# Ticket Weight Factor Function

Ticket weights are dependent upon Price Premium and Sponsor Tokens applied to a ticket, as [previously mentioned](https://dropshop.gitbook.io/docs/dropshop-lottery/lottery-process/tickets-the-pool-and-the-ticket-weight-factor).

It is the Sponsor that determines the TWF function parameters for each lottery. One may value tokens more, other's price premium - note though that the overall weight is a combination of both. The prototype of the function is a polynomial of form:

$$
TWF = (\frac{stake}{price})^m \times (tokens+1)^n
$$

The following graphs are the results of [Selection Function](https://dropshop.gitbook.io/docs/platform-information/logic/selection-function) simulations of the case n=1 and m=2,3,4. The winners are red dots and the size of the dot represents the ticket weight.

![Winners from a Set {P} of participants with randomized Price Premium (x-axis) vs. Sponsor Tokens applied (y-axis) for m = 1 and n = 2.](https://3812897419-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FlsfsmRXNlhJaO2JDT72o%2Fuploads%2FK75iuowBNmR2Y1Esc7aJ%2Fsimulation_n1m2.png?alt=media\&token=926609d6-8856-49b1-8d64-522026fa5c64)

![Winners from a Set {P} of participants with randomized Price Premium (x-axis) vs. Sponsor Tokens applied (y-axis) for m = 1 and n = 3.](https://3812897419-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FlsfsmRXNlhJaO2JDT72o%2Fuploads%2FFWolhge2eoLQBbgjn5Tf%2Fsimulation_n1m3.png?alt=media\&token=fa58182f-9f67-4a1f-9941-a7b7de3459dc)

![Winners from a Set {P} of participants with randomized Price Premium (x-axis) vs. Sponsor Tokens applied (y-axis) for m = 1 and n = 4.](https://3812897419-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FlsfsmRXNlhJaO2JDT72o%2Fuploads%2FYLaOF2TV51ZrU8I6fA7z%2Fsimulation_n1m4.png?alt=media\&token=44172cf0-4b50-4b5e-ad61-824a9f9f8277)