Don't envy my life. It's not as glamorous as it seems.

Here is something I don't quite understand about regression to the mean and what the prof said. He made it sound like in the future events are more likely to be favorable to even out past bad luck. This is the same that I read on this forum all the time about ev graphs ("don't worry. it will even out in the long run").
Shouldn't regression to the mean only make assumptions about future events and ignore past results? If I had a string of bad luck I cannot expect that future good luck will make up for that. I do not get some kind of karma or ev credit. So no matter how bad I ran lately my future results should be close to my ev in the long run and I still have my bad results from the past. Otherwise every recent WSOP ME winner should quit poker immediately.

The probability of #T is still 50%...nothing has changed simply because the first 1trillion flips were all H. The events are independent.

Let's assume you actually do have a true and constant BB/100 (say 4) and the games never change, etc. Now, a new year starts and you track your BB/100 for this year. After a week, you are running at 1BB/100. Your YTD BB/100 is more likely to go up than down from here- and it doesn't require you running above average. If you run average for the next 6 months, your YTD BB/100 will consist of 6 months of 4BB/100 and 1 week of 1BB/100 for a weighted average just under 4BB/100. Your YTD average has "reverted to the mean" without you getting lucky (in the future 6 months) at all.

You flip a coin 50 times and get 50 tails. For the next 1mil flips you can expect 500K of each option, with variance of course.

Things will regress to the mean not because you are likely to flip an extra 50 heads during the next 1mil trials, but because after 1mil trials your 50 flip variance isn't going to amount to squat: 500,000 heads vs 500,050 tails is ~50/50. The rate should regress to the mean, not the actual total, because of how the rate is affected by the number of trials.

Also, in a large enough sample you're likely to get larger than 50 flip runs of a single outcome, so any "long" run of X will become "short" by comparison to the expected runs in increasingly large sample sizes.

For instance (shifting to poker), a 5BI downswing in a fairly low-variance playing style might be very rough in a 5K hand stretch, but if you plan on playing 5mil hands afterwards, you're likely to get all sorts of crazy down/upswings perhaps 10x as large (albeit rarely). Even if you had an ~0BB/100 WR for that 5mil stretch, the 5BI swing would get lost in the 15, 25, and 40BI swing noise.

Perhaps this has all been said already, though. Correct if wrong.

Are you even reading the posts?

No one is arguing that the events aren't independent. All they're saying is that YOU'RE LIKELY TO RUN BETTER THAN YOU DID IN THE PAST. Since you ran the worst you could possibly run on the first set of flips, you're a lock to run better this time.

To quote lastcardcharlie:

"I'm not sure this is that difficult."

How do we calculate regression to the mean in our lives? It's a useless concept to apply in day to day life unless we have concrete probabilities of events.

QFT?

This is different from the regression to the mean...regression to the mean thinking is basically the gambler's fallacy...but the above is not.

ugh...why is this so hard...

I'm convinced durkadurka is just a very effective troll.

Yes, it is more likely to go up but my total results are less likely to reach 4BB/100. As you said in the long run my average should be just under 4BB/100 but many users in this forum treat this regression to the mean concept like I can expect in the long run to reach 4BB/100 "because things will even out". All the Sklanksy bucks in the world won't get me back to 4BB/100 unless I run above expectation in the future but this has not become more likely due to my past running below expectation.
I guess instead of stating "in the long run things will even out" they should say "in the long run the past run of bad luck will appear less significant".

Only when used incorrectly.

To add yet one more example to make this simple point: Say you flip 5 times and come up heads only once. Currently, heads has come up 20%. If you flip 100 times more, the percent that heads will have come up is overwhelming likely to be closer to 50% than it's current value of 20% (which means you must have more probability for heads in a future sample than came up in your current sample). This doesn't mean it's likely to come up more often than 50% in the future, just that the total times heads comes up will tend closer to 50% the more you keep flipping (i.e., IT WILL REGRESS TO THE MEAN). This in no way assumes events are dependent.

Either you aren't reading my posts or you need to work on your reading comprehension.

