Category Archives: Game Discussion

Game Data Analysis: Splendor

Splendor has become a very popular game recently, likely due to its Spiel des Jahres nomination. Splendor is a card game about using limited resources to build an efficient engine. There are five colored gems, and playing only a few times it might feel like the costs and distribution of the colors are the same. In other words, the colors are different currencies with no other differentiating qualities. If that were true, we’d be able to add up all the costs and find that the colors are evenly distributed. But even with a few plays of Splendor that assumption is difficult to maintain. The rules are simple and there are no exception-based cards, so it’s a great game to analyze by number crunching. I’ve set out some research questions to help guide the analysis. Some of them are basic, but I think they’ll open up other directions for exploring the data.

Research Questions

RQ1: are color bonuses evenly distributed?

RQ2: are color costs evenly distributed?

RQ3: what is the average point:cost ratio for a level one, two, and three card?

RQ4: what is the percentage of “on color” cards? (Cards that give a bonus for a color that is also in the cost).

Process

CardRules

Figure 1. Card Description.

It’s always useful to communication the analysis process, but if you’re interested strictly in results then scroll down to the Results section. The process first involved developing a taxonomy to store the attributes, entering and cleaning the data, then validating the data. Some of this may seem excessive for a small project like this, but there are always unexpected events that a formal procedure can mitigate.

To operate on the card data I input it into Excel. The data entered would consist of the cards and all their attributes, including the bonus, level and cost (see Figure 1). Noble cards would also be input. There was some taxonomic thinking that went into the process: how should I manage the terms used? For example, instead of writing out the word “black,” it’s easier to input “b,” but there’s also “blue” then term management needs to standardize that “blue” becomes “u” instead.

Data validity was also an issue because I was manually uploading the information; I didn’t perform a second check nor have others do it, so I had no reference to determine whether the uploaded data was correct. I did do a card count to ensure I had input the correct number of cards, but nothing beyond that. An auto-incrementing CardID attribute was created to ensure I could individually track each card.

Analysis and data visualization was performed in R Studio.

Results

Table1

RQ1: are color bonuses evenly distributed?

Yes. See Table 1.

RQ2: are color costs evenly distributed?

No. If you sum all the card’s costs, the colors are relatively equal. But when slicing those costs by level, the distribution becomes uneven.

Table 2 charts the frequency of color cost. That means it counts occurrences of color cost. So the Black row under Level One indicates that White and Blue occur as a cost in four level one black cards. Note that this table does not track intensity of those costs (that’s for later).

Table2

In terms of frequency, on-color costs are infrequent (few cards with a color bonus also have that same colored cost). There are some other odd frequency dynamics: level two blue cards feature a blue cost five times, with other colors appearing two times. So each color has a unique frequency of cost, as seen in the figures below.

Rplot02

Figure 2. White costs by card color.

Rplot03

Figure 3. Red costs by card color.

These figures displays the distributions of White and Red costs among the cards. Because the two figures are different, we can conclude that certain card colors require varying degrees of red and white costs. Because the figures are box plots we can also discern the expected white or red cost depending on the card color. A white card will have a higher red cost on average when compared to a green, red, or blue card.

While each color has a unique frequency of cost, those patterns do not occur from level to level. In other words, investing in white bonuses to buy red cards at level one will not be a reasonable strategy at level two or three because the white cost frequency changes.

Table 3 charts the intensity of color cost, which is where the uneven distribution really comes into perspective. The level three cards are representative of this trend. Like a lot of other games, the expensive cards reward a vertical strategy of investing a lot in a few colors. For example, the sum total of white costs in level three blue cards is 23, with all other colors totaling less than 8. As a proportion of the total costs of all level three blue cards, that’s 70%. So there are clear color affinities, but they change at each level, so white costs won’t always be strongly tied to blue bonuses.

Table3

RQ3: what is the average point:cost ratio for a level one, two, and three card?

For cards with point values, the average cost of a point goes down as the card level increases. At level three, the average cost a point is 2.7, level two is 3.7, and level one it is 4 (every level one card with a point costs 4). This isn’t too surprising; a lot of games reward big investments by making them more efficient. The trade off, of course, is that they require long-term planning to efficiently buy them, while low-level cards require little.

Rplot01

Figure 4. Card Points and Card Costs.

After a few plays of Splendor you’ll probably notice that some cards cost more for the same point value. Indeed, Figure 4 shows that some cards are just strictly more efficient. However, the cards that cost the most (14)  spread the cost among 3-4 colors, while the highest value cards (5 points) are concentrated on high costs of one or two colors. So the design of the costs provides two clear paths to efficient point gain.

Table4RQ4: what is the percentage of “on color” cards (Cards that give a bonus for a color also in the cost)?

My playgroup assumed these cards are high value because players have a tendency to collect things they already own. They occur infrequently in level one, but in card levels two and three they’re at least 50% of all cards.

Conclusions

One important aspect of this analysis is that it’s dealing with static information. This data tells us about the set information of the game, but it doesn’t describe any behaviors. We can infer some behaviors based on the incentives provided by the set rules of the cards, but we should be conservative in those conclusions.

That said, the frequency and intensity of the color costs does validate the potential for a vertical, one or two color strategy. But it seems like those strategies require careful planning, as by level 3 each color is essentially “locked” into buying up one particular color. So if that color is available to buy, well, you might have some problems. At the same time, it may be a viable strategy if every other player is competing for a wider strategy with nobles.

