Algernon,
So we are in agreement that with your die, the odds of rolling a six on any given throw is always .02, and whether or not a six was rolled on the preceding throw is completely irrelevant to that probability?
Manduck,
I think I see what your saying. If, say, player has had only one good year out of three, we should, all else being equal, predict that the player has only a 33 percent probability of having a good year this year.
Yes, I completely agree with this statement. While that sounds like I’m contradicting myself, it is completely consistent with Variation to the Mean.
For a baseball player with a career average of .200, the probability of batting .300 (which is like rolling a six with my weighted die) is extremely low compared to the probability that the year after he bats .300 he’ll have a season more like his career average (like rolling a three). Manduck and I are essentially saying the same thing.
There is not equal probability that a baseball player will hit .100, .200, or .300. That is where it differs from the Gambler’s Fallacy. Variance to the Mean is what happens when the probability of the mean occuring is high.
To the point of the OP, most people come to the exact opposite conclusion when discussing sports performance. After a player has a great year, optimism reigns and everyone is excited about the prospects of another great year. (“Wow, Favre had a great year. Just think what it’ll be like next year when he performs like that with Javon Walker, our new rookie receiver.”(BTW, I’m not claiming Favre had that great of a year.)) I’m always the one to throw a damper on the conversation by claiming that the great year the player just had was most likely an anomaly, not a new plateau of greatness.
Boy, can we hijack a thread, or what? ~grin~
I was once involved in an evolution argument. I don’t think the person I was talking to was particularly religious, though this was in a philosophy course, and during the semester, he had agreed with some pretty bizarre things.
Finally, with a tone of finality, he rebuted my entire argument with one simple statement.
“The only reason we’re different than animals is that we adapted differently!”
:rolleyes:
“People have been doing it for thousands of years, so it must work!”
re: variation to a mean
I still don’t see that past success indicates future failure. It may be true that players will tend to a certain average over their careers; it may be true that a particular year’s success is an anamoly.
However, I don’t see that next year is likelier to be a failure just because this year is a success. I’d think next year is equally likely to be a failure whether this year is a success or a failure.
(Except, of course, that we won’t know a player’s career average until his career is done; this year, if it’s a success, will bump up his average, making me predict that next year will be more of a success than I woulda thought it’d be if this year had been a failure).
My father’s girlfriend is the queen of the “huh?” Once we were sitting around the table discussing Einstein, and she blurted out, “I don’t see why everyone thinks Einstein was so smart. All he did was that one thing!”
Or the time she told my girlfriend that sometimes she goes to the grocery store, but she doesn’t know what to buy…so she looks in other people’s carts to see what they’re buying…but then she doesn’t buy it…then her eyes unfocused and her train of thought ran out of coal, and my girlfriend made her excuses and got away.
Or the time that I was working temp jobs over the summer, and she kept trying to lecture me on how to hunt for a job. Nevermind that she’s been fired from three of her last four jobs, and now works for my father. Hmmm…I guess at least she’s experienced at hunting for work.
Daniel
When my high-school boyfriend was trying to persuade me to have sex with him, we had the following debate:
Me: I can’t do it. I just can’t. It goes against everything I was raised to believe in. My parents taught me that it was wrong to do it when you’re not married.
Him: You don’t have to do what your parents say. We’re old enough to make our own decisions.
Me: I’m afraid of having a baby.
Him: There’s no danger. We’re too young to conceive a child.
Me: No, we’re not. It could happen. I’m almost seventeen. Girls my age have babies all the time.
(By the way, he didn’t get what he wanted, and we eventually broke up.)
Do you see the faulty logic here? First he claimed that we were old enough to decide for ourselves what was right and what was wrong, and then he turned right around and claimed that there was no danger of pregnancy because we were so young.:smack:
Hmmmm. “Success” and “failure” are such emotionally charged words. How about I re-word your statement as follows:
“I don’t see that next year is likelier to be a .200 year just because this was he batted .300. I’d think next year is equally likely to be a .200 year whether this year is a .300 year or a .200 year.”
I absolutely agree. The point is, assuming his normal most probably result (career average) is .200, then regardless of how he does one year the most probable result the following year is .200.
That’s Variation to the Mean.
If I ever implied cause and effect between one year’s performance and the next, I apologize. The point I was trying to make was that after an outstanding year, the next year is likely to be average. Not because the previous year was outstanding, but because, well, that’s their average (and most likely) level of ability.
By the way, I haven’t meant to be snobbish about all this. I’ve really enjoyed reading the examples of faulty logic that people have posted.
Sorry to continue the hijack, but I am a little curious about Algernon’s variation towards the mean.
If an unusual event occurs (eg, batting .300 when you are a career .200 hitter) then next time around, it is very likely that you will experience a result closer to the mean than your previous unusual result. This is simply due to the fact that you were way out on one tail of the probablity distribution.
However, the odds of the second event assuming any particular value are unchanged from before. The only thing that changes is the probability that the second event will fall closer to the mean that the first, unusual event.
I have never run into the term “variation to the mean” before, so I am a little reluctant to argue about what it can or cannot mean. However, I feel safe in saying that is does not mean:
[list=1]
[li]The fact that an unlikely event occured in the past in any way affects the future[/li][li]Events always tend toward the mean[/li][li]The chance of actually achieving the mean changes based on past results[/li][/list=1]
You cannot make any predictions about future absolute performance based on past events if the events are independent. So to say that since Ventura had a bad year, next year will likely be good is not quite right. It will likely be better, relative to his bad year.
In light of these observations, I would like to note that “past success indicates future failure” is wrong, unless you interpret failure as diminished success (a pretty depressing viewpoint, to my thinking). That is, following a .300 year, you are extremely unlikely to hit .300 or better next year. You are likely to hit closer to .200 than last year, but this is not ruling out the possibility of hitting .250.
It’s an Extended Analogy fallacy. The arguer derives a general rule from circumstances that are analogous at best in irrelevant ways. Bill should respond: “But by smoking, you’re only exacerbating the problem of car exhausts.”
Note, however, that Bill also committed a fallacy called Selective Observation (relied on heavily by casinos) by apparently cherry picking his research. Dick’s response to Bill’s first assertion should have been this.
I think ( and it’s been a long time) the term is “regression toward the mean”. But you’ve essentially got it here