Too Much of a Good Thing?

My last blog talked about the basics of mathematical models and how they can be used in game balance. Almost universally, when players play a game, they’re encouraged to look for “powerful” cards, characters, abilities, etc. to reach certain goals. Even in fully cooperative games, players gravitate to what they perceive as strong and shy away from weaker options.

Since the goal of the game, by definition, is to accomplish the goal of the game, it makes perfect sense for players to seek out the tools that will be most effective at helping them reach that goal. It also makes sense for players to stratify the available options. It even makes sense for them to critique certain options as “overpowered” or “underpowered” when those options continuously rise to the top or fall to the bottom. It also makes sense, however, to dislike a game because it is too balanced.

I’d be willing to bet that most readers have never claimed a game was too balanced or heard other gamers do so, but without some differentiation between the capability of different cards, characters, abilities, etc. in an asymmetrical game, there is very little meaningful player choice. If playing any given card, miniature, tile, etc. in any way it could be played had no net impact on whether a player won or lost the game, the game wouldn’t be enjoyable. There needs to be some differentiation to encourage players to interact with the game, to explore its possibilities.

Too-balanced games aren’t typically criticized for being “too balanced,” though. They’re dismissed as “boring” or as not having “meaningful player choices.” Given that games need some degree of imbalance to be enjoyable, it begs the question “how much is enough?” The answer depends on the game in question.

For casual games, the degree of imbalance should be very small. Games like Lanterns and Sushi Go give players choices, but the difference in score between a player making the right choices and a player making the wrong choices is typically fairly small. Scores are very close, options are narrowly balanced, and that suits these games very well.

For intermediate games, there’s more leeway for imbalance between game components. Players want their various characters, monster races, kingdoms, etc. to feel varied in their strengths and weaknesses. Some might excel slightly or lag behind slightly, but having lots of flavor is more important than perfecting the balance. Plenty of board and card games fall into this middle category, as do most dungeon crawl games and role-playing games.

For hardcore games, the balance pendulum swings back again. If a game has frequent large-scale tournaments, it qualifies as a hardcore game that needs tight game balance. The various games that fall into the category of “esports” certainly fall into this category as do many hobby miniatures games and collectible card games.

With such an emphasis on balance, though, how do such games avoid the trap of being boring?

First off, they recognize that only the top choices truly need that razor’s edge of game balance. In a pool of 100 player options (deck builds, heroes, army generals, etc.), it’s difficult if not impossible to make all 100 choices truly unique and truly balanced. But you only really need the top choices among these player options to have such finely tuned game balance. “Lesser” options should still be interesting, creating more diversity in the game and generating additional appeal for gamers approaching it as an intermediate-weight game rather than jumping into hardcore tournament-style play.

Second, though, they recognize the power of situational effects. If one option is more powerful in certain positions, match-ups, combinations, etc., while another options excels in others, it creates additional depth of gameplay without creating an option that is strictly “more powerful” or “less powerful” than the alternative. Collectible card games embrace this direction. Games like Magic: The Gathering and Hearthstone have plenty of cards that are more or less powerful than other options based on some aspect of the game state – what you have in play, what your opponent has in play, what you have in hand, etc.

Third, they shake things up on a regular basis. New gameplay formats, new releases, new balance updates, and new editions all force players to reassess the strengths and weaknesses of the tools in their toolbox. Sometimes, players resist or even resent changes to the status quo, but those changes are necessary to keep the game fresh and to keep gameplay engaging.

I hope that you’ve enjoyed this look at how a little bit of imbalance is critical for good game balance. I’d love to hear your thoughts in the comments!

YTN Episode 015

The 15th Episode of Your Turn Next is now available!

First, I want to say a big “Thanks!” to our community for making the last podcast our most downloaded show thus far by leaps and bounds. We’ll definitely be sticking to the new format. Be sure to tell us what aspects of the show you particularly like, and we’ll try to focus on similar topics in the future. This episode, Ryan and I are joined by Reese, and we kick things off with a brief discussion of what we’ve been up to lately game-wise.

