Board Game Breakdown: Catan, Resource Value
Updated: Sep 4, 2022
In part 1 of my breakdown of Catan, I established what an average game of Catan looks like. Today, we are going to take a deep dive into the value of each resource and how it changes throughout the game.
First, just some basic background. In the base game of Settlers of Catan, there are 5 resources you can gain throughout the game: wood, brick, sheep, wheat, and ore. We know that we need an average of 76 resources to win the game and that a higher than average amount of ore is related to winning. Today I want to try to quantify how much each resource is worth, and how different aspects of the game may change a resource's inherent value.
I will again be turning to my dataset of 306 Catan games collected from colonist.io. As a reminder, these use the base map with 4 players. Note thank you to those of you who have contributed their games to the database using the web app I built. I plan to build this out more in the coming months to provide more statistics on each game.
To define a resource's value, I am going to look at the trade market throughout each game. For instance, if someone trades 1 wood for 1 brick, we can assume that wood and brick have equivalent value at that moment. Alternatively, if someone trades 2 wood to receive 1 brick, we would say that brick is twice as valuable as wood. If we assume that the base value for all resources is the same going into a trade, any deviation from a 1:1 trade represents a discrepancy in the value of the resource.
We can therefore define the value of a resource as simply the number of resources received divided by the number of resources given.
So if we have a trade for 2 wood for 1 brick, we would be giving 2 wood, receiving 1 resource total, for the person trading wood, the wood value would be 0.5 since it took 2 wood to receive 1 resource. For the person giving brick, the brick value would be 2 since it only took 1 brick to receive 2 resources.
The same principle can be applied to more varied trade. For instance, I could trade 3 bricks for 1 wheat and 1 ore. In this case, the value of brick would be 2/3 while the value of wheat and ore would be 1.5 each. Note this actually exposes a flaw in the metric. It could be that the ore is worth 2 while the wheat is only worth 1 or wheat is worth 2.5 and ore is worth 0.5. This bias should even out across a large number of trades, but will likely have the effect of pulling everything to a more even value. keep that in mind when we look at the results, as the truth is likely more extreme than what I am reporting here.
Because the bank will always trade a resource at 4:1, the bounds of resource value would be 0.25 (4 resources given for 1) and 4 (1 resource given for 4).
Let's start by understanding the dataset but charting how many trades are throughout the game. In order to normalize the number of turns in a game, I have plotted the trade count vs the % of game completed. Additionally, As we will get into later, I have charted both the general number of trades (blue) and the number of trades that are solely among players (orange, excludes any trades with the bank using ports or 4:1). As we explore the value of resources we will see a discrepancy here. Additionally, I think the most interesting aspect of this chart is that while the total number of trades increases as the game progresses, all of that growth is through an increasing number of trades with the bank, as the number of bankless trades remains the same or even decreases as the game progresses.
Now that we can see the number of trades that we are using, let's start to explore the value of resources.
Bar plots of the estimated average value of each resource. Error bars represent the standard error of the mean (SEM).
To start we will look across all trades across all points of the game. What we find is that Brick is the most valuable resource. Then we have Ore, followed by a tie between Wood and Wheat. Finally, we see Sheep as the least valuable. Interestingly, every resource outside of sheep is worth more than 1, with brick being more than 2! That suggests that on average it will take 2 resources to get 1 brick. I think that trades with the bank are a large part of this, especially since trades early in the game (when people need more brick) are also when trades with the bank are the most expensive (since most people don't start with a port).
So let's take out trades with the bank and see what we get.
Bar plot of mean resource value excluding trades with the bank. Error bars represent SEM. Note the plot is zoomed in to help see the differences.
Interestingly when we remove trades with the bank from the equation, we see wheat becomes the most valuable resource followed by brick, wood, ore, and finally sheep in last again. We also see the resource value move back towards 1 with only sheep being significantly less valuable than any other resource. Between the general and bankless resource value charts, I think they make the case of trying to secure a good source of wheat and brick early on as they will cost the most to buy and can be sold for the most. Additionally, The discrepancy in the value of ore between the general and bankless charts is interesting, suggesting people are reluctant to trade it with other players and end up trading with the bank for ore more often than not.
Bar plot of the mean resource value excluding trades with the bank and with bots. Error bars represent SEM. Note the graph is zoomed in to help see the differences.
