Statistically Proving Bad Luck (Help Appreciated)

[Wolfspirit]

After years of PnP RPing and continously getting horrible rolls everywhere from character creation to attacks and skill checks, I've decided to statistically prove that I, in fact, just am unlucky. I know how silly that sounds, but I'm serious here.

I've begun keeping track of all of the rolls I make in my D&D games I play, and noting whether or not it was involved in combat, 100 rolls per die. At the time of writing this I've gotten 179 rolls recorded.

What I'd like is some advice from the stastically minded as to ways to improve my research, and what a decent sample size would be to say "Yep, your luck just sucks"

(Oh, yeah, for those that might be curious, right now 2/3 of the combat rolls I've made are below 10, with a mode of 6 and 8, median of 8. Non-Combat's mode is 6, median is 10. This may be an issue of sample size, but we'll see.

It should also be noted that, yes, I am a geek)

 

[DanMcS]

Use many dice- if you use just one d20, for instance, you're actually measuring the fairness of that die

I'd say you'd need 5 or 10 thousand rolls to really "prove" that you're unlucky. 179? Piffle.

 

[Olgar Shiverstone]

Make sure you have someone else roll your dice as a control. Otherwise you're more likely to prove non-random dice than bad luck.

Make sure, too, that you're counting every single roll. You can sample by classifying, but you'll really learn more just by counting total rolls and results. You'll want a lot of rolls to get the variance down pretty small.

I suspect you'll ultimately prove one of two things:

- Your dice are flawed (ie, non-random), or
- You're superstitious

 

[Gnarlo]

I'd say you'd need 5 or 10 thousand rolls to really "prove" that you're unlucky. 179? Piffle. [/B]

5 to 10,000 roles, huh? 12,594 roles on ENWorld, I'd say if half of us wrote in to say you were unlucky, that should prove it.

You're unlucky

 

[Wolfspirit]

Use many dice- if you use just one d20, for instance, you're actually measuring the fairness of that die

I'd say you'd need 5 or 10 thousand rolls to really "prove" that you're unlucky. 179? Piffle.

Yes, I know this is a very small sample of recorded events, however, that's all that I've recorded over a couple of games. I know that I need many, many more. Right now I've just got a few years worth of observer bias.

Make sure you have someone else roll your dice as a control. Otherwise you're more likely to prove non-random dice than bad luck.

Make sure, too, that you're counting every single roll. You can sample by classifying, but you'll really learn more just by counting total rolls and results. You'll want a lot of rolls to get the variance down pretty small.

Yeah, I'd been thinking about controls, but that might be difficult. Might have to just ask someone to roll the dice outside of game or something.

Also, I have been keeping track and recording every roll, and as I'd mentioned, planned on swapping out dice after 100 rolls. I have enough d20s that I should be able to do this for quite some time (Friends buy me dice all the time, hoping to find one that works for me ). The Combat / non-Combat designation is just to check and see if there is a bias there.

 

[dok]

The illusions of probability

I have some bad news for you, friend. Actually, bad news both ways...

The first piece of bad news is that you can conduct statistical analysis on a sample of practically any size. In fact, once your sample size exceeds 30, it becomes pretty routine to anyone who knows the numbers.

By the way, you'll need more than just the mean, median & mode. If you really want someone to help you, you'll need to post not only those numbers, but also the total number of trials, and the standard deviation & variance of the set. It'd also help to have the upper & lower quartiles. (I'll come back to this last line later)


In terms of "controls", for this situation, I'd say simply record every d20 roll you make, regardless of the situaiton or which d20 you use. Since you're in a d20 system game, high is good & low is bad, so there's no fancy record keeping. Just have a notepad with 20 boxes, and put a hash in the appropriate box after each die roll.

Here's where the second piece of bad news comes in:
All the statistical analysis will tell you is whether or not the results you've experienced lie within the "probable" range of possible outcomes. And I'm fairly confident that it will.

This is the biggest mis-conception people have about statistics. Statistics apply over huge sets. There's an old saw about a health worker coming into a resteraunt kitchen & telling them they can't serve a four-egg omlet because according to the USDA, one in four eggs contains salmonella bacteria. You chuckle, but let me give you another example:

The 'double-20-confirm-kill' rules variant says if you roll a '20', and roll a second '20' on your confirmation roll, and roll a confirmed hit on a third roll, you kill your foe instantly. Most people, when considering this rule, think "The odds of even rolling for an instant kill is 1:400, so this seems like an OK rule." Here's where probability & statistics part ways. The odds of any single attack threatening an instant kill are 1:400. However, a random sample of 400 die rolls only has around a 50% chance of containing one or more instant kill threats.