The second segment covers our featured games, and this episode we feature:

Our topic segment for the episode goes a little bit long as we talk about rebooting franchises, adapting them to new media, and our thoughts on reboots that have been handled successfully and… less than successfully.

YTN_AvatarWe’d love to hear from you! Let us know in the comments or via email if you have any topics, questions, or ideas you’d like us to discuss in a future podcast.

The email is:

Getting Started with Mathematical Models

In an earlier blog, I briefly mentioned mathematical models and how they’re a great tool for game development. Some folks are already familiar with mathematical models in the context of gaming. For those who aren’t, however, I’d like to take a look at the basics in today’s blog.

The goal of using a mathematical model during game development is to assist game balance efforts by creating a formula to help determine the value of similar components. Those components are most often cards, but they can also be miniatures, dice, tech upgrades, treasures, or any other game component that we wish to present as a viable option that is not an overpowered option relative to other choices. A good mathematical model behind the game can save a lot of time in the playtest process or even lead to a better balanced final product.

As noted in the asymmetrical game balance blog, not every game has components that need to be balanced against one another. Even for the games that do, some games are a better fit for mathematical modeling than others.

For our look at a few building blocks of a mathematical model, let’s assume we’re talking about a card game with lots and lots of different cards that fight against one another (a very good type of game for which to use a mathematical model). We’ll assume they have some sort of Attack stat, Health stat, and Mana cost. The most basic place to start our mathematical model is with ADDITIVE terms in our formula. We could, for example, say that “Attack + Health = Mana.” It’s not a terrible place to start, and it could even lead to some decent game balance. We don’t typically see games use this as-is, because the in-game math surrounding the Mana resource would become unwieldy for players. Unwieldy math behind the scenes is fine, but not in front of the players.

So let’s add a SCALING term to our formula. Let’s move to “(Attack + Health) x (Scaling Factor) = Mana.” A scaling factor of 50% is a decent starting point. It’ll reduce the mana our players need to track, but it also introduces some new questions. We’ll have to figure out how to handle rounding, for one. We also need to consider whether the game in question values Attack and Health comparably. We might need to go to “(Attack x Attack Scaling) + (Health x Health Scaling) = Mana.” If the game favors min/max-ing your Attack and Health stats on different cards, we could even start squaring, scaling, adding, and then taking a square root, scaling that, and then… hmm… I seem to be getting ahead of myself.

There’s something else to consider in our cost beyond just mana, though. Playing a card costs mana, but it usually also costs a card. Most card combat games allow just a single free card draw per turn, so let’s put an OFFSET into the formula to account for the cost of the card. This brings us to “(Attack + Health – Offset) x (Scaling Factor) = Mana.” Now we’re cooking. For those who are familiar with Hearthstone, consider “(Attack + Health – 1) x 50% = Mana.” Glance through a few Hearthstone cards, and it sure won’t take long to find one that fits this formula.

On the topic of Hearthstone, we know there’s more to a card than just Attack, Health, and Mana, but the tools we used in our foundation of mathematical models will continue to serve us well! Cards with a specific minion type (like Beasts or Dragons) have card synergy that increases their value. Well, let’s just add a “Minion Type Scaling Factor” customized for each Minion type (typically in the 105% to 115% range). Cards that belong to each Class could also have an additional scaling factor by Class (typically 85% to 95%). Then we’ve got abilities. Yikes! Some simply add to Attack or Health, which keeps things simple, but others get quite a bit more complicated. Some are direct damage. Some are conditional increases to Attack or Health or are conditional direct damage. We’ll ultimately need a lot more terms in our formula.

We’ll also need to add quite a few more tools to our toolbox before we’ve got a comprehensive mathematical model for Hearthstone or for our hypothetical card combat game. This gives an idea of how to start the ball rolling and hopefully gives a slightly better idea of what’s going on behind the scenes. By the time I completed my model for High Command, I had dozens of individual terms in my formula, and some of those terms had separate mathematical models generating just one term.

I hope you enjoyed scratching the surface of mathematical models for game development. The next time you look at the numbers on a card, I hope you can catch a glimpse of the mountain of numbers behind those numbers and appreciate how that card came to be.