A Quick Introduction to Probability

Given enough repetitions, the ridiculously unlikely becomes almost certain. After all, someone wins the lottery all the time, even if the expected value of a ticket is always less than it costs.

I mention this because at any given time, for every game, someone is posting that something is wrong with accuracy, or the random number generator, or they are otherwise a victim of how things are being coded. Occasionally they are right, and there is a mistake in the game, but the vast majority of the time a normal random distribution explains what happened. Even for the most hideously freakish events.

Let us try a few examples to demonstrate things.

First, you hit ten times in a row. Woo, you rock! Lucky day! You may not even notice, since you expect to hit. After all, the odds are better that you will hit than miss on every swing.

Second, you miss ten times in a row. Ouch. You are probably dead and bitter. Let’s quickly run some numbers to see what those odds were.

For ease of calculations, let us assume that you have a 90% chance of hitting. This means that your probability of missing ten times in a row is 0.1^10 = 0.0000000001. Roughly one in ten billion sets of ten swings will be all misses. Wow, that really sucks. Pretty unlikely, from your point of view.

Let us look at it from a game-wide point of view. With 6.6 million World of Warcraft players, let us assume that 1 million play each night. Assume that each gets 1000 attack rolls in a full night of play, and we will call that 100 sets of ten attacks (more, really, due to overlap, but we’re keeping it easy here). So there are 100,000,000 sets of ten attacks every night.

We expect that, on average, someone will miss ten attacks in a row (with 90% accuracy) every 100 days, so three or four times a year. Yes, the one-in-ten billion event will happen several times a year. The odds that it happens to you are still very small, but it will happen to someone, and that person will be epically displeased. It is a far more noticeable event than hitting ten times in a row (which happens in roughly one-third of sets of ten attacks at 90% accuracy).

That is probably a conservative estimate. Your chances of missing ten times in a row are probably better than one-in-ten billion, and there are probably more than seven billion attacks made each week in World of Warcraft.

Shall we run that again with different probabilities? Let us try a 75% chance to hit. Hey, that drops it to a 1 in 1,048,576 chance. That should happen to someone every night, even if the one million players make only ten attacks each. If we still assume that everyone fires 100 sets of ten attacks, that means 100 different people would miss ten times in a row every single day, still thinking that they are the victims of outrageous fortune.

Ponder that one for a moment: one-in-a-million events happen all the time. Not only are there a large number of possible events that are one-in-a-million, there are billions of everything happening everyday. There are more than 6,000,000,000 people in the world. If anything has even a tiny chance of happening, it will most likely happen to someone, soon. Let’s say that you are smarter than 99.9999% of the population; there are still more than 6,000 people who are smarter than you.

Pulling this back to game, there are buffs, debuffs, level differences, penalties and bonuses, exceptions to rules, and maybe a dozen other things that could affect your chance to hit. Your chances of missing five times in a row are trivial, almost 1 in 1000 at 75% accuracy, even before considering all the things that could keep you from hitting. If you are a hardcore player, this will happen every single day.

Finally, barring a streak-breaker code like City of Heroes has, your odds of hitting next time are completely independent of whether you hit last time. That is (part of) what random means. You are never “due” to hit, any more than a coin is “due” to come up heads. No matter what it may feel like, by definition there is no pattern to random events. You just happen to be part of a species that is neurologically hard-wired to look for patterns in everything.

So no, most likely, accuracy has not been nerfed.

: Zubon

3 thoughts on “A Quick Introduction to Probability”

1. Inhibit says:

One thing you can not overlook.. those odds can not be grouped together. Then 10 misses in 10 attempts… is on a per-person basis, not a per person within a set chance group.

And yeah, sucks bawlz when your number comes up. But the good part is that the odds of a 20 streak are so rare… you are golden when it hits you.

2. Oz says:

Leading wizards have deduced that one-in-a-million chances pop up nine times out of ten.

/pratchett

CoH has streak breaker code? I was not aware of that. From played EQ so long, I’m used to the patch day complaints of “X is hitting less than it did before the patch!” and other such fun. Pretty much standard in any community.

3. NBarnes says:

I hear Onyxia is deep breathing more….

….

That line of argument lead to amusement when a patch really did break Onyxia so that she was deep breathing more.