Sunday, February 13, 2011

Why "Dicing It" Doesn't Work - Statistics, Probability and Bias

Yes, my post title sounds like a peer-reviewed journal article title.

Sue me.

Anyways, there's been a few comments made recently regarding Shattershard Beetles.

References were made to the usefulness of rending versus the increasingly common Feel No Pain USR. The kicker came from comments made both here and in a few other blogs about how they had "diced it" and come to the conclusion that it was a good idea.

By dicing it, I'm assuming that they set up an imaginary scenario of some kind (much like my imaginary deep-striking Blood Angels squad HERE) and then picked up the dice and started rolling to see how things would turn out.

Well, I wanted to talk less about the Shattershard Beetle/Dessicator Swarm discussion (it's really not an important enough issue to warrant the title "debate," - in the final calculation it's not going to make THAT big of a difference), but about the practice of "Dicing It" itself and how the human brain makes that a very poor proposition in most cases.

Now a quick word about statistics and probabilities. Whenever I (or anyone) tells you that such and such a weapon will statistically inflict X number of wounds of which Y number will fail inflicting Z casualties, we are talking about probabilities. These numbers are perfectly accurate and valid, but you have to be careful how you use them.

Probabilities are only true with a "Large" sample. For example, if you flip a coin, the probability of it landing heads side up is about 50% (depending upon the particular coin). Does that mean that if you flip the coin twice you will get one heads and one tails? No! You could get two heads, you could get two tails.

But the more times you flip the coin, the more the overall number of heads and tails will trend towards 50% each. So "in the long run" the 50% ratio is "true" but it doesn't guarantee any results over the short run or for any particular set of flips.

Ok, so when we are trying to see how well a particular weapon is going to perform in a certain scenario, we have two options. We can CALCULATE the probability using some basic maths, or we can "Dice it."

Before we talk about calculating basic probabilities we should probably go into the the two biggest problems with Dicing it which are very closely related:

-Inability to get a sufficient sample size.
-Inability to accurately recollect the actual results of the sample we have (which gets harder and harder as the sample size grows).

What do I mean by this? Well, if I flip a coin twice, it's pretty easy for me to remember what the results are. But the sample is WAY too small to take accurate measurement from, so I need to flip it more. As I continue to flip it 10, 20, 30 times, my recollection is likely to get muddled unless I'm carefully keeping track of the numbers as I go.

Now we come to an interesting quirk of human psychology which makes this an even trickier proposition: recollection bias or hindsight bias.

This means that we have a hard time accurately recollecting things and almost always tend to overestimate the number of times that something "extraordinary" happened.

This is a problem in terrorism studies, they note that most people vastly over-estimate the number of people killed in terror attacks, because these events are so emotionally charged and extraordinary that they leave a magnified impression in our minds.

This is also the mechanism that leads many people to feel that their dice are worse than average, because rolling 1's is usually an emotionally traumatic experience.

Especially for Deathwing players. ;D

So, if "dicing" Shreddershard Beetles and Dessicator Swarm, what are we likely to find "extraordinary?" or would leave a distinct impression?

Well, when rolling Dessicator Swarms we are likely to feel every "one" that we roll to wound. Likewise, when rolling the Shreddershard Beetles we are likely to celebrate every "six" we roll. (It's important to note that these "exciting" events don't have to be positive, they can be bad too).

So I would guess looking at it that people would tend to OVER-estimate the number of failed rolls from Dessicator Swarms, and OVER-estimate the number of rends from Shattershards. This would of course lead the observer to believe that the Shattershard Beetles are more effective than they actually are.

The best way to avoid both these problems (inadequate sample size and recollection bias) is to simply use maths to perform the probability calculation. Maths can't tell us everything, but they allow us to accurately compare, for example, two weapons firing at the same target very accurately.

Next post I will talk about basic probabilities.