Synergy in the Woodland: Analysing almost 3000 games of Root

One of the best parts about Root as a game is the dynamic interaction between factions. Most factions, and certainly the factions with more expansive design goals, will cause games to feel fundamentally different than games that do not feature them. One of the best examples in my opinion is the Riverfolk Company. Having the Otters in a game fundamentally changes how many factions play, as they gain access to much more card selection, with some policing power and movement options thrown in. Some of the relationships are a bit more subtle, like Lizards or Woodland Alliance limiting movement and locking down clearings with their rule/sympathy. The impact a faction can have sometimes extends to the map as well, with Vagabond and Rats both changing the board by removing ruins.

I find this interaction fascinating, and one of the main reasons I enjoy returning to Root over and over again. By analysing recorded game data, I intend to codify and define some of the faction relations statistically. I'm hoping to gain insight into which factions benefit from each other's presence, which are sworn enemies, and who is favoured by being at the table wth other specific factions, ultimately with the goal of being a better player.

The Data

The data I'm using in this analysis is the result of the hard work of many people. There are three sources I have used:

Data set	Games	Provider	Notes
Root Digital League	2484	Digital League admins	All ADSET, no marauders, default landmarks, default infamy.
Tournament games	216	MakeCraftGame	Mostly ADSET, some other drafts, some landmark changes, mostly despot infamy. Includes SCPT, Winter and Rootcon tournaments.
HRF Web App	257	JT	Mostly ADSET, default landmarks, mostly standard infamy, some other optional rules tweaks on specific cards.

A huge thanks to everyone who made their data available or let me scrape the data from their platforms, having such a big sample size helps immensely, and simply isn't possible without a lot of work going on behind the scenes.

Since there are some inconsistencies in the games that went into these different datasets, it is worth being careful with the some of the conclusions below, but I'll be drawing attention to any issues based on those inconsistencies as they come up. Although we could avoid this by only examining the Digital League results, that would miss out all of the Marauders games we have access to. By far the most common way that games have been played is on the Digital client, so the results should hold for that environment. If you're interested in how aspects of these differences change the results, feel free to ask and I'll do my best to answer, perhaps in another blog.

A few notes on the data before I jump into results, mostly due to the Vagabonds being slippery agents of chaos and a pain to analyse:

Although there are a number of 2, 3, 5, and 6 player games in some of the Tournament and HRF datasets, in the interests of a consistent meaning to "win rate", I have only included 4 player games. If you just count up "games a faction won" divided by "games a faction played in" you heavily skew win rate towards militant factions that get to play in 2p games where they can expect to win 50% of their games, as opposed to 4p games where 25% will be the expectation.
All Vagabond characters have been treated as the same faction for these results. I have character info for some of the games, but not all of them, so for now we'll lump them together and leave the rest for another blog.
Whenever two Vagabonds appear in the same game, "Vagabond2" is the name given to the second Vagabond selected in the draft, and so represents the Vagabond going first in turn order.
Coalition victories have been removed. Every tournament/league treats them differently, and they don't translate well into win rate calculations.

Win Rates

First up, some overall win rates. These are not too different to what you get from the individual datasets, and the results can be found on MakeCraftGame or the Digital League spreadsheet.

Faction	Win Rate	95% Confidence Interval
Rats	35.80 %	7.38 %
Duchy	30.74 %	2.21 %
Eyrie	29.57 %	2.10 %
Vagabond	25.51 %	1.96 %
Alliance	25.14 %	2.41 %
Badgers	24.83 %	6.94 %
Riverfolk	22.42 %	2.51 %
Marquise	22.37 %	2.43 %
Crows	20.50 %	2.33 %
Lizard	17.38 %	2.25 %
Vagabond2	16.57 %	5.42 %

Bearing in mind that a 25% win rate is the expected value in these 4 player games, this roughly matches the community's assessment. Rats are boosted by high win rates in the 2021 Winter Tournament, but still considered strong overall. Duchy and Eyrie are solidly in the top tier, while Crows and Lizards struggle. Picking a second Vagabond in a draft is also unlikely to lead to success due to competition for items and ruins, as well as there being one fewer faction in game for both players to get infamy and aid points from.

