[Masu485]

I know I may get slammed for this, but I'm thinking about this philosophically.

If every spin of a roulette wheel, or every flip of a coin is independent, how can regression exist?

Doesn't regression mean that if 'heads' comes up more often than it should, eventually it will regress, and 'tails' will come up more to even it out?

Does this mean regression only exists if you are doing Infinity coin flips? If heads comes up a disproportionate amount of times, we can't expect tails to then come up, as each flip is independent... but we should at some point expect tails to come up in order for regression to be true. Right?

[warriorfan707]

Dude you are getting regression mixed up with probability

[evo34]

Here is Wikipedia's answer:

Regression toward the mean simply says that, following an extreme random event, the next random event is likely to be less extreme. In no sense does the future event "compensate for" or "even out" the previous event, though this is assumed in the gambler's fallacy (and variant law of averages). Similarly, the law of large numbers states that in the long term, the average will tend towards the expected value, but makes no statement about individual trials. For example, following a run of 10 heads on a flip of a fair coin (a rare, extreme event), regression to the mean states that the next run of heads will likely be less than 10, while the law of large numbers states that in the long term, this event will likely average out, and the average fraction of heads will tend to 1/2. By contrast, the gambler's fallacy incorrectly assumes that the coin is now "due" for a run of tails, to balance out.

[warriorfan707]

Regression is when a shit team like the Lions starts out as a hoax and smart gamblers like me know they are about to lose to the 49ers

shit like that

[suicidekings]

I know I may get slammed for this, but I'm thinking about this philosophically.

If every spin of a roulette wheel, or every flip of a coin is independent, how can regression exist?

Doesn't regression mean that if 'heads' comes up more often than it should, eventually it will regress, and 'tails' will come up more to even it out?

Does this mean regression only exists if you are doing Infinity coin flips? If heads comes up a disproportionate amount of times, we can't expect tails to then come up, as each flip is independent... but we should at some point expect tails to come up in order for regression to be true. Right?

If an event is a 50/50 random occurrence, then as your sample size increases, the probability of the total number of occurrences approaching 50/50 increases proportionally. You should reach equilibrium (within reasonable tolerances) long before you get to infinity

A sample size greater than 10,000 would not be adding much additional data to the experiment.

[FourLengthsClear]

What you are talking about is regression to the mean.

[Wrecktangle]

Whoops, we've been found out guys; regression is a figment of our collective imaginations.

Now somebody needs to scrub all those entries in Wikipedia, for starters.

[Wrecktangle]

Whew, and I was worried I was starting to "regress" back into RickySteve.

[mathdotcom]

I know I may get slammed for this, but I'm thinking about this philosophically.

If every spin of a roulette wheel, or every flip of a coin is independent, how can regression exist?

Doesn't regression mean that if 'heads' comes up more often than it should, eventually it will regress, and 'tails' will come up more to even it out?

Does this mean regression only exists if you are doing Infinity coin flips? If heads comes up a disproportionate amount of times, we can't expect tails to then come up, as each flip is independent... but we should at some point expect tails to come up in order for regression to be true. Right?

If you didn't know the probability of a fair coin landing on heads or tails is 0.5, then regression would provide you with an accurate guess provided a number of assumptions hold. If your sample size is reasonable, your regression would come up with an estimate very close to 0.5. In fact in this example it would just be the mean of your sample.

[mathdotcom]

Also, never read Wrecktangle's posts and you will be a smarter person for it.

[Wrecktangle]

Also, never read Wrecktangle's posts and you will be a smarter person for it.

Whew, and I was worried I was starting to "regress" back into RickySteve Mathdotjerk.

[RickySteve]

I'd be jealous of me too.

[AlwaysDrawing]

for some reason everyone is at each other's throats in these regression threads.

[antifoil]

no they are just regressing back into being internet neckbeards.

[Wrecktangle]

aggression not regession!

[sneak-a-peak]

it exists in sports betting....... thanks to "odds makers"

[Masu485]

It is just had to grasp, since each coin flip is supposed to be independent of the other, yet at some point, if regression exists, you can begin to expect an evening out of sides. This doesn't seem right.

[suicidekings]

It is just had to grasp, since each coin flip is supposed to be independent of the other, yet at some point, if regression exists, you can begin to expect an evening out of sides. This doesn't seem right.

Are you making the assumption that the mean is always 50%?

[FourLengthsClear]

It is just had to grasp, since each coin flip is supposed to be independent of the other, yet at some point, if regression exists, you can begin to expect an evening out of sides. This doesn't seem right.

You are misunderstanding what regression toward the mean is.

If you flip a coin ten times and it comes up ten heads, it had no bearing whatsoever on the probability curve for the next ten flips or the ten flips after that.

Regression to the mean refers to the overall sample including those ten flips.

Put it this way. If those first ten come out 10H and 0T and then the next 90 come out 45H and 45T, you have cumulative totals of 55H and 45T. As the number of trials is increased is the probability of there being a significant variance from the mean (in percentage terms) gets lower and lower over the total sample.

Again, you are no more or less likely to see a big variance on subsequent trials.

Think of it another way. Suppose after 100,00 trials you have had exactly 50,000H and 50,000T. There is then a one in a million occurrence (actually slightly more) of 20 straight heads. That only changes the percentage of heads over the total number of trials from 50.00% to 50.01%.

[mebaran]

You are misunderstanding what regression toward the mean is.

If you flip a coin ten times and it comes up ten heads, it had no bearing whatsoever on the probability curve for the next ten flips or the ten flips after that.

Regression to the mean refers to the overall sample including those ten flips.

Put it this way. If those first ten come out 10H and 0T and then the next 90 come out 45H and 45T, you have cumulative totals of 55H and 45T. As the number of trials is increased is the probability of there being a significant variance from the mean (in percentage terms) gets lower and lower over the total sample.

Again, you are no more or less likely to see a big variance on subsequent trials.

Think of it another way. Suppose after 100,00 trials you have had exactly 50,000H and 50,000T. There is then a one in a million occurrence (actually slightly more) of 20 straight heads. That only changes the percentage of heads over the total number of trials from 50.00% to 50.01%.

^This. As your sample size approaches infinity, the % of Heads/Tails approaches .50

At some point (ie. 1,000,000,000,000,000 trials), your heads/tails percentages will be almost assuredly .500000000xxx and .500000000xxx....

Akin to what FLC just said, at that point, even 1000 heads in a row doesn't shift the distribution significantly.