One of the very first posts I wrote mentioned the idea of “balancing using spreadsheets”. My dream was to somehow build up the machinery to perfectly balance a game without ever having to do a playtest.

That didn’t work out so well…

But I can say I’ve been using spreadsheets as a tool to help in balancing game elements.

I was reminded of all of this because of a comment from Martin of Double L Games (who got inspired to write something about games from the viewpoint of his own expertise: Ecology. Awesome!) on a previous blog post. They were also hoping to be able to use quantitative methods to balance their game.

So hopefully I’ve picked up a few things about this over the past period. We’ll find out!

Structure of this post

I’d love to write a general and understandable “how to” post explaining exactly how to use calculations for balancing. I do think that is an impossible goal as there are so many things that could be in a game.

So instead I’m going to use Voluntarios, my own game, as an example. This means I will have to explain parts of how the game works. I hope I’ll be able to do this succinctly while still getting the essence across… If I fail miserably let me know so I can update this post?

Introduction of Voluntarios

The game has gone through many iterations (I’m at official prototype version 61 now!). I’ll mostly be talking about the latest version and skip all the (necessary!) steps that I took to actually get here.

In Voluntarios players are at the head of a family, trying to rebuild their village after it was destroyed by an earthquake. However it’s not just about rebuilding the village, but also about doing as much good as possible.

Mechanically it’s (almost) a worker placement game. Players earn karma (victory) points for many of the actions they take. Specifically, points are gained for finishing a building you started and for anything that benefits another player

Choosing a base “currency”

In this post about cost and value in board game design I suggest to take a “base currency” into which you can translate all other resources.

From the moment I started trying to use spreadsheets to balance my game I used “karma points” as the base currency (as also suggested in the article). This because karma points are a very close translation of “value” (as explained in this post: Value is anything that helps you get closer to winning). As the player with the most karma points wins the game, this certainly works.

The first source of currency: Finishing buildings

As mentioned, every finished building gives the owner a certain amount of karma points. Each building requires between 1 and 3 “construction materials” (wood and / or money) and between 2 and 4 “work” (which can be provided by normal and expert family members).

I assigned a “score” to all of the four “raw resources”, as follows:

Normal family member: 0.8

Expert family member: 0.8

Wood: 0.6

Money: 1.0

The value of the “scores” was chosen through adjustments over time.

The “base” karma points for a building then are equal to the sum of the score of the required resources (rounded to the nearest integer). E.g. a building that requires one expert, two normal family members and one wood, would give 0.8 + 0.8*2 + 0.6 = 3.0 karma.

The “base” score can be adjusted based on the abilities that a building has. More about that later.

The “score” given above gives an initial value for all of the 4 available “raw” resources: If I have a normal worker I can say it’s worth 0.8 karma. If I use that worker for something I “lose” 0.8 karma (as I could’ve used it to construct my own building with instead, for a gain of 0.8).

Obtaining building materials

The simplest way to obtain building materials is by “cleaning up” a destroyed building: Place 1 worker (of any type) on a destroyed building. At the end of the round the destroyed building is flipped over, showing either 1 or 2 “salvaged” resources (in any combination of wood and money). These resources go into a communal space, thus the player who “finds” them does not get to keep them!

From the communal space they can be “distributed”, meaning other players can make use of them. Thus, the player who “found” the resources is doing something that is useful for the other players. In line with the theme of the game, they are rewarded with some karma.

This also works well game-wise, as it creates an incentive to “clean up” (and make resources available” (see this post for more on incentives in board games). If players wouldn’t get anything, there would hardly be any reason to clean up: You’d much rather have other people do it so that you could take the resources without having to give up a worker.

So how much karma to give? I ended up giving the player 1 karma for each resource that they found. On average they will find 1.5 resources, so they get on average 1.5 karma. How does that compare to building a building?

You need to give up a worker to take this action. That worker could be used to gain 0.8 karma by placing it on your own building, so your “net gain” is 1.5 – 0.8 = 0.7 karma.

However, through this action, on average 1.5 resources are made available for anybody. The chances of getting money is 1/3th and getting wood is 2/3th (by design), so using the “scores” from building a building of 0.6 and 1 for wood and money respectively, the expected value of the salvaged resources is (1/3 * 1 + 2/3 * 0.6) * 1.5 = 1.1.

So while you’re gaining 0.7 karma, you’re making 1.1 karma available for other players, so the final gain is 0.7 – 1.1 = -0.4 karma!

This would be significantly worse than placing a worker on a building!

Except that anybody can take those resources made available, including yourself.

In a 3 player game the chances of you getting a resource is 1/3 and the other players getting them is 2/3. So of the 1.1 karma made available you “lose” 1.1 * 2/3, while at the same time you “gain” 1.1 * 1/3, giving a net loss of (2/3 – 1/3) * 1.1 = 1/3 * 1.1 = 0.37 karma (instead of the 1.1 karma mentioned above).

If we subtract that from the 0.7 karma you get for making these resources available you get 0.7 – 0.37 = 0.33, somewhat better than placing a worker to construct a building.

Doesn’t it matter that this is a “better” option?