One other thing to consider about Rats and Badgers is that there are significantly fewer games played with these factions due to them not being available on the digital client yet, so there's more uncertainty in their measurements. We have enough data to be 95% sure that the "true" win rate of each is within 7% of what has been measured, as opposed to the other factions where the 95% confidence interval is plus or minus 2%.

These win rates are also heavily impacted by what seat the faction is most likely to end up in. Seat order and drafting is on my list of things to write about properly at some point. For now I'll just point out that Eyrie being passed up by the players choosing first and second in a full 38% of drafts is not something that should be happening.

This is for sure interesting data, and worth keeping an eye on. While it provides a good baseline though, it doesn't really answer any of the questions I had about specific matchups. To investigate those matchups, below are the matchup win rates. To read this table, first find a faction you're interested in on the left hand side to get your row. Then, to see how often that faction wins against another faction, find that second faction on the top and look for the cell in that column. For example, The Marquise wins 19.9% of its games that also include an Eyrie player.

This is starting to get interesting, as we can see some initial results about faction matchups. In particular we can identify things like the Eyrie having a particularly good win rate when Crows are around, and the Duchy having a poor Rats matchup. Although our confidence intervals do get a bit worse here since there's less games for each specific matchup, we've still got enough of a sample size to get good info (more on confidence intervals later if that's something you care about).

Defining Synergy

Although the matchup table provides more context and information, there's still a few things missing. For example, I know the Rats win a lot against the Moles, more than their fare share of 25%, and more than they normally win over all their games combined. What is harder to tell from this table is whether the Rats win more because they're taking equity from the Moles, or because they're good at teaming up with the Moles against the other factions. To try and answer some of those questions, I want to look at synergy.

Synergy as a concept is often applied to card games to discuss how well two particular cards interact and work together. Here, we're going to apply it to factions. If faction 1 and faction 2 both win more than normal when they are in games together, we'll call them "synergistic". If they eat away at their shared win rate, and devolve into bickering and knee-capping, both winning less often than they would on average, we'll call them "anti-synergistic". The other two possibilities are that one faction wins more while the other wins less. This has less of an impact on the other factions at the table, as it doesn't strongly impact their win rate.

When drafting factions you ideally want to end up in a spot with good individual matchups, but also spots where neither of your opponents have synergistic relationships with each other, as their increased win rate will come out of your expected result. On the other hand, if you can end up in a spot where two of your opponents have an anti-synergistic relationship, it will leave more room for you. This can also inform how important it is to police different factions in the early game.

In order to visualise synergy between two factions, we need to know a few things:

How much do each of them win on average?
How much do each of them win in games that do not include the other?
How much do each of them win in games that do include the other?

Starting with number 2, we can work out the shift to number 3. Here's an example with the Crows and Otters, along with a diagram that describes what each of the cases discussed above would look like:

In this case, when playing together the Riverfolk win slightly more than normal, whereas the Crows win far less. We can be quite confident in this conclusion too, as shown by the 95% confidence interval (the ellipse in grey). To reiterate, given the sample size we have, we can be 95% certain that the "true" win rate of these two factions in this matchup ends up inside the grey ellipse. This result makes sense to me based on how these two factions work. Crows are particularly vulnerable to exposure, but the main limitation on exposure is having enough cards of the right suit. Riverfolk's presence in the game makes cards of particular suits much more accessible to the rest of the table. Riverfolk players can also draw plenty of cards to expose the Crows by themselves. This is a massive detriment to our anarchist friends, resulting in them being crushed under the weight of capitalism. On the other hand, the Riverfolk don't get a large benefit from exposing plots, and they only win slightly more than normal when playing against the Crows.

Synergy Matrix

"That's just one matchup" you say, "what about the others?" An excellent question, and one that deserves one of the more complicated plots I've ever put together. Below is all the matchup data that comes from the nearly 3000 games I have access to currently. This time, the results are symmetric across the diagonal (the Cats v Eyrie plot is just the Eyrie v Cats plot flipped). For ease of reading, the axes for each row and column is entered on the average win rate for that faction, so, e.g., you can read along the Woodland Alliance row and see that they have pretty stable win rates against all factions except for losing to Cats and winning against Vagabond2. I recommend taking your time to explore, there's many interesting things going on. Find your favourite faction, take a look at how they fare against the others. Does it match what you expect? Does anything surprise you? Come back when you're done, and I'll highlight some of the things I found most interesting. (Click to enlarge).