That said, I remain skeptical of a strategy concerned with concentrating on level three high value cards, and remain convinced that Splendor is very much a game of opportunistic, incremental victories that rewards turn-by-turn efficiency rather than grand strategies. Consider for example that the average point value of a level three card is four. To win, you would need to purchase three plus something else or four. That’s a tall order, especially considering the bonus return is the same as a level one or two card. Instead, it seems much more likely that–like all other parts of the game–level three cards are purchases of opportunity. If a player is able to efficiently purchase a level three card, it is because they just happen to have the correct bonuses and gems at hand, rather than a “from turn one” plan. That said, without behavioral data to acknowledge that, I can only speculate.

Tagged ,

Thoughts on Innovation

Jason (JA): Innovation is a two to four player card game – there’s no physical board itself, but it plays like a board game. It was published by Asmadi Games in 2010. We’ve all played this game a bit, but haven’t looked at it from a design perspective before.

Aaron (AR): I’ve played it at least six or seven times. It’s nice because it’s fast, generally not too difficult to learn, although the instructions are terribly written, and people seem to enjoy it because it’s not too competitive.

Jordan (JO): One thing that sticks out for me is that it’s always different. Every game is so different and I think that’s probably due to the very fast-paced nature of the game play. It’s one, maybe two turns until you’re into the next age, so things move quickly. It’s very easy for someone–by chance of combination–to skip two ages ahead. You get to see a fair share of the cards, but there are only a few card effects that come into significant play in any given game, so you really do get a different experience each time.

Mechanics

AR: On your turn, you have two actions: you can achieve, use an action, draw a card, or play a card. But besides achieving and activating a card, everything seems a little weak. Drawing is slow because using cards often lets you draw and do something else. This motivates players to try out these new, wacky actions that everyone can do.

JA: Most of the time I’d say that games end by people gaining enough achievements or victory points, which you’re competing for throughout the entire game.

JO: From a design standpoint, the game suffers from poorly-written rules, and clunky visuals. I’m not saying the game is bad, but it could use streamlining. Even the words they use to indicate an action are poorly chosen – what is a splay or a meld? Part of game design is to get players comfortable with how the game environment work, and the easiest way to do that is go the simplest path possible with language.

AR: I think there’s a good level of interaction in this game. While you’re only playing on your board, you can attack others, but you can only do that once, twice per turn. Comparing your symbols to the ones on other people’s boards also offers a nice way for you to interact at all points in the turn, even though you’re not playing cards yourself.

JO: The whole game is based around those fun things that allow you to make crazy things to happen. You get excited when you have something ridiculous happen that gives you a a lot of points.

AR: The designers create exceptions to rules because they want an epic win where something magical happens. That’s kind of the feeling I get with these really random win conditions. You can’t predict that, you can’t plan that, but if everything aligns, it feels really satisfying.

Thematic Elements

JA: I think the game is based around creative-driven design. I wouldn’t be surprised if the designers came up with the names of the cards first, such as The Wheel and Atomic Theory, and then assigned rules. It’s also reflected by how certain states work – you start to be able to destroy castle icons once you get gunpowder, and overall, it’s generally reflective of technology advancing at an increasing rate.

AR: The pacing of the game is interesting. It starts out fairly slow, but once you get past age seven or eight, everything turns to chaos. What you had going on before playing your age ten card doesn’t really matter. It makes you kind of think – is that balanced?

JO: There’s a very evident sense of the game changing pace as you go along. You have castle icons in the beginning and time icons at the end. With many games that are age-based, the end is kind of glossed over and I don’t get to experience the complexities as much as I like. I get that the point is that technological advances move at an exponentially rate. I understand what they’re doing, and I like that toa degree.

JA: Part of the design impetus is to give the feeling that you have to keep building your civilization and replacing old tech. You can never become complacent with one particular card, because there are hard counters, or because it becomes obsolete. I think your previous decisions not mattering so much is completely appropriate for the theme of this game.

Similarities to Other Games

AR: I might describe this game by its opposite. It’s very different from Citadels. Citadels is very calculated and everyone plays a different role. Also, once you’re behind in Citadels, there is no catching up.

JO: I like the game, it fits the design intent, which is a more complicated Fluxx that fills a similar slot in that it’s not too difficult to learn or too long and has a bunch of combinations. It is a smarter game than Fluxx. Fluxx frustrates me to no end and I hate it – this is the Fluxx I would like to play. It’s smarter on the interactions, it’s more strategic and it’s more fun.

JA: I think this is a game of adaptation and flexibility. I don’t think this is anywhere as random as Fluxx, where you really have no idea what’s going on. I think you’re rewarded for your good decisions more here, but you’re right, it is “swingy”.

AR: It kind of feels like Race to the Galaxy in some way, since you’re building something on your board. But in other ways, it’s completely different – there’s zero interaction in Race to the Galaxy.

JA: And interaction is crucial to this game – it’s at the heart of the design.

Kudos and Critiques

AR: I’d be lying if I said I never got frustrated when playing this game. I really do enjoy the game for the most part, you just have to have a mindset that this isn’t a game of chess where you can predict what will happen next.

JO: I like it for what it is, which is a fun, quick game. It does allow for really fun things to happen, which I think is one of the primary design intents. And I think they prioritized this over a balanced, careful design.

JA: They’re frustrating at times, but I really like the game’s resource mechanics. The resources and different elements there are pretty cleanly executed, but so much of the game relies on splaying later on, and I think there are only so many options to do so later in the game. And if you don’t get your splays down early, you become reliant on winning through an age ten card.

JO: Because your resource management and creation are so dependent on the cards in play, it’s hard when you don’t get a card that allows you to score or tuck a card.

JA: Regardless, I’m always excited to see what’s next to come. The designers made the game in such a way that every card, more or less, is exciting.

AR: I think it could have used a bit more careful play testing; they could have kept some of the same elements of randomization and the feeling of being on a train barreling down a hill not being able to stop. I would have probably kept out a few cards and made the game a little less crazy at the end. But overall, I really like it.

Tagged ,