Thursday, March 29, 2012

Just the lies, no statistics

I noticed a link to this article on TheBack40K's blog roll.  It was pretty basic probability theory stuff, but I noticed an error in his calculations.

He had calculated the probability of a Sherman killing a Stug at range as 5.5556 percent.  This is correct, but when he applied it to a whole platoon firing ten shots he said the probability was 55.556 percent. Or, that you would kill "Half a Stug." This is wrong.  You don't just multiply the probability on one thing by ten to get the probability of one thing happening in ten chances.

A correct way to determine this is to use a binomial probability calculation.  If you do this you get the probability of at least 1 kill as 43%.  At least 2 kills is 10%. At least 3 Kills is 1.5%.   I even pointed him to this handy online calculator to figure out these probabilities very quickly.

Basically, I was just telling him his math was wrong and showed him how to correct it.

He responded:
Hi CaulynDarr,

The purpose of Expected Value is to give you a rough calculation for tactical purposes. It will not give you the exact percentage chance to kill one or more StuG's (in this case).

The main reason for using EV's over Binomial Calculations in Flames of War is that it gives you a single value instead of a set of values, allowing you to compare results between disparate sets of information (eg. Standing RoF vs Moving RoF). The second reason is that, with practice, you can begin to calculate EV's on the fly - or at least approximate them.

If you want to work out Binomial Calculation on the fly, then go for it - this class is not for you :D
 So he thinks that being able to quickly get the wrong answer is better than being able to quickly get the right answer.

Never mind that in his article he said that:
I should also mention that these types of equations should all be worked out before each game - taking 10-20 minutes to figure out the exact odds in the middle of a round might negatively impact your Sportsmanship score!
My response:
         But, you're giving the wrong impression about the odds. You say that you should kill half a stug,                    but that's not useful. If they see 3 of their stugs die when they where confident that not even one should die, you haven't really helped them. It's more useful to say that approximately half the time you will loose at least one. 
         With a smart phone and the link I provided, you can figure these values out on the fly.

His counter-response is a bit longer, so I'll just summarize.  He says that since the chance of loosing a Stug is less than half then he's not worried about the loss of any more Stugs.  This is exactly the misconception I warned about in my response.  I was trying to show that loosing one Stug is an average coin toss, and losing more than one is in the realm of possibility.  The math he provided makes it look like Stugs are nigh invincible compared to Shermans when in half of your games you'll be loosing 1 or 2 a turn.   Half is less than one, and saying you will kill half a Stug can easily be misinterpreted as you shouldn't be able to kill any.  A bit different than saying that in 1 out of 10 volleys you will probably lose 2 Stugs to a single volley from a platoon of Shermans. In fact, over the course of 10 volleys you will probably loose 5 or 6 Stugs.  If you start playing around with the number of Shermans and the number of kills you are wanting to get, you can learn some real interesting things.

He then goes on to say that my math may be more accurate, but is less useful.  BS!  More data is never less useful.  Not my fault if you can't comprehend the additional information.

Then someone dumps this useful gem:
Just a friendly reminder.. the 'Comments' on posts are for quick questions and 'thanks!' type stuff. Remember no 'counter-articles' to the articles. If you want a long discussion, please head over the the forums and write pages and pages of point/counter-point til your little fingers bleed. Enjoy!

So comments are only for stupid inane stuff, not for, you-know, useful comments.

 The article was to teach people how to do statistics in the context of a miniature games.  It's wrong and counterproductive to point out that you are teaching bad statistics?  Who do you think is doing the more harm here?

If you are going to write an article about statistics, do the homework and get it right.  At least point out where you are fudging the numbers.  People get so bent out of shape when they play miniature games and unlikely stuff happens.  It's a bad understanding of probability that causes it, and this article just propagates the same misunderstanding of probability and statistics that is all too common.

BTW, the only appropriate comments to this post are to tell me how awesome I am, or to ask me how I manage to be so awesome.

1 comment:

  1. yur teh awesumust bestust statistician evar!

    now that that's done. I stopped reading the stats when I started to see errors. I didn't feel like going through with a poor Stats/probability article. they run rampant (more like Sprint) in 40K.