Points of Interest

Synergistic Relationships

Of all the matchups we have, there's actually only two truly synergistic relationships: Otters/Lizards, and Otters/Rats. It makes sense for Otters to be involved in synergistic relationships, as they provide benefits to other factions with their services, and get compensated for them. Lizards and Rats in particular are both factions that make use of the extra cards, while having the warrior count to buy often without fear of running out.

Anti-Synergistic Relationships

There are a few more anti-synergistic relationships around. Ones like Eyrie/Moles make sense as high performing factions that find it harder to compete against the other top tier factions. Vagabond/Rats and Vagabond/Vagabond2 make a lot of sense too, as they are directly in competition for items.

Corvids/Moles and Corvids/Rats are interesting to me, and I was initially unsure why they fell into this category. Upon reflection, I believe this result may be because the Rats and Moles are frequently responsible for policing the Crows due to their action economy and the necessity of interrupting the Crow's late game burst. This policing is almost always successful, resulting in a reduced win rate for the Crows, but costs the Rats and Moles personal equity at the table.

Badgers also have two anti-synergistic relationships, with Vagabond and Eyrie. Badgers and Eyrie clearly are at odds with wanting to rule, and the Badger's migratory path across the woodland comes into conflict with an entrenched Eyrie, to the detriment of both. With Vagabond, I think it's similar to Crows, as Badgers must often contribute to policing at the cost of their own engine or stability. If Badgers don't hit hard enough, the Vagabond can often do a lot of damage to the smaller stacks of warriors that Badgers end up with.

The Impact of Marauders

One thing that stands out to me, despite the smaller sample sizes, is the impact of the Marauders expansion. Both the Badgers and Rats add variety to the matchup spread for many factions, especially the ones that dominate in the Underworld meta. Moles in particular picked up a slightly favoured matchup (Badgers) but a significantly unfavoured too (Rats). Eyrie and Vagabond, two of the other bogeymen in the pre-Marauders meta, both pick up poor matchups, adding a balancing force. The praises of Marauders have been sung many a time, but this data shows how much of an impact it has had in rebalancing the militant faction meta in particular.

As for the strong overall win rate of Rats, it is worth noting that while no faction has a good matchup against them, the Rats do have anti-synergistic relationships. If someone picks Cats, Vagabond or Crows into Rats, maybe that should buy them some good will in the table meta. These results also suggest to me that Rats should be forced into most of the policing work that needs doing at the table.

Woodland Alliance

The Woodland Alliance have the most stable matchup profiles out of anyone. They don't love the Cats (because of martial law and the space they take up), they love when there are two Vagabonds (the 4th player has their hands full and can't police effectively), and don't mind a Moles player (the outrage tax is so impactful). Against the other 6 factions though, they have a surprisingly consistent 25% win rate. This is probably due to the self correcting nature of Outrage and the difficulty in policing.

Conclusions

Hopefully, dear reader, you have found these results interesting and are able to leverage them in your endeavours to get better at Root. There are plenty more things I want to dig into with this dataset if I get the time, but understanding the synergy between factions has been something I've wanted to do for a while now, so I'm incredibly grateful to all the people who contributed towards collecting this excellent sample size.

The main points I've taken away from this analysis are:

Eyrie, Duchy and Rats should be first pick and last in seating order much more often. Expect another blog covering this in the future.
Forcing Rats into a policing role is an effective way to reduce their win rate.
Lizards and Otters should lean into their mutually beneficial relationship.
Woodland Alliance are especially repeatable and reliable against almost any opponent.
Playing as a second Vagabond is a great way to make sure neither you or the other Vagabond win.

If you've enjoyed reading this, please let me know either here, on Twitter (@ArcKayNine), or in the Woodland War Machine Discord (@Rk9). If you'd like to support more of this kind of in depth analysis into games we play for stakes no higher than pride and Leder Games gift cards, feel free to buy me some Root Tea over at Ko-Fi, and consider supporting the fine folks who helped with data collection, MakeCraftGame and JT.

Until next time,

May all your Lizards find Otter friends.