# Market Price

Market price is the culmination of all of the statistic modules available in Auctioneer. Statistic modules monitor the various components of the economy individually, and offer their own, independent estimation of what the actual price of an item should be. Each module might have different formulas or even different data that it watches to make these calculations. The "Market Price" is calculated by the Auctioneer core, combining all of the statistics modules into one.

## Module Confidence and PDFs

Because each module has its own way of calculating data, each module also may be more or less confident, because it uses different techniques or data to come up with its result. As more data is available to the module, it may become more confident (or less confident, if the data suggests the value was off). Because these modules may have varying levels of confidence, they all report to the Auctioneer core in the form of a Probability Density Function (PDF).

A probability density function is a simple form of representing the probability that a given price is correct. The area under the curve of this function is always 1 (indicating 100% chance that the price is somewhere between negative and positive infinity), and varies depending on what value is being tested. The blue and green graphs below represent two potential PDFs from two independent modules tracking the same item. They both use the standard bell curve to report the probability (note that this is not a requirement, however it is a quick, easy, and statistically sound manner of doing so -- any PDF is valid, so long as it is continuous).

The green module is more confident about its answer due to the standard deviation being less. As a result, the probability rises higher at certain prices, and sharply lower as the price moves away from its suggestion. Similarly, the blue module is less confident, so a wider range of prices give approximately the same probability (and the peak probability is lower).

## PDF Summation

The Auctioneer core needs to take the green and blue modules and combine them in a manner such that they both have some say in the pricing (while ensuring that the green module is taken more seriously, as it is more confident). To do this, we return to the fundamental purpose of the PDF: It indicates the probability of the given price. Thus, we can create a new curve which indicates the summation of those probabilities, as is indicated by the red curve. This is the first step in Auctioneer's determination of the market value: The PDFs are added together to create one "master PDF." This indicates the summation of all of the probabilities from all of the modules reporting.

With a new graph built, Auctioneer determines the 50% point on the graph. Note that this is not the peak of the graph -- while the peak would represent the single price that has the most likely chance of being correct, it does not accurately represent the market price because the likelihood that it is greater than that price may be far greater than the likelihood that it is less than that price. A better representation of the true market value is to determine the graph's midpoint, using simple calculus.

Auctioneer locates the 50% point on the graph by making a first integration pass (trying to match a pre-set error margin), and then integrating again at the same level to determine at what point 50% of the area under the curve is to the left, and 50% of the area is to the right. At this point, it is equally likely that the price is less than the given value as it is greater than the given value. This is an accurate representation of the estimated market value of the item. The below image shows the previous sample with 50% of the curve shaded. The point at which the shading stops and the unshaded portion begins is the 50% point, which would then become the market value.

Note that the market value reported is closer to the peak of the green graph than it is to the blue graph, however the blue graph does still have some say in the outcome. As the confidence levels of the modules change, so does the market value's weighting of the modules together.

## Auctioneer's Extensibility

This simple example only shows two modules competing for pricing options, but Auctioneer can support a theoretically infinite number of statistic modules reporting data. Auctioneer will only take into account those modules reporting data for the given item, and will weight all of them according to the PDF they supply. Thus, users can "snap in" and "snap out" statistic modules as desired to create a truly accurate market value representation.

## Currently Supported Modules

Any Auctioneer statistic module implementing the GetItemPDF() function is automatically considered in the market value computation. However, because this is a new feature, not all modules yet implement that function. Below is a list of modules that currently have the GetItemPDF() function implemented, and thus weigh in on market value calculations:

## Tooltip and Options

The market price is displayed in the tooltip. Options for the tooltip are found in the Tooltip section of the Auctioneer "Core Options":