Now one last check is the impact of bots. Interestingly, when we remove trades that involved bots, we see that brick returns to the most valuable, followed by wheat and wood. surprisingly we see that ore and sheep are equal when we exclude the bank and bots. Overall, trades are a little more lopsided in terms of resource count when trading amongst human players (though not much). Given the variability in resource value, I don't think there is a significant difference between trades with a human and trades with a bot, at least in terms of resource value.
But that's when we look over the entire game, what about at different stages within a game?
Resource value vs turn
Line plots of the mean resource value at different points of the game. The first plot includes all trades, the second plot excludes trades with the bank and the third plot excludes trades with the bank and with bots.
When looking at the value across the length of the game, we see brick peak early and decline in value (though still remaining rather valuable). In comparison, wood, wheat, and ore all increase in value while the value of sheep remains largely unchanged. My guess is that this is largely driven by port trades with the bank, where players are increasingly likely to do a 2:1 or 3:1 trade with the bank later in the game, both because they now have the option and because other players may be more reticent to trade with each other towards the end of the game.
When we look at the bankless value (second graph in the slideshow above) we actually don't see much change in the resource value across the game. Even the small differences in resource value overall are hard to see when we look at the smaller sample sizes of individual time points in the game. In fact, it looks like most players want/are willing to do a 1:1 trade throughout the game, with most resources value hovering just above 1.
Similarly, when we look at bankless and botless values (third graph) we see largely just noise though maybe a general increase in resource value as the game progresses.
Based on these three graphs, I think there may be a missed opportunity to trade more with other players, especially later in the game. More 2 for 1 trades later in the game looks like an efficient use of your resources. Though the mentality of trading your opponent a win is hard to overcome, so do this at your own risk.
Resource Value vs Point Total
Line plot of how mean resource value changes depending on how many points one player has. excludes any trades with the bank
Instead of looking by turn, we can look at the point value of the players involved. Here we see that the value of resources still stays around 1, but that the price does increase slightly and becomes significantly more variable as the players involved have more points. Note that I excluded any trade with the bank (as the bank does not have a point total), so the noise may be due to fewer trades happening later in the game (when higher point total players are).
We can look at this relationship slightly differently, specifically by charting the resource discrepancy vs the point discrepancy between two players
This was not what I was expecting. I essentially expected a negative slope here, which would suggest that if you have more points than your trade partner, you need to give them more resources in order for a trade to occur. Instead, as we've seen previously, people really arent that flexible with how they value resources, whether that is with point discrepancies or relative to timepoints in the game. This feels like an obvious inefficiency in the game that we players should try to take advantage of, specifically being willing to pay more to secure a victory towards the end.
Resource Value vs Board Availability
Another factor that can drastically affect a resource's value is how easy it is for the board to
produce the resource as a whole. We can therefore define a resource's availability by the sum of the dots on all the tiles that produce the resource (this is equivalent to the expected number of times a resource tile produces its resource over 36 rolls). Now, wood, sheep, and wheat will always have an advantage in terms of resource availability because they have 4 tiles, compared to only 3 for brick and ore (which we can see on the right), but the same principles should apply. We would expect resources to get more valuable as they become less available on the board (and vice versa). Basically, that supply and demand holds, but let's take a look at that relationship. Note, I am only looking at the total possible availability, there will likely be changes in a resource's availability based on where people settle that is not accounted for here.
In general, we see what we expected, with resources becoming more valuable as their availability decreases. Interestingly, the availability of sheep actually does not affect its value much (especially compared to the other 4 resources). The others follow a relatively similar path going from being worth around 2.5 resources in their most scarce to around 1 resource in their most abundant.
My main takeaway here is that the change in a resource's value does not seem to relate to that resource's inherent value. For instance, there is likely value in going after sheep when they are abundant because their value does not seem to change with supply. Similarly, more valuable resources (like wheat and brick) should be avoided when they are abundant because their relative value has dropped the most.
As mentioned above, the biggest limitation is that I am not assessing the number of resources actually available for trade at any given time. A resource's value will likely depend more on its current availability along with its expected availability in the future (which I tried to capture with the resource base idea). I also do not have trades that did not go through (though this may be available in the future). That being said, I think there are still some conclusions we can take away from this
The first takeaway is to be more cognizant of how a resource's value changes game to game or turn to turn. There are opportunities to make plus value trades if we are willing to trade with our opponents, particularly later in the game. Additionally, knowing what will likely be available on the board should help determine what resources to target. Finally, I would try to secure a supply of brick and wheat early in the game (such as with your initial placements) with the ability to expand to a supply of ore later in the game.
Want to contribute your data to future posts? You can do so at colonist_data (anvil.app)
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