My problem with the regression to the mean response to the gambler's fallacy is the focus on percentages over absolute numbers. Over time, with a fair coin, the percentage of heads vs tails will trend towards 50/50, but the difference in the absolute number of heads vs tails can widen. For me, this usually comes up in the context of investments, where the rate of return over time can trend towards an expected value, while the dollar shortfall continues to grow.

In the context of life events, assuming a 50/50 probability for good and bad events, I may experience 2 good and 8 bad events on a particular day - a run of bad luck. After a week, I could have a total of 30 good and 40 bad events. I am regressing towards the mean, but I am still experiencing more bad than good events - just not quite as bad a ratio as the first day. I am not suggesting that this is the most likely result, but it is just as likely as 28 bad and 32 good events over the balance of the week.

When I read the teacher's response in the OP, I took it to mean that good luck would follow bad, though I realize that what the teacher actually said is consistent with earlier posts about future results being better, simply based on future expectations vs earlier actual (bad) results.

It appears that we agree...but it still doesn't make the prof's comments correct. The prof seems to be making a claim other than the one that we are. We aren't actually discussing regression to the mean at all...we're talking about comparing prior probabilities for various outcomes.

So, we're merely comparing the probability of an average outcome of flipping a coin 5 times having an outcome of winning >$1. Since the EV is $2.5, we expect >50% of outcomes to be >$1...so, if you play the 5-flip game, and you only win $1, then we can obviously say that you can expect to do better in the next game.

BUT, the justification is NOT regression to the mean. The justification is merely the comparison of prior probabilities.

Please post your definition of regression to the mean.

Crudely:

In the limit, the frequency of outcomes will regress to the a priori probability.

So, for a fair coin, in the limit, the frequency will be 50% H, 50% T.

OK, you're describing a real phenomenon, but it's not regression to the mean. Check out http://en.wikipedia.org/wiki/Law_of_large_numbers .

Regression to the mean is exactly what you talked about in the second paragraph of the previous post. If you sample a random variable and obtain an extreme result, you expect to obtain a less extreme result if you sample again.

I think the guy that flipped 1 trillion heads will get 1 million more on his next 1 trillion flips too because he's liking flipping a double-headed coin.

I'm not sure I would argue this with the professor, but I don't agree with the professor.

What she wrote may seem true for most people who live relatively comfortable, privileged lives. "Oh crap, I have a cold. Life sucks." Next week: "My cold is gone, and my cousin just had a baby. Life is awesome."

See? Proof. Things were bad, now they are good.

The truth is, this concept is fraught with poorly defined terms, emotions, and biases. The more you attempt to deal with those problems systematically, the closer you get to a classic Gambler's Fallacy situation

You bought a $1 lottery ticket yesterday, got extremely lucky with it and won $1 million. You decide to buy another lottery ticket today. You are just as likely to get lucky with this one as you were with the one you bought yesterday. But it is far more likely this one will be a loser. When the lottery results come in it is far more likely than not you will be able to say your luck today was worse than your luck was yesterday.


PairTheBoard

That would be the better way of putting it imo.


PairTheBoard

Durkadurka, for the love of all things sacred, please stop redefining terms ITT. The first bold statement is EXACTLY what "regression to the mean" implies.

Wiki:

If you want to create new meanings for terms, that's fine, but don't chastise others for not using your own personal meanings.

There is a complete misunderstanding here...
About what "regression to the mean" is...
And how traders profit from it.

It does NOT apply to random events...
Or "independent events" = "random events"...
Random events DO NOT HAVE TO "regress" to anything...
They may or may not.

The whole idea applies to non-random events...

For example, real estate prices are NOT random...
They are highly correlated with economic activity.

Bond prices are NOT random...
They are highly correlated to other bonds and FOREX.

Non-random events that become temporarily "mispriced"...
More often than not "regress to the mean"...
Meaning they return to a historically rational level.

What? Almost everything you wrote is wrong.

Regression toward the mean applies only to random events.

Just because an event is correlated to something else doesn't mean that it's not random.