that index, every sale of every card in a player index can be understood in relation to

the price of the index on the date of that sale.

*(B) Price Modeling*

Assuming that there is predictive value in the historical relationship of these ratios – or, put

differently, assuming that there is reason to believe that the price ratio between a card and its

player index will remain constant going into the future – the fact that player indexes log a new

data point every day, whereas certain cards can go for weeks, months, or even years without

recording a new sale, provides the opportunity to use these historical ratios to project current

card values.

*Example*: Suppose that the ratio between the 1996 Metal #181 Kobe Bryant PSA 10 and

its player index is 0.33. Suppose further that the index values for the first 5 days of the

month of April, 2021, are $10,250, $11,100, $10,300, $9,400, and $10,200. This

produces the following index-suggested values for the card.

A card and its respective player index could have dozens, hundreds, or even thousands of

historical ratios, depending upon how frequently the card sells. By the same token, an

exceedingly rare card might have only one or two sales in its sales history, and thus will have

only one or two historical ratios.

Card Ladder’s index-suggested pricing model uses a card’s “last sold” price to generate the ratio.

As noted above, “last sold” means the average value for which the card sold on the most recent

day that it sold. Practically speaking, this means that the ratio will update every time a new sale

is recorded.

*(C) Confidence Levels*

Because the relationship between a card and its player index can change over time, index-

suggested prices that are based on recent ratios probably hold more predictive power than index-

suggested prices based on older ratios.

To underscore the existence of this spectrum of uncertainty, Card Ladder displays a confidence

level next to each index-suggested price.

There are 5 confidence levels:

- Level 5: the “last sold” date occurred within the last 2 weeks.
- Level 4: the “last sold” date occurred more than 2 weeks but less than 1 month ago.
- Level 3: the “last sold” date occurred more than 1 month but less than 3 months ago.
- Level 2: the “last sold” date occurred more than 3 months but less than 6 months ago.
- Level 1: the “last sold” date occurred more than 6 months ago.

*(D) Price Modeling for Cards Not Yet in Card Ladder's Database*

For cards not yet included in Card Ladder’s database, members can add the card to their

collections and utilize the index-suggested pricing model themselves. Once the member enters

the date and price of their purchase of their card, Card Ladder’s software automatically syncs

these data points with the appropriate player index, which allows a ratio to be generated. That

ratio will then be used going forward to create a new index-suggested price for the card every

day.

**IV. Final Thoughts**

Total market player indexes offer an analytical lens through which to study the sports card

market. The limitations of this approach are worth noting.

From a practical point of view, player indexes are limited in scope by the number of cards that

comprise them. Some indexes will have thousands of cards while others will have a few dozen.

Second, by their nature, player indexes create generalizations about a market that run the risk of

overlooking unique trends that might be happening in different segments of that market.

Third, player indexes are calculated based on the “last sold” value of every card in the index,

subject to the above-mentioned limitations that if the card has not sold at least twice in the last

year, as well as at least once in the last 6 months, then it is temporarily excluded until it meets

those criteria. It is conceivable that a player’s market can shift during a period in which their

cards are not transacted frequently, which means the index may not track the true market trend.

These three plausible shortcomings of player indexes are not exhaustive; it is wise to

contemplate all conceivable shortcomings when utilizing a player index to perform analysis.

The limitations on player indexes extend to Card Ladder’s index-suggested pricing model as

well. In short, any pricing model – even one that is based purely on “comps” – should be

conceived of as a theoretical tool for performing analysis, rather than a definitive determination

of value.