The Myth of Luck: Part Two

If you don’t know anything about statistics, then the Myth of Luck: Part One: https://willowrants.wordpress.com/2006/07/26/the-myth-of-luck-part-one/ is required reading for this post.

So we know a little bit about random distributions and bell curves.  What do we do with that?

In gaming, we use randomizers quite a bit.  Some people develop reputations as being “lucky” or “unlucky.”  The question is: are they?

Let’s think about randomizers.  For simplicity, we’ll use coin flips (perhaps you’re playing d02):  one has a 50% chance of success, and a 50% chance of failure.  If we logged the total spread of all “chances of success”(the population), there would be only one point: 50%.

Now, think for a moment.  Suppose you flip a million coins during your life time.  Do you think you’re likely to flip exactly five hundred thousand heads?  You aren’t, however, you’re incredibly likely to flip close to five hundred thousand heads.

The grouping of all the coin flips a given person makes is a distribution- a sample of possible outcomes.  And from our knowledge of statistics, we know that distributions do follow a bell curve.

So we look at that bell curve: it’s high in the middle and low in the sides.  The absolute middle is going to be 500,000.  Most people will be in that middle area, and have (say) 400,000 to 600,000 “successes” in their lifetime.

But let’s look at the sides:  there are going to be people who are outliers, who based on their coin-flip history, would seem to have a 30% success rate, or a 70% success rate (or lower or higher, but the more you deviate from the mean, the less common you are.)  These people have years and years of unlikely failures or successes behind them, and people have noticed.  They think they’re lucky, or unlucky.

So yes, these people MUST exist.  Statistics tells us there must be outliers; if there weren’t it would be more of a surprise.  So we shouldn’t be amazed that these people exist.

However, it’s gambler’s fallacy to think that these people’s history will affect their future rolls.  Someone with a history of failures blames their failures on luck, and dismisses their successes.  But what’s really going to happen?

Suppose we took all the “unlucky” ones and put them in a room, and forced them to roll dice and flip coins for the rest of their lives.  Would we see a mass statistical anomaly?  No!

The distribution of these people would follow a bell curve!  The majority of them would have a future sample that was middling average- however, they would still have had a majority of failures over their lifetime, and they would continue to be considered unlucky, based on past performance.  Some few would have an excess of success, and come back to average (over their lifetime), or even exceed it.  However, they would be matched in number by those that got failure after failure, digging themselves an ever deeper whole.

So are some people “luckier” than others?  No.  They operate under the same probabilities as everyone else.  It’s just statistics at work, not the supernatural.

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