[Snowman]

Originally Posted by BobC

Andrew,

Some very insightful points. In particular about the measure of "luck" in regards to BABIP. Kind of like predicting the outcome of flipping a coin and whether it lands heads or tails. That outcome is always a 50/50 probability. And so over time, and all other things constant and equal and assuming a sufficient sample size, anyone flipping coins would eventually expect to see them ending up with exactly half heads, and half tails. To me, I've always thought of this as kind of what is meant by "regressing to the mean", in this case ending up 50/50 on heads or tales. But what is interesting is say you start out flipping coins to test this, and everything being constant and nothing abnormal with the coin, the first 9 flips all come out tails. Now the absolute probabity of a head or a tail is still just 50/50 on that next, 10th flip, or is it? Since over a large enough sample size we expect the number of heads or tails to come up to regress to that expected mean of 50/50 for each of the two possible outcomes, if in starting out with getting tails 9 times in a row, you know you eventually have to start flipping heads, but the probability of each and every single flip is still always going to be just 50/50. So now you have somewhat of a paradox on what the actual probability of flipping a head or tail on all future attempts should be, at least it seems like one to me.

This is referred to as the "Gambler's Fallacy".

From Wikipedia - The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the incorrect belief that, if a particular event occurs more frequently than normal during the past, it is less likely to happen in the future (or vice versa), when it has otherwise been established that the probability of such events does not depend on what has happened in the past. Such events, having the quality of historical independence, are referred to as statistically independent. The fallacy is commonly associated with gambling, where it may be believed, for example, that the next dice roll is more than usually likely to be six because there have recently been fewer than the usual number of sixes.