No, that’s not really a problem: It will depend on the state of the game how many points something is actually worth and so having basic actions that are “on average” of different value is fine. They however shouldn’t be completely different as then it will be hard to incentivize your players to do the things you want them to.

In fact the value for cleaning up came about through playtesting. It was first 1 karma for cleaning up, regardless of how many resources you found (for a “gain” of 1 – 0.8 – 0.37 = -0.17, which is actually closer to the option of placing a worker on a building than current 0.33 value is!). With that “reward” however I found that players tended to do relatively little cleaning, meaning that fewer resources were made available and the game stalled. So I gave them a bit more karma and they start doing what I wanted them to!

And it makes sense that players weren’t really incentivized to clean: There was a better option available, namely place a worker on their own building (remember that I subtracted the value of a worker, so this is the “additional” value)!

Distributing wood

I mentioned that resources go into a communal space form which all players can make use of them. The way this works exactly is that any salvaged wood is placed on the “distribute wood” card. This has one action space (space for 1 worker). When a player takes this action they “distribute wood”, meaning that they first can take as much wood from the card as they can place on their own projects (no stockpiling your own wood!). Then in clockwise order the other players get to take wood from the card (if any is left).

Here you’re clearly benefiting other players as well, so you should get some karma reward. I tried different things but I finally ended up with “get two karma if at least one other player takes a wood”.

This can be an incredibly strong action: You get to take a lot of wood and you have the possibility of gaining a quite substantial 2 karma!

However, there are also ample moments where this action is quite pricey: If there is only a single wood on it you can get that but it costs you a worker. Using the “construction score” from the beginning this means you’re giving up a 0.8 karma worker for a 0.6 karma wood, so you’re “making a loss” of 0.6 – 0.8 = -0.2.

And while it’s certainly possible to have a decent pile of wood on the space, in general the amount of wood is fairly limited.

And if there is a lot of wood, you’ll be benefiting other players by quite a bit as well. Say you can take 2 wood (you have to be able to use it) while other players also take 2, then your net gain is 2 + 2 * 0.6 – 2 * 0.6 – 0.8 (for the karma from the action, the wood you gain, the wood other players gain and the worker you use respectively) = 1.2 karma. A very nice amount indeed!

Making this action potentially strong means that players will have to plan to make use of it. This then generates interesting decisions (see this post on interesting decisions), which of course are the bread and butter of board games!

Distributing money

The way money distribution works is exactly the same as the distribution of wood (except you take the “distribute money” action, obviously).

Money is “worth” more points, so wouldn’t that screw over the calculations? Not so much, as money is also more rare, so getting a really big haul of money is even more difficult than getting a big haul of wood.

And money is also less required for building buildings, so the chances of being able to place a lot of money are also smaller.

I’ll not do the calculations here, but you can do them yourself if you want to 😉

Alternatives for getting resources

Some of the buildings allow players to place a worker to get a money or wood (depending on the building). If you use someone else’s building for this then that player gets one karma.

So you’re giving up a worker (0.8 karma) to get a wood (0.6) or a money (1.0). For the money this seems like a reasonable deal, but for the wood less so.

However, at some point the “destroyed buildings” are all cleaned, meaning that you cannot get “easy” resources anymore that way.

At that point the wood and money become bottlenecks: Without them you cannot create buildings and so even with all of the workers in the world, you wouldn’t be able to gain karma. And so the value of such a resource goes up.

Compare this to the value of a glass of water: If you’re in your house the value is basically zero. If you’ve been in a desert for a day you’d happily pay half a kingdom for it! This is further explained in this post on scarcity).

It is then not unreasonable to say that without this wood / money you would miss out on the entire value of a building (which we’ve seen is somewhere in the order of 3 karma). So the choice then becomes getting an expensive wood / money and getting the value of the building, or getting neither of them. So as long as the “price” of that wood / money is below 3, it would still be a good deal!

At this point it’s really hard to do exact calculations, as it depends very much on how scarce wood and money have become and what kinds of buildings you’re making exactly. The take-away though is that it’s ok for the “price” of something to go up if it becomes scarce.

Helping with construction

It is possible to place workers on other players’ construction plans to “help” finish them. The player who helped the most (who placed the most workers) gets 2 karma. In this any workers placed by the owner of a construction plan are not counted when determining who helped “the most” (you cannot “help yourself”).

Next to this, whenever a player places an expert on an expert space, they get 1 karma (regardless of whether the expert is placed on your own or someone else’s construction plan).

Finally, the player who places the last worker (finishing the building) gets 1 karma (regardless of whether you finish your own building or someone else’s.

Most plans require 3 workers, one of which will be an expert. Thus if you want to help the most you generally will need to place 2 workers, which will mostly get you three to four points (placing an expert gives the first point, then helping the most gives an additional 2 points. Finally you might be able to “finish” the building and get the final (fourth) point.)

However, it is possible to place a worker and not get any points, if it’s not an expert on an expert spot, it doesn’t finish the building and you don’t help the most.