You're suffering from what statistics teachers like to call "Gambler's fallacy". It's the notion that any kind of short term results must mirror the population distribution. Normally, the example is "I've lost six hands in a row. I'm overdue to have a winning hand!" In this case, you've reversed the assumption: because your data set has a low mode (and an average median and we don't know the mean), that the "population" of your dice rolls overall must be similar. ("I'm unlucky")


Remember how I mentioned the upper & lower quartiles being needed along with the median? That's to identify possible outliers, or unusual elements of the data set. Odds are, (forgive the phrase, please) that the range of 1.5 * (3rd quartile - 1st quartile) is larger than 1-20. Which means that every die roll is relevant; in other words, rolling higher than a '15' is not a fluke for you.

Here's my prediction. Post the statistical data: Sample size, mean, variance, & standard deviation. Then either you or someone else figure out what the interval is for the population mean with a margin of error of +0.15%, (That's +/- 3 SD for any statistics buffs out there) and what the confidence level is. I'll bet money that the true population mean of 10.5 lies inside that range.

 

[ichabod]

Okay, here's what you do. Put all the numbers into excel. Type into one cell "=stdev(a1:a179)" (a1:a179 is the range your rolls are in, adjust this if they are in a different range). That gives you the standard deviation of your dice rolls. Take the mean of your die rolls (which can be calculated with "=average(a1:a179)") and subtract it from 10.5. Then multiply the result by the square root of the number of die rolls, and divide it by the standard deviation you calculated. If the number you get is less than 2, you don't have bad luck. If it is greater than 2.3, you can't confidently say that you don't have bad luck. Note that that is different than saying that you do have bad luck. If it's inbetween 2 and 2.3, it will depend on which statisticians you talk to.

A major caveat: as has been stated, if you are using the same die the whole time, you are confounding your results. The deviation from the mean may be due to the die you are using, and not your phenomenoscopic transprobability curve warping field. For the best results, use different dice from different manufacturers.

Also, the more you roll the dice, the more you are sure of the result. I'd wait until about 400 rolls before complaining too much about your bad luck. And remember, this will never tell you that you have bad luck. The best it will do, in classical statistics terminology, is fail to reject the hypothesis that your luck is normal.

 

[Henry]

I have another suggestion, totally non-statistical:

Roll your dice differently.

I have had several friends with positively TERRIBLE dice-rolling technique: It ranges from letting the die just FALL from their hand, to rolling it in a certain predictable "zone" of the table, with exactly the same hand motions. Roll out of a cup, roll with a backspin on the die, roll from the tips of your hands instead of the side, roll by spinning it from between your clasped hands - just try different techniques and see if you are getting into a "rut" that causes one small set of numbers on one side of the die to keep reappearing.

I find I have worse die luck playing than when DM'ing - and it's possibly because I am standing most of the time when I am DM'ing, and altering the way I roll my die.

 

[Essex]

I don't have the exact numbers, but this is a true story.

Roommate, who's an fanatic wargamer and myself who is just a newbie. Warhammer 40K. He's Orcs. I'm Blood Angels.

He outnumbers me 3.5 to 1 due to our army selection. In previous battles, our luck has been average, but he is a better tactitian and usually wins with only moderate losses at worst.

This night I decide to give it another whack. Basically what proceeds is the worst slaughter in the history or war. He loses all 70 orcs to my 20 Space Marines with my only suffering 2 casualties.

How?

Not through any skill on my part. He COULD NOT HIT, while I COULD NOT MISS. I have never seen such a battle in all my days and I have never been able to replicate that feat again. I was rolling all 1s and 2s, he was rolling all 5s and 6s. You could see the veins popping out on his forehead all through that battle. Our other roommate looked on in awe and horror as the only person he killed was ONE Space Marine in HtH and my Priest who got caught in the crossfire.

While I lack the numbers myself, my roommate is a math major and he was venting how that was that by all laws of probability he should have killed at least 3 times the number he did, just be virtue of his tactics (if one had watched the game) he should have slaughtered me. This is why I always try to win the coin toss on setup )

 

[diaglo]

This is why I always try to win the coin toss on setup )

Heads I win. Tails you Lose. an old wargamers trick