Does Mathematical Tuning Make Games Better?

simoniker writes "What do game designers need to know about statistics? Age Of Empires DS designer Tyler Sigman focuses on statistical topics that he believes should be understood by game designers, in a new article. His reasoning: 'In the game I just finished, we recorded data from play sessions and then set challenge levels in the game based upon the mean and standard deviation values from those recorded data. We set Medium difficulty to be equal to the mean values, Easy difficulty to be equal to the mean minus a certain amount of standard deviations, and then Hard difficulty equal to the mean plus a certain amount of standard deviations.' Would all games be better if they were tuned mathematically?"

Comments

You call that "mathematical modelling"?!

[6350']

We set Medium difficulty to be equal to the mean values, Easy difficulty to be equal to the mean minus a certain amount of standard deviations, and then Hard difficulty equal to the mean plus a certain amount of standard deviations
Wow. If this is "mathematical modelling", then me swapping the coffee mugs out for wine glasses in my kitchen cubbard would be "advanced sphere packing analysis and optimization".

Game tuning as more art than science. The goal is not to create an interestingly distrubuted difficulty curve, but to create an "easy", "medium", and "hard" amount of enjoyable challenge. Huge amounts of time can be (and frequently are) wasted focusing too-strongly on a "cool" and intriguing difficulty model that some under-experienced junior designer is all fired up about, instead of keeping the focus tightly and solely on the how the game actually feels.

Re:You call that "mathematical modelling"?!

[SnowZero]

The sad thing is the article teaches people the tools but not when to apply them. For example, it introduces the normal distribution, but no tests to check the normal assumption on a dataset are given. It also ignores the incredibly important subject of outliers. So in the end, he balances his game using a mean and variance, when its quite likely that a median and percentiles would have been better. Oh well.

I am constantly amazed at how much game programmers know about the mathematics and algorithms for computer graphics, and how little they know of everything else. And if you want to help them out by writing something, it is usually the case that a crap article or book on the subject has already been written by a game programmer.

I bet Easy isn't actually easy.

[onion2k]

I'm a bit of a fan of computer games. I've been playing them pretty close to my entire life. I'm 29 now and since the days of the Zx Spectrum I've probably played at least a couple of hours a week, often much more.

Unfortunately I suck at games. My coordination is all over the place. I have NO patience. I play games for a laugh, I don't want to invest a great deal of time learning a game or practising it. I want to pick it up, play for a while, and be entertained. As a rule I always play games on Easy because I don't want a challenge. I don't want to get frustrated playing the same level over and over. I want that feeling of progression like I'm getting somewhere. I can honestly say that if I get stuck for more than an hour in a game it gets turned off and never switched on again. I make a mental note not to buy a game from the same people again.

Easy is for people like me. Lazy, good-for-nothing "casual" players who have no skill to speak of and a life of some sort that means there isn't the time to learn perfection. I expect Easy to be easy. I very much doubt that "mean minus standard deviation" of some enthuiastic professional testers or Beta players is really going to be down at my level.

Please, for the love of Mario, when you're writing a game, sit your mother down in front of it for a few hours and tweak the difficulty of "Easy" to something she can cope with. That way I might buy your sequel.

Alternatively, give me God mode. :)

Re:I bet Easy isn't actually easy.

[Boronx]

Sid Meir Solved this problem years ago: Have a whole slew of difficulty levels from braindead to impossible. Somehow I doubt he needed much math for the easiest Pirates! level, where it's nearly impossible to lose in any situation, and in a few minutes play time you are god of the sea.

Re:Leave out "Mathematical"

[SimHacker]

BlackEmperor writes: "Is the intelligence of an object being tuned (cool)" or is the object just being given a x% production/whatever boost (sucks).

"Intelligence" generally does not have a "knob" that you can simply tune up and down. How smart a character acts is an emergent behavior that depends on many other factors in the system, themselves which include many tunable knobs like "x% whatever boost", and complex dynamic behavior scripted into the code.

That said, you can still add more layers to tune the higher level behavior of the AI, which randomize the emergent behavior and diminish the effect of the "intelligence".

For example, The Sims uses a complex dynamically tuned algorithm to figure out what action each character does next, based on scoring "advertisements": It asks all the objects in the house to enable and score all their action "advertisements", as the advertisement applies to a particular Sim at the current time. For example: the fridge's "fix dinner" advertisement is enabled in the evening; the toilet's "use toilet" action gets a higher score the fuller your bladder is; the bed side you usually sleep in remembers the relationship and raises the score, which increases when your energy is low, so it's more likely you will go back and sleep in the same place every time you're tired.

That algorithm produces a list of all possible actions, which is sorted by score. But if perfect Sims always performed the first action with the highest score, it would have made the game frustrating and un-challenging. Because if you didn't interfere with the Sims lives, they would automatically always do the right thing all the time, without they player's help. They didn't need you, because they were theoretically smart enough to live the optimal most efficient life. (I think that's what BlackEmperor means by "a clinical feel".) Anything the player told the perfect Sims to do would only make their lives worse off. The game was more fun and engaging if player intervention was required to help the Sims be happier.

So instead of choosing the first action on the list, the Sims choose randomly from the "n" top scoring actions. So "n" is a positive whole number that can be increased to "dumb down" their automymous behavior, and roughly controls how "whimsical" (or "stupid") they are.

Of course that's all assuming the ideal virtual world in which all the advertisements are truthful, mathematically correct, in your best interest, internally and externally consistent, without any contradictions, and perfectly fair and balanced. Which of course they're not, because there are many false advertisements, exagerated scores, distorted curves, and arbitrary tweaks, hacks, quirks and ironies in the code (especially stuff written by twisted players like SimSlice), that make simulated life more interesting. So tuning "n" to different values has a non-linear complex effect over their "intelligence", and it's quite coarse with a small range of useful values.

So of course you have to use lots of play testing to figure out the best value for "n", not pure mathematics.

-Don