By Coverage

Introduction

As opposed to the Evaluation by Score, which produces a tier list containing all items, this functionality uses a mathematical algorithm in order to generate a small combination of items that provides a good total coverage. The results are presented in the form of a tier list, but that is secondary.

The main goal of the calculator is to answer the following questions:

1. What is the smallest combination of items that provides a target coverage?

2. What is the combination of a given size that provides a maximum coverage?

3. Given a combination size and a target coverage, what is the most valuable combination of that size, which provides that coverage? Here, the value is composed of elements such as the items' levels, age, skill, etc.

The results are visualized as a tier list. Additionally, items recommended by YouTuber Studfit for the current tour are marked with a red "S" in the top left corner.

Options

General Options

Option	Description
Algorithm Type	The Simple algorithm has less options but might be faster for certain calculations, since the program runs on the user's browser. The Extended algorithm provides more functionality but runs on the server, meaning that the waiting time might be longer. In the following, we assume that the option "Extended" was selected.
Include City Courses	If selected, all courses will be considered by the algorithm.
Rarity	The user can choose which item rarities to consider in the tier list.
Compact Tiers	If selected, the results will be shown on less tiers. This has no impact on the calculation.

Inventory

The options in this tab are closely related to those in "Skills and Points".

Depending on the option chosen for "Inventory", the settings are different:

Ignore

If this is selected, the algorithm assumes that the user owns all items, and that they are all maxed.

Option	Description
Simulate Level	This defines the level assumed for all items.

Consider

Selecting this reveals additional fields:

Option	Description
Simulate Level	This defines the level assumed for all items, both in the inventory and outside it. The only exception is for items in the inventory at a higher level than the simulated level. In that case, their real level is considered.
Max New Items Allowed	This is a limit on the number of items outside the user's inventory that are allowed in the combination.
Level Threshold	This acts as a filter on the items in the inventory: If it is selected, items at levels below the threshold will be ignored by the algorithm. However, if that leads to no solution found, the calculation is repeated with a threshold of 1.
Simulate Additions / Upgrades	This lets you simulate changes to your inventory, to see how new investments would affect the selection without having to edit your "proper" inventory.

Optimizations

This is the most important option, which will determine the basic type of optimization to be done. The optimization types are:

Option	Description
Minimize Items	Selecting this option reveals a coverage percentage bar below. The algorithm will find the smallest number of items that as a group achieve the target coverage. For example, as of the New Year's Tour 2022, if the inventory is ignored, the algorithm will return a set of 17 drivers that achieve 100% coverage.
Maximize Coverage	This is the right option if the user wants to focus his resources on a small, given number of items. The number of items needs to be entered in the box below. The algorithm will find a combination of that size that achieves maximum coverage. As expected, setting a value of 17 while ignoring the inventory will find a combination with 100% coverage. But a value of 5 returns the combination of Peach (Explorer), Luigi (Lederhosen), Mario (Penguin), Builder Toadette and Dry Bones (Gold). Together, these 5 drivers cover 102 out of the 188 courses (as of the New Year's Tour 2022).
Maximize Value	The first two optimization types have the disadvantage that they return only one optimal combination, but there might be others more suited to the user's inventory. The "Maximize Value" option requires the definition of both a coverage percentage and a maximum number of items. Then, out of all the combinations of the given size that achieve the given coverage percentage, it will find the one with the maximum value. This value is defined in the "Values" tab, and can be customized. It includes factors such as the item's level, rarity, skill and age. It's recommended to run the algorithm with one of the first two optimization types, in order to find good values for the target coverage and number of items.

Skills and Points

Points

Once the algorithm has found a good set of items, they are sorted and ranked in the tier list by using the parameters defined in "Points - Unique" and "Points - Shared". These have no effect on the algorithm.

Skills Priority

This option does have an impact on the algorithm.

The main disadvantage of optimizing based purely on coverage is that item's skills (especially drivers') get ignored. The idea of this feature is to include items which the user would probably want to have in the final selection, such as coinbox drivers or boomerang drivers. This works as follows:

1. The user selects the skills that they consider to be most valuable and defines their parameters (well described in the Toolbox).
2. The Toolbox goes through the skills, from highest priority to lowest. It adds all items to the selection, as long as they have at least as many unique tracks in the selection as the count threshold.
3. Once all the skills have been considered, the optimization algorithm runs on the remaining items to fill the gaps.

Note that a more reliable and more general way of achieving this is by leaving the Skills Priority list empty and using the "Force Inclusion" tab instead.

Exclusions / Force Inclusion

These tabs let you specify items that you want to exclude from the final selection or definitely want to include. For example, you might want to exclude the Gold Mii Suit if you are in Tier 40 and you don't think you'll get to Tier 80 anytime soon. And you might want to enforce all items you own above 6/2. You can also use exclusions to make the algorithm show you a different solution. Often, there are many combinations with the same coverage, but the Toolbox only visualizes the first one found.

Values

This tab only appears if you have selected "Maximize Value" in the "Optimizations" tab. As that algorithm is based on an initial value of the items (disregarding coverage), here you can fine-tune these values. The options are similar to those in Evaluation by Tiers.

Scoring Tiers

The results are displayed as a tier-list for an easier visualization. However, keep in mind that in order to achieve the coverage promised, all the items in the list must be obtained.

The evaluation simply gives a "priority" to the order the items could be get. So if you have only rubies for one DKG and you have to choose between a SSS tier and a G tier, get the SSS. But the G one needs to be get too.