Resource Distribution and Accessibility

Today's topic deeply concerns the professional analysis of the board layout, which may not be suitable for casual but high-level Catan matches only. To begin with, we will explain the technical terms used in the article - distribution and accessibility. For both indicators, resources are divided into 02 groups, rare resources which have 03 hexes on the board each (i.e. Brick, Ore) and common ones which have 04 hexes each (i.e. Wood, Sheep, Wheat).

Resource distribution indicates how sufficient the resources are based on their total amount of pips on the number tokens. The minimum amount for a rare resource is 04 pips, which will occur when its numbers on the board are a 2, a 12, and either a 3 or an 11. It reaches the maximum amount of 15 pips when its board numbers are exclusively 6s and 8s. For a common type of resource, the min. and max. numbers of pips are 6 and 20 respectively. To put all of that into a chart, we apply the following formula for the math problems: Resource distribution (%) = (total pips - min. pips) / (max. pips - min. pips). Let's take this board right here to make some examples:

• The distribution of Sheep with 15 pips in total is (15 - 6) / (20 - 6) = 64%

• The distribution of Wood with 12 pips in total is (12 - 6) / (20 - 6) = 43%

• The distribution of Brick with 12 pips in total is (12 - 4) / (15 - 4) = 73%

• The distribution of Ore with 08 pips in total is (8 - 4) / (15 - 4) = 36%

• The distribution of Wheat with 11 pips in total is (11 - 6) / (20 - 6) = 36%

Given the statistics, we are able to draw the first half of our D&A radar chart; however, the information it gives does not seem to be satisfying yet. As can be inferred from the diagram, there exists more Wood than Wheat on the table. Despite that, Wood will be more difficult to get access because the only 02 good Wood hexes (5 and 8) stick together in a cluster. Therefore, we have to come up with an additional solution to properly illustrate the current board situation.

Resource accessibility represents how easy it is to acquire the current amounts of resources on the board. Before we get there, we need to calculate the accessibility of a single hex, which is identified by the current number of pips times a corresponding multiplier. Below is how we defy the multiplier.

The more desirable spots for settlements a hex has, the easier to obtain the resource it produces. There are 03 tiers when it comes to evaluating settlement locations: triple-hexed, double-hexed, and single-hexed. Each triple-hexed spot is worth 03 points, double-hexed is worth 02 points, and single-hexed is worth 01 point. A hex's multiplier is the highest sum of points it could reach. As a result, unless the hex being considered is adjacent to the desert, its multiplier will be:

• 09 if it is either the centrepiece or in the inner ring

• 07 if it is on the edge of the outer ring

• 06 if it is in the corner of the outer ring

In case the hex is next to the desert, simply reduce the given multiplier by 01 so it will be 08 for an inner hex, 06 for the hex on the edge, and 05 for the one in the corner. Knowing the hex's current number of pips and the corresponding multiplier, we can find out its accessibility by multiplying them together (e.g. a central 11 Wheat hex with no desert nearby is worth 2 x 9 = 18 points). Then, we get each resource's total number of points by adding up the results from hexes of the same type. Now once again, the resources are divided into 02 groups, rare ones and common ones. There is only one minimum value for each group, which is 23 points for rare resources and 37 points for common ones. However, their maximum values are a bit more convoluted to understand as they adjust themselves according to their current numbers of pips on the table.

Looking at the bar graph, it is apparent that the peaks in point value do not come from the highest number of pips. In other words, higher amounts of resources do not necessarily mean it is easier to get them. The main reason for this is that among the 6s and 8s, three out of four are located on the outer ring. Meanwhile, there are a 5 and a 9 on the inner ring. To visualise things into a radar chart, we apply the following formula: Resource accessibility (%) = Distribution * (total points - min. points) / (max. points according to pips - min. points). We will make some examples from the board layout we shared earlier in this thread.

• The accessibility of Sheep with 90 points in total is 64% * (90 - 37) / (135 - 37) = 35%

• The accessibility of Wood with 79 points in total is 43% * (79 - 37) / (108 - 37) = 25%

• The accessibility of Brick with 103 points in total is 73% * (103 - 23) / (108 - 23) = 68%

• The accessibility of Ore with 58 points in total is 36% * (58 - 23) / (72 - 23) = 26%

• The accessibility of Wheat with 93 points in total is 36% * (93 - 37) / (99 - 37) = 32%

Putting the above results into the D&A radar chart, we have a finished product. The white outline represents the distribution of resources, while the gray fill shows their accessibility.

We really appreciate that you have been following us through this very ambitious article. Since the topic is new, we find ourselves struggling to explain it in the most appropriate way. Over time, we will keep the article updated with better terminologies and vocabulary. Please let us know if you have any suggestions or feedback in mind. Thank you for reading!