• Alex Cates

Catan Breakdown: Longest Road and Largest Army

If you haven't seen them, please check out the first 3 posts in my Catan Breakdown series to better understand the data I am using. In part 1, we looked at what an average Catan game looks like. In part 2, we examined how valuable the 5 resources are in different scenarios, and in part 3, we talked about when to build throughout the game. Today we will talk about the longest road and largest army bonuses.


We have all been there. You shoot out to an early point lead by claiming the Longest Road only to fail to maintain your lead after wave after wave of being targeted by the robber. Or the happier version, you snag Longest Road or Largest Army right at the end, creating a 2 or 4 point swing to secure your victory. Today, I want to dive into these two bonuses to look at how valuable are they, and when should you be trying to claim them.


The Data

As with previous posts, I am using data collected from ~300 games played on colonist.io. All of the games are on the base map and include 4 players, though some of them include bots rather than all human players (I have separated out all human games for some of the analysis below, though beware it makes the sample size even smaller). For today, I am collecting a couple of statistics, including who earned Longest Road/Largest Army (which I'll refer to as LR/LA from here on), who finished with LR/LA, and when a player earned LR/LA (in terms of percent of game played).


I also want to take a moment to thank everyone who has reached out to help with this data-based exploration of Catan. I have a couple of new datasets in the works, one from simulated games and one of a larger collection of human-only games so stay tuned for those.


Base Odds

Win Odds If You...

All Games

Human-Only Games

Finish with Longest Road

61%

69%

Finish with Largest Army

50%

53%

So right off the bat, we can see that these bonuses are valuable. Remember that your odds of winning due to random chance at the beginning are 25% so finishing with the Largest Army doubles your odds and finishing with the Longest Road increases your odds by ~2.5x. Both are obviously valuable IF you end with them. To put that in context, your odds of winning if you finish with Longest Road is roughly equivalent to your odds of winning if you finish with 4 cities! Now, these 2 datapoints are likely related as if you have 4 cities you are likely generating lots of resources which makes it easier to buy lots of development cards or build lots of roads. Still it puts the value of LR/LA in perspective.

 
 

How to end with Longest Road or Largest Army

How Many Roads/Knights do you need?

Number Built by LR/LA Owner at End of Game

All Games

Human Only

Number of Roads

12.8 +/- 3.5

11.9 +/-3.0

Number of Knights

3.6 +/- 0.8

3.7 +/-0.9

Before I dive into these numbers, an important caveat. For the number of roads, this is the total number built by the player who finishes with the longest road, not how long the actual longest continuous road is. This is a limitation of my current dataset as I do not know where a player places each road. I hope to remedy this in future datasets.


That said when we look at how many roads/knights it takes to finish with the longest road or the largest army, we see that most people finish with well over the minimum. We also see a large standard deviation in terms of the number of roads. My guess is that there are a lot of games that claim longest road with a road of just 5 or 6 while others get into a war with another player having to build a road of 12 to finish with it.


The Largest Army is a little more consistent with most players finishing with about 4 Knights. I'd imagine that the cost of building more knights is a big part of this. Compared to roads, knights need more resources, more valuable resources in the end game, and have some randomness in that each dev card is not guaranteed to be a knight.


When to claim longest road/largest army

So given that we know how many roads/knights we need and that we want to finish with LR/LA, at what point in the game should we try to claim the bonus? To investigate this I have plotted the odds of ending the game with LR/LA based on if you have LR/LA at a certain point in the game.

Odds you will finish with longest road (left) or largest army (right) based on if you currently have the Longest Road or the Largest Army at a certain point in the game (% of the game completed). All Data required at least 20 games where a player had earned the Longest Road or Largest Army at that point in the game.

Includes both All games (blue) and human-only games (orange).


We can immediately see that the first step to finishing with the LR/LA is to earn the bonus at some point with the odds immediately jumping above 50%. Interestingly, we can see that the Largest Army is rarely disputed once owned, as the earliest data points have ~90% odds of finishing with the largest army. Longest Road is more disputed, with your odds sky rocketing at the end but remaining around ~60% until we are in the last 10% of the game. In general, this matches with my experience. While Largest Army is normally baked into one players strategy and therefore hard for another player to contest, longest road can be taken when the opportunity arises, often as an ending move to win the game.


Next, we can actually combine our win odds with the odds of finishing to look at when to target LR and LA.

 
 

When to secure Longest Road and Largest Army.


Line plots of your odds of winning the game if you have Longest Road (left) or Largest Army (right) at different points in the game. Includes both all games (blue) and human-only games (orange). Also includes a red line marking the odds of winning at the beginning of the game due to random chance.


Here we see an interesting twist. Remember that it is beneficial to finish with longest road or largest army and that you have a better than 50% chance of finishing with them once you earn them. Despite this, getting either of these early actually hurts your odds of winning the game (though it should be noted the difference between human only and all games for Longest Road). Assuming it does hurt you, my guess is that it makes you a target such that you are more likely to get robbed, less likely to have people trade with you, etc. Either way, we can see that both of these are late-game targets. In general, you should try to claim LR/LA in the last 20% or even 10% of the game. For reference, we know from the first post in this series that the average game lasts ~71 rolls. So you should try to snag either LR/LA with about 7-14 rolls left (~3 more chances to build).


Limitations

The limitations of this post are frankly the same as all of my posts on Catan so far. I don't know where someone is placing their roads on the map. I have included some games with bots (though as we can see the overall effect is minimal). Hopefully, I will have some better data soon with which we can try to replicate these results.


Conclusions

Overall, I think you should definitely have a plan to compete for at least one of these bonuses. The benefit of finishing with Longest Road or Largest Army is just too great and comes out as an integral late-game strategy. That last point is important though as claiming either too early may hurt your odds of winning the game rather than help.


Questions? Comments? Let me know at ac@alexcates.com. Want to read more breakdowns like this? sign up for my newsletter here. Finally, like what I do? Consider supporting me on buy me a coffee.




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