Theoretically it is also possible to get 4 points with a single worker: If the owner of the building already “filled” the building but left the last place free which is an expert spot. Placing that expert would give you 1 point for the expert, 1 for finishing it and 2 for helping the most (the owner’s workers don’t count so nobody else helped). This however is an extremely rare case.

When you place a first expert, you already get 1 point. You’re also helping the owner with 0.8 points (based on the score given above). And you cannot use your worker for something else, so you are giving up something that is worth 0.8. The total score then becomes 1 – 0.8 – 0.8 = – 0.6, so significantly a negative score compared to the standard option!

If you are able to place a second worker you are earning 3 points, for an average of 1.5 per worker. In this case the math becomes a little bit better: 1.5 – 0.8 – 0.8 = -0.1. In this “helping” someone else is less valuable than placing workers on your own buildings.

But If you’re able to get 4 points (which is not uncommon) then you get an average of 2 points per worker, while giving up 2*0.8 – 1.6, for a total benefit of 0.4: 50% more than placing a worker on your own building!

So here you have a decent chance of getting less than taking the “standard” option, but you might also gain 50% more than it. Thus, this a bit of a “gamble”.

In playtesting this is a favored part as there is quite some tension as to whether you get the karma points for helping the most and whether you get the full amount or just part of it.

Building values revisited

In the previous paragraph I mentioned that some buildings can “produce” materials and that if another player makes use of your building to do so, you get a karma.

This means that the final amount of karma that such a building produces goes up! It is the karma that it says on the building, plus any karma it produces over the lifetime of the building.

If you build a production building early in the game you might see it used by another player 4 or 5 times. But if you build it in the last round it won’t ever be used. So the “average added value” should be somewhere between these values 0 and 5.

Playtesting shows that buildings on average get used somewhere between 1 and 2 times and so the average benefit of such a building is 1 to 2 karma higher. I don’t know what it is exactly, but let’s say it’s 1.5 karma on average.

This then means that the value of building a building goes from 3 to 4.5, an increase of 50%.

Which then also means that the “base score” for every resource placed on a building should be increased by 50%.

Revised resource costs

So doesn’t that completely screw up the calculations we did?

I’m not going to redo all of them (this post is already the longest I’ve ever written!) but let’s take a look at one.

If you “clean up” then we said you got a score of 0.33 above the “base” option of placing a worker on your own building, when we use the “old” scores.

Now let’s increase all those scores by 50%:

You still get (on average) 1.5 karma for cleaning up. But you are now using a worker that is worth 1.2 karma. And you’re making available 1.5 * (1/3 * 1.5 + 2/3 * 0.9) (average number of resources times the chance of money times the (new!) value of money , plus the chance of wood times the (new!) value of wood) = 1.65

Of that you will get 1/3th and the other (2) players will get 2/3th, for a total loss of 1.65 * 1/3 = 0.55.

Your total score then becomes 1.5 – 1.2 – 0.55 = -0.25.

Thus, this now became a worse option than placing a worker on your own building!

So is this a bad thing?

Not really. It should always be the case that some options are stronger than others. And if everybody is only ever working on their own buildings, resources becomes scarce and players will be wanting to create more just so they can continue getting karma from the buildings they want to build.

It does however provide a useful insight: Under the new calculations there is less of an incentive to clean than there is to build. Which also conforms to what I observed during playtesting, where players preferred to work on buildings over cleaning, but not so much that they would never clean.

In the end all your mathematics doesn’t mean anything in the face of what real players do!

A recap

I didn’t touch upon all the aspects of Voluntarios, but I think I touched upon enough to explain the idea of quantitative balancing.

Still, it’s good to have something of a recap, in case you want to do this yourself:

Find a “base” currency in your game, something in which you can express all other resources. Victory points are ideal, but others can be used as well.

Express every “raw” resource as a value of this currency. When you start out just make some guestimates; you’ll refine these numbers over time.

Express the value of “higher” resources in your base currency, using your raw resources and perhaps other higher resources as stepping stones.

Calculate the value of every action that players can take, by taking the value of what they get minus the value of what they give up and minus the value of what other players get.

Compare the values of different actions. If for all states of the game they are extremely different (more than a factor 2 difference?) then you might have a balance issue.

Use the values you have found to fine-tune the incentives in your game: Want players to do a bit more of one action? Tweak your numbers until the value of that action goes up.

Playtest to make sure that what you’ve created actually works!

Closing thoughts

It’s possible to put all the calculations I did into an Excel spreadsheet so that you can twiddle the numbers and automatically see what happens when you do. I made some inroads that way but never saw it through to the end. I can however see myself doing exactly that for the next game I’ll create.

And while all of these calculations can be very useful, they are no substitute for playtesting! Only when your game is played by real-life humans can you see whether it truly works.

As so many things, quantitative balancing should be seen as a tool in your belt, to be used when appropriated and put aside when not useful.

Further reading

This post is one in the series of “in-game economics”. What I did not touch upon much is how to do “valuation” if you have resources that produce resources. You can find some ideas in this post on feedback loops and more in this post on “assets” in board games.

About the author

Hi, I’m Bastiaan. The goal of this blog is to learn about game design. That’s hopefully for you as the reader, but just as much for me as the writer.

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