Variance, Part 2

Ok:  so where am I?

Yet another example of variance:  a strategy game that uses die rolls to determine outcomes of battles is higher variance than a strategy game that does not.

Somebody out there might be saying, "*I* can beat the first boss in Ninja Gaiden every freaking time.  It's not such a high variance game."  What I mean is - (wishing my blog could support graphics right now) - if you were to graph the probability of succeeding a challenge against player skill, a low variance game would show a steep jump from 0% to 100% when player skill reached a certain point, whereas a high variance game would show a gradually increasing slope.  My Ninja Gaiden skill puts me at around a 10% success rate against that first boss - yours may put you near 100%, but that doesn't mean it's a low variance game.

High variance games violate Scott Miller's "God concept" - even God (assuming he doesn't cheat) won't always win at poker.

My first instinct - because I usually dislike high-variance games - is to say, "Variance is bad."  In fact, I used to think of variance as "slop" - mushy, chaotic randomness that got in the way of a game's true expression.  (And I was pleased with myself, because that gave me a formal aesthetic with which I could argue that Tony Hawk 4 was a superior game to SSX3...albeit not as pretty.)

But this, as with all else, really is a matter of taste, and a matter of whether the variance fits the game. 

Because there are good things about variance:  in a low-variance game, once you've solved a challenge once, there's no reason to ever play it again.  In a low-variance game, you can memorize patterns - and the game stops being about solving problems on the fly and starts being about memorization.  High-variance can dump you in situations you aren't prepared for and get your adrenaline pumping.  One of the exciting things about SSX3 is that your runs don't usually go as planned, and you make do with what you end up with.  Spider-Man 2 is the same way - subtle differences in timing can mean you land on a completely different building than you intended to - now you have to make do with the hand you've been dealt.

In fact, one could argue that low-variance is boring, predictable, and that we should always strive for some variance because it adds replay value.

A good case in point is Mercenaries - (The good people at Pandemic are my new heroes, by the way, now that Ion Storm has bitten the dust.  First Full Spectrum Warrior and then Mercenaries.  Game design geniuses over there.) - Mercenaries is high variance.  With one of the ace missions it took me a dozen tries or so to get to the first objective;  then I died;  and then it took me another dozen tries to get there again!  Was I frustrated to be doing the same stuff over and over again?  Yes, I was, but I probably would have been even more frustrated if that stuff was predictable, because it would mean however many minutes of being bored for each replay.  Each time I played the situation shook down a different way, creating a varied gameplay experience.

What I need to do is pin down why the Ninja Gaiden and Devil May Cry boss fights bother me, but the SSX3 runs and Mercenaries missions do not.  It's possibly in the kind of variance.  With SSX3 and Mercenaries and poker the variance is more situational.  SSX3:  subtle differences in timing and action put you on a different part of the slope where different moves are going to be effective.  Mercenaries:  subtle differences in where the enemies go after you engage them creates different warzones.  Poker:  differences in the hands dealt create different landscapes to play in.  The variance in Gaiden and DMC is usually just:  which attack is the boss going to do next? (And is he going to be on camera when he does it or am I going to get blindsided?)  My thoughts here are still murky, even to me.  I'm certainly not suggesting that we take away the randomness of the boss attacks and replace them with patterns.  Shudder.

One last note:  high-variance games are easier to develop than low-variance ones.  In particular, 3d videogames bring a lot of chaos with them that their 2d brethren didn't necessarily have, and tricks to make 3d less variant usually involve constraining the gameplay into two or one dimensions (the wall running of Prince of Persia, the rails of Tony Hawk, Jet Grind Radio, or Sly Cooper).

Comments

[Paul Du Bois]

The "variance" you mention in the last paragraph seems different than what you're talking about elsewhere in the essay, but it lets me bring up this anecdote. In Psychonauts, a lot of the action elements ended up evolving into variance-free, PoP-like forms. Cantilevers (horizontal poles that you swing on) always send you on the same trajectory; trampolines are given a maximum height no matter how fast you land on them; trapezes always send you along the same trajectory whether you let go at the optimum angle or wait until you've reached the apex of your arc (and wasn't _that_ a pain to implement); tightropes no longer force you to balance upon them.

Internally we think of it as skill-based vs non-skill-based.

[Walter]

Interesting thoughts, Jamie. You might want to take a look at my old Ludonauts article, "Agonistic Integrity vs. Epistemic Conditions" (assuming you can get past the arcane terminology--you can skim through the stuff on Caillois). I take a look at one way in which game challenges needlessly dissolve: their inability to thwart factual knowledge harvesting.

http://www.ludonauts.com/index.php/2004/01/26/p156

[PaG]

Interesting ideas here.

It seems a scale from total chaos which the player can't control (like many casino games) to patterns perceivable in chaos and on which players have some influence (SSX, Spider-Man) to absolute patterns and control (chess).

The chaos can be fun to deal with as long as you have some control over it. If you just lose on the game's random whim then it ain't fun, but if you can deal with the chaos in different ways then dealing with chaos becomes one of the skills to master in the game. The better at handling the chaos wins.

Poker, for example, gives you random cards but a good player can win a lot of money on a poor hand and a poor player can lose money on a good hand. This is especially true when playing many games in a row -- the superior poker player will most likely win a long string of games even if he can lose any individual game.

[Nathan McKenzie]

Jamie:

Maybe randomness goes better with games that are generally fairly non-linear to begin with.

I think poker's pretty fun, but if I had to beat the first boss of Ninja Gaiden at a game of poker to get past him to advance the plot, and I had to reload at my checkpoint every time I lost, I'd be pretty pissed off. That boss plays like a character from Dead or Alive, not a typical linear single player Japanese pattern-based boss. I think it's kind of the same situation.

Maybe variance on a single encounter level just fits well with fighting games / sports games / racing games / tournament FPS games (like UT) / RTSes / turn-based strategy games because the whole game is built out of an enormous amount of those single encounters (so things tend to average out after a while) and because the reward for succeeding at any given encounter is the opportunity for more such encounters. It probably also doesn't hurt that when you take damage in a fighter, or die once in UT, or let a run be scored in baseball, or mess up a trick in SSX, the game isn't over, it's just impeded a bit.

The worst examples for me of variance in a game recently were several sections of Call of Duty. There were occasionally fields that just seemed to rain bombs down from the sky, and when I ran across those fields, I would usually die. Unless I didn't. It was obvious, as I was saving and reloading, that I was going to get through that section eventually. There really wasn't a question. The only question was how long the game would randomly make me wait. I probably should have turned on god mode, since that would have required the exact same amount of skill.

[Anonymous Coward]

Maybe this is tangential to what you're talking about, but I disagree with your characterization of DMC and NG as high-variance games. The bosses attack in somewhat random ways, yes, but each attack is avoidable or counterable. And it takes you a little time to learn how to deal with each attack, but that's totally different from what you are calling high-variance, because once you learn how to handle the attack, you can beat it every time. It's not like the game rolls a die and just deducts half your health. And it's not like you can't see the attack coming (not counting camera problems, which are a flaw in the implementation, not in the basic game design).

And in fact my personal experience in Ninja Gaiden is that it works in exactly the way you describe for a low-variance game. As soon as I figured out that after the first boss does a certain attack, he is vulnerable for a specific time only, and you will just get whooped if you attack him at any other time, I could beat him easily at will. That's the steep jump. I just had to watch and think. And I'm not just saying I'm uber or whatever, just I think NG is more like chess than you seem to think.

[Gary]

I'd say that variance is good as long as it doesn't set the player back and the overall difficulty remains the same (or in the case of multiplayer, is fair to all players). It improves the replayability without the player feeling like they've been cheated in some way. I would also highly agree with Scott Miller's "God concept". As a player I don't ever want to lose due to some random event(s).

My most recent experience in a game with this is in the Kotor games with the pazaak minigame. I absolutely hate the mini-game. Similar to poker, on a bad hand I'll lose and there's nothing I can do about it. Afterwards I'll reload the game because it's quicker. Probably not too good of an example though because it would be a terrible mini-game even if it was possible to win every time since there's little skill required. Not being able to win with perfect play just means it takes longer to get through. Of course I don't need to get through it, I just want the extra money and I'm a completionist. Luckily it has less prominence in the sequel than the previous one.

[Penguinone]

I think I put my finger on what Jamie was struggling with between the types of variance that he enjoys and those that frustrate him- they are the same that bother me.

Variance is different than totally random to me. A game that is completely random feels like the developers took a cheap way out. There's no way at all to determine how to "win" (which is the point of all games) because you can never predict what will happen when I do X.

The type of variance that Jamie and I like is the variance that is somewhat predictable, and it really is more like real life than not. Yes, its impossible to get exactly the same run down the hill in SSX, but you *know* for a fact that you can hit that rail everytime once you get good enough- I started out getting all bronze in Tricky and now I have all golds, I can attest to this. The variance is not completely random either- I know I increase my chances of hitting the rail if I'm not screaming down the hill at 200 miles per hour- so I slow down at a particular point and I get that rail and I get my gold.

And anyone who says that Poker has a totally random variance has never really studied the game. There are elements of randomness, its not totally random- there are distinct sets of probabilities for each individual outcome. If I have a pair of aces in my hand in Texas Hold Em, there is set probabability that I'll draw another Ace on the flop. Yes, this is random, but the skill comes in knowing whether I fold, raise, or call based on my analysis of my opponents, the probability of catching my winning card on the River, and my confidence in my ability to convince the rest of the table that I'm the Man.

[chrisf]

Seems like you mean variance as non-determinism. Although Ninja gaiden seems random, I don't think there is much random number generation in it at all.

Basing NPC AI decisions on the very slight user inputs that you get from an analogue control can give the impression of high variance (which I think is a good thing - people laud farcry's AI simply because the baddies rarely do the same thing, even though they still walk into walls all the time) while keeping the choice of an enemy (to say, wait, use attack A, or use attack B) based in large part on the player input.

So you end up with a game that plays differently each time, yet is based entirely on patterns and the propogation of those patterns through the system. This seems more elegant to me than randomness, and it also allows for players to use their pattern recognition skills.