Tuesday, September 3, 2013

Rules and Exceptions

You might be familiar with the phrase, “the exception that proves the rule.”  Most people use it incorrectly.

First off, the idea is that because you bother to make an exception, the rule holds true in all other cases.  For instance, if you have a child and tell them, “you can eat candy when I tell you to,” you’re implicitly saying, “you aren’t normally allowed to eat candy.” You create a rule through the exceptional circumstance: “you can eat candy when I say it’s okay, but otherwise, you may not.”

People frequently misuse the expression.  Somebody might say, “tall people can’t be good at video games,” and then you say, “well, what about TallDude72 who is the best Gritty World War II Shooting Game player in the world?”

The response?  "Well, he’s the exception that proves the rule. Normally, tall people aren't good at video games. He's an exception." Used in this way, it’s another way of saying, “doesn’t count, I’m still right.”  

This exception should help us refine the rule.  It should help us say, “this is the real rule.”  We should ask, “why is it every tall person but TallDude72 bad at video games?”  And we discover, “well, he’s been playing games competitively since he was two years old, and every other tall person is forced to play basketball by their gym coaches, instead. So they don't get to practice anything but sweet dunks, all the time.” A new rule: if you spend all your time practicing sweet dunks, you won't get good at games.

The exception should force you to look for more data to explain it.  It helps you explain why that rule was normally true, and why it’s not true in this case.  And that should help you figure out a newer, more accurate rule, to better describe reality.


Why the heck did I say all that stuff?

It’s to highlight a certain point, which is that even when confronted with evidence that totally conflicts with their current rules and views of reality, most people just don’t update their rules.  They go, “Huh, weird,” and keep going.  Exceptions don’t make them refine their rules; they end up reinforcing them.

See?  It wouldn’t be an absolute, iron-clad rule if it didn’t have a goofy exception!  Now we know it’s true, forever.

Here is another example.

Recently I got into a conversation about various characters in League of Legends, and went on to the topic of Poppy, a character who currently has a rather low win-rate.  Her late-game is very strong, but she’s held back by having zero presence at the start of the match.  So even though we both agreed she’s extremely strong if she can reach her potential, she normally has a tough time doing that in a given game.

Then I pointed out an exception to the rule; there’s a player who, on his alternate account, only plays as Poppy.  Not only that, he completely disregards the normal roles set by the current metagame, and uses this specialized champion in every capacity.  And his win-rate with her was--at the highest level of non-competitive play in North America--something like 60%.  Over the course of hundreds of games.

That’s really good.  The most overpowered champions in the game hover around a 57% win-rate, typically.  Currently, the highest win-rate champion is at 54%.  Since you have four other people on your team (and five on the other team, and then the possibility of character-counters added into that) it’s really hard to get much higher without being insanely broken, because the win-rate will get averaged down by bad players who don’t know what they’re doing.   Poppy, historically, is almost always in the bottom 10 of winrates, out of over 100 characters.  As far as most people are concerned, she’s just not a very good character.

So we have a rule: Poppy is not good.  We have an exception: one player, Zekent won over 60% of his games with her, and did so at a very high level of play.  This exception must force us to redefine our rule.  The question, at this point, is how.  Many people just go, “well, that’s Zekent for you, he’s really good” and leave it at that.  That’s not very interesting; at least, not to me.

What it tells me is that--in non-arranged play--Poppy is capable of winning a majority of her games.  It’s not just a question of, “you must be as good as Zekent to do it,” because Zekent is playing against people at his own level and rating.  So even between players and teams where the skill levels are relatively even, she’s capable of succeeding.  In these types of games, there’s a simple equation:

Player Skill + Unlocked Character Potential = Output

How good you are at understanding the rules and general nature of the game, when combined with what you’re capable of doing with a specific character, will yield your output.  PS(you) plus UCP(your character) equals O(you).  And Zekent is good, but not so good that he’s a million miles ahead of everybody else.  So if PS(Zekent) is equal to PS(everybody else), but O(Zekent with Poppy) is higher than O(everybody else), what does that mean?  At the very least, UCP(Poppy) is higher than people think.

It might mean that Poppy is actually quite strong, but that it’s also very easy to be bad with her, hence a high ceiling and low win-rate.  It might mean that Poppy is only good when her team knows how to work with her; hence, Zekent wins at lower levels because he’s that much better than the low level players, and later on he gets teammates who will support him properly, causing his wins to remain consistent at all levels.

We might need more information.  It’s possible that, due to Poppy’s low popularity and success, most people don’t know how to handle a good Poppy, and if Zekent is the only one at high levels of play, even his main competition just won't have experience.  So her potential is relative to how much people know how to fight her, and if more people had experience, her win-rate would go down.  It’s hard to say for certain, without further investigation.


Okay, why did I bring that up?

I wanted to give you an example of analyzing an exception, relative to conventional wisdom. The question here is, what do you do when something breaks the rules you believe in?  Do you stop and think about it?  Or do you shrug, and say “well, that’s weird,” and go back to your old model of reality?

In Super Smash Brothers Melee, many people believe you must use certain skills in order to be successful.  Yet there are some people who don’t or can’t use them, and still succeed way more than average.  I injured my hand, and beat many people with a slow-paced, dumbed down style.  Most of them did not stop to analyze what that meant about winning, and good decision making, and improvement.  How was it possible that I could just stop using advanced tools, yet continue to beat people?  There had been a rule, and then an exception to the rule.  It forced me to redefine what I thought about skill and success in the game.

Likewise, when a player takes a low-tier character and makes waves with that character, we have to ask some questions.  “Is this person doing things with their character that nobody else has done yet?”  If so, that means the character’s potential is higher than we thought before.  If not, and the player is using old tactics and they just continually work, it tells us that not only is the player really good, but that mastery of this game’s system is more important than mastering character nuance.

We also must ask things like, “is their win-rate decreasing over time?”  Because that would suggest that the character potential is based on gimmicks, and shut down by intelligent counterplay from equally skilled opponents.  But if the character continues to do well, then we can give more weight to either the player’s general skill, the character’s potential, or both.  We must refine the rules and ideas when confronted with the exceptional circumstance. We do that by asking questions and gaining more information.

One of the ways that neuroscientists and biologists began to really learn about brain function was by studying people with brain damage.  When part of the brain stops working, you look at how that person lives and functions afterward.  It’s been discovered that what we call “seeing” is handled by multiple parts of the brain; for instance, you might suffer damage to the part of the brain that causes you to experience visual reality.  But if put in front of a door, and asked to open it, the part of vision that recognizes and perceives objects will still function; you can confidently open the door even though you can’t consciously see it.  The term for this phenomenon is blindsight; people are able to interact with things they can’t even see, because a certain part of their visual functioning remains.  You don’t just have one chunk of brain labeled “vision center,” you have multiple parts of your brain that handle different aspects of visual function.

A rule: blind people can’t see things, and must rely on other senses to find and interact with them.  An exception: when only part of their visual centers are damaged, using sight they can’t consciously process, they can interact with things anyhow (without first using other senses to locate them).  The rule is then refined, to incorporate the exception.

Don’t settle for saying, “huh, that’s weird’ when your rule has an exception.  Integrate it and refine your rules.  Try to dig deeply and critically into the exception, to find a newer rule that tells you more about reality.

Thanks for